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Universidad de Cantabria
Departamento de Física Moderna
CSIC - Universidad de Cantabria
Instituto de Física de Cantabria
Evolución y agrupamiento
a gran escala de una muestra
de fuentes extragalácticas en rayos-X
Memoria presentada por el Licenciado
Jacobo Ebrero Carrero
para optar al título de Doctor en Ciencias Físicas
2008

Francisco Jesús Carrera Troyano, Doctor en Ciencias Físicas y
Profesor Titular de la Universidad de Cantabria,
CERTIFICA que la presente memoria
Evolución y agrupamiento a gran escala de una muestra
de fuentes extragalácticas en rayos-X
ha sido realizada por Jacobo Ebrero Carrero bajo mi dirección.
Considero que esta memoria contiene aportaciones suficientes para construir la
tesis Doctoral del interesado
En Santander, a 1 de Octubre de 2008
Francisco Jesús Carrera Troyano

A mis padres

Resumen de la tesis en castellano
0.1 Objetivos de la investigación
Las emisiones de rayos-X en el Universo están asociadas a los fenómenos físicos
más energéticos como, por ejemplo, partículas relativistas sometidas a intensos
campos magnéticos, plasmas a temperaturas del orden de millones de grados
o intensos campos gravitatorios. Por lo tanto, el estudio del cielo en rayos-X
significa estudiar el Universo más violento y extremo.
Dentro de nuestra propia Galaxia existen distintos tipos de fuentes que emiten
rayos-X como pueden ser estrellas aisladas o en sistemas binarios (enanas blancas,
estrellas de neutrones) y remanentes de supernova. Fuera de ella, también
existe una variedad de objetos emisores de rayos-X como las galaxias, cúmulos
de galaxias y los Núcleos Galácticos Activos (AGN, en sus siglas en inglés).
El cielo en rayos-X se encuentra dominado por una radiación difusa procedente
de todas direcciones, altamente isótropa, conocida como Fondo Cósmico
de Rayos-X (FCX). Hoy en día sabemos que el origen del FCX es la emisión
integrada de una miríada de fuentes individuales extragalácticas. A energías
superiores a ∼0.2 keV la emisión del FCX se encuentra dominada por AGN, estando
una fracción importante de su emisión absorbida por grandes cantidades
de gas y polvo.
Los AGN son galaxias que emiten cantidades ingentes de energía procedente
de una pequeña región situada en el núcleo de las mismas (de ahí su nombre).
La energía emitida por los AGN es muy superior a la emisión integrada de la
galaxia que los contiene, siendo la región emisora mucho más pequeña (∼1 pc)
que la galaxia anfitriona. Además, los AGN son las fuentes persistentes más
brillantes del Universo, tan sólo superados en brillo por los estallidos de rayos
gamma (aunque éstos últimos tan sólo duran unos segundos). Es imposible
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explicar las altas luminosidades de los AGN por la emisión integrada de las
estrellas de la galaxia huésped o por la emisión del gas interestelar, ni tampoco
por brotes de formación estelar. El único fenómeno conocido capaz de explicar
estas altísimas luminosidades y la rápida variabilidad observada en la mayoría
de estos objetos, es la acreción de materia en un agujero negro supermasivo.
De acuerdo con el modelo unificado de los AGN, éstos contienen en su centro
agujeros negros supermasivos con masas entre 10 6 -10 9 M 1 ⊙ . En las regiones en
las que el campo gravitatorio del agujero negro domina sobre el producido por
las estrellas del entorno (∼10 parsecs para un agujero negro de ∼10 8 M ⊙ ), el
agujero negro está acretando materia (gas y estrellas). Como el material acretado
tiene momento angular no cae radialmente, sino que forma un disco plano
alrededor del agujero negro llamado disco de acreción. La materia en el disco
se calienta debido a procesos de fricción y la influencia de fuertes campos magnéticos,
alcanzando temperaturas de 10 5 -10 6 K y liberando energía en forma de
radiación térmica emitida en el rango óptico/ultravioleta (UV). A pesar de estar
generalmente aceptado que la fuente de energía primaria de un AGN es la
acreción gravitatoria de materia, los detalles de cómo se produce la emisión de
rayos-X en estos objetos aún no están totalmente determinados.
Uno de los modelos más aceptados capaces de explicar la emisión de rayos-X
en AGN es el de la Comptonización inversa. Según este modelo, un plasma
caliente de electrones e iones (y, quizá, pares electrón-positrón) rodea la zona
del disco de acreción más próxima al agujero negro. Este plasma reprocesa mediante
efecto Compton inverso los fotones ópticos/UV emitidos térmicamente
en el disco, impulsándolos hasta el rango de los rayos-X. Este proceso produce
un espectro de emisión con forma de ley de potencia, como se observa en espectroscopía
de rayos-X de AGN.
Los AGN muestran una gran variedad de propiedades, dependiendo de las
cuales se clasifican en distintas categorías. Una de las clasificaciones más extendidas,
la cual hemos usado para el trabajo presentado en esta tesis, está basada
en las propiedades de los espectros ópticos de los AGN. Los AGN para los que
se observan tanto líneas de emisión anchas (anchura a media altura ≥ 2000 km
s −1 ) como estrechas (anchura a media altura < 2000 km s −1 ) en el espectro óptico/UV
se clasifican como AGN de tipo 1, mientras que para los que sólo se
observan líneas de emisión estrechas se clasifican como AGN de tipo 2.
1 Las masas se dan en unidades de masa del Sol M ⊙
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Los modelos de unificación pretenden explicar la presencia o ausencia de líneas
anchas en los espectros ópticos/UV de los AGN como anisotropías en la geometría
del material absorbente. Según estos modelos, las propiedades observadas
en el óptico/UV dependen de la visual del observador con respecto al núcleo
del AGN. Así, los AGN de tipo 1 serían fuentes en las que se observa directamente
el núcleo, mientras que en los AGN de tipo 2 el toroide intercepta la línea
de visión del observador oscureciendo el núcleo y la región donde se emiten las
líneas anchas.
Se cree que las líneas de emisión anchas se forman en nubes de gas denso (≥
10 8 cm −3 ) que se mueven a altas velocidades (entre 1000 y 10000 km s −1 ) en las
proximidades del agujero negro y el disco de acreción, a distancias del orden de
100 días-luz de los mismos. Esta región se la conoce como la Región de Líneas
Anchas. Por contra, las líneas de emisión estrechas son emitidas en nubes de
gas menos densas (∼ 10 3 − 10 4 cm −3 ) más alejadas de la región central del
AGN (distancias del orden del kiloparsec) y que, por lo tanto, se mueven a
velocidades menores (entre 100 y 1000 km s −1 ). Esta región es conocida como
la Región de Líneas Estrechas.
Otra componente, el gas molecular, se encuentra situado a distancias intermedias
entre la Región de Líneas Anchas y la Región de Líneas Estrechas y, muy
posiblemente, presenta geometría toroidal. La materia presente en el toroide
absorbe la radiación procedente del disco de acreción y de la Región de Líneas
Anchas, oscureciendo así el núcleo del AGN para ciertas líneas de visión. La
radiación absorbida es reemitida en el infrarrojo (IR).
Los AGN son emisores de radiación en todo el rango del espectro, desde IR
y radio hasta los rayos gamma, aunque la emisión en rayos-X (que normalmente
supone el 3-10% de la emisión total del AGN) es una propiedad común
de los AGN. Esta fuerte emisión X supone una prueba directa de la existencia
de procesos muy energéticos y de origen no térmico, ya que son imposibles de
producir en cantidad suficiente mediante procesos puramente estelares.
Los modelos de síntesis del FCX intentan explicar la emisión del fondo cósmico
y la distribución en flujo de las fuentes como una superposición de AGN. Sin
embargo, para que las predicciones teóricas y las observaciones ajusten es necesario
que una fracción importante de la emisión de los AGN se encuentre absorbida
por grandes cantidades de materia. Es decir, los modelos predicen que
la mayor parte de la emisión por acreción del Universo se encuentra oscurecida.
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Además, una importante fracción (∼50%) de las galaxias activas cercanas observadas
se encuentran también oscurecidas. Los rayos-X más energéticos son
capaces de atravesar importantes cantidades de material absorbente sin verse
apenas afectados, proporcionando así la única manera (exceptuando el infrarrojo
lejano, FIR) de ver directamente la emisión procedente de las regiones más
internas de los AGN oscurecidos. Por lo tanto, la mejor manera de estudiar la
estructura y los mecanismos de emisión de las regiones más cercanas al agujero
negro central es estudiando la emisión de los AGN en rayos-X.
La actual generación de observatorios de rayos-X, Chandra, XMM-Newton y
Suzaku, está proporcionando datos de calidad sin precedentes que nos están
permitiendo incrementar significativamente nuestro conocimiento acerca de la
naturaleza de los AGN. En concreto, XMM-Newton, gracias a su gran área colectora
nos permite detectar AGN débiles y situados a una gran distancia. No está
clara la dependencia de los mecanismos de emisión de los AGN con distintos
parámetros de las fuentes tales como el flujo, la luminosidad en rayos-X y el
desplazamiento al rojo. Por ello, para entender la naturaleza y evolución de
los AGN es necesario cuantificar estas dependencias. El mejor modo de hacer
esto es mediante análisis estadísticos de muestras amplias y representativas de
fuentes. Este es el camino seguido para la investigación llevada a cabo para esta
tesis.
Algunos de los aspectos que nos hemos planteado abordar en nuestra investigación
son los siguientes:
1. Estudiar la distribución en flujo de fuentes extragalácticas de rayos-X a
flujos medios y débiles. Esta distribución depende de las propiedades
cosmológicas de las fuentes y puede ser descrita por medio de un modelo
empírico que es función del flujo en rayos-X. De esta forma será posible
estimar la contribución de las fuentes emisoras a estos flujos a la intensidad
total del fondo cósmico de rayos-X. ¿A qué flujos contribuyen más las
fuentes que dominan el FCX?
2. Explorar la posible estructura cósmica subyacente del Universo en rayos-
X. Es conocido que las galaxias en el Universo local (con desplazamientos
al rojo de hasta ∼0.2) se agrupan formando estructuras a gran escala en
forma de filamentos alrededor de grandes vacíos. Los AGN se encuentran
a distancias cosmológicas y, por tanto, nos van a permitir descubrir si estas
super-estructuras estaban presentes cuando el Universo era más joven y
x

cuantificar el grado de este agrupamiento.
3. Estudiar como se comporta la fracción de AGN oscurecidos a distintas luminosidades
en rayos-X y desplazamientos al rojo y modelar la absorción
intrínseca de los AGN como función de estos parámetros. De acuerdo
con el modelo unificado descrito con anterioridad, es más probable que
los AGN detectados en rayos-X más energéticos (> 2 keV) sean AGN de
tipo-2, ya que sólo esta radiación puede atravesar el toroide que rodea el
agujero negro central. ¿Depende la fracción de AGN oscurecidos de la luminosidad?
¿Había más AGN oscurecidos en el Universo joven que en el
tardío?
4. Investigar la evolución de los AGN en distintas épocas del Universo. ¿Eran
más o menos luminosos en el pasado? ¿La densidad de AGN ha cambiado
con el tiempo? Podemos integrar un modelo de absorción con modelos
evolutivos para obtener resultados intrínsecos de las fuentes. ¿Ha
cambiado la tasa de acreción de materia en el tiempo? ¿En qué época del
Universo ya se habían formado plenamente los AGN?
El objetivo último es cuantificar qué aportan las muestras seleccionadas en
rayos-X a flujos medios, como las empleadas en esta tesis, a los conocimientos
existentes sobre los temas enumerados anteriormente. Es de esperar que
una selección a estos flujos, en los que la población dominante son AGN, nos
proporcione un mejor muestreo de estos objetos a desplazamientos al rojo bajos/medios
y, en especial, mayor número de AGN absorbidos en las bandas
de rayos-X duros que en otras muestras. Esto nos permitirá estudiar mejor sus
propiedades de absorción, que podremos usar posteriormente para derivar sus
propiedades cosmológicas sin sesgos.
0.2 Planteamiento y metodología
Las misiones XMM-Newton de la ESA y Chandra de la NASA, ambos lanzados
en 1999, son los observatorios de rayos-X más potentes en órbita hasta la
fecha. Chandra es principalmete un observatorio de imagen: se encuentra optimizado
para obtener altas resoluciones angulares (con precisiones del orden
de ∼0.5"). Por su parte, XMM-Newton tiene una resolución espacial moderada
(∼15") pero una mayor superficie colectora, siendo un observatorio ideal para
xi

ealizar estudios de espectroscopía en rayos-X. XMM-Newton lleva a bordo tres
instrumentos operados en paralelo: RGS, que consta de dos espectrómetros de
dispersión de alta resolución (E/∆E ∼ 100 − 700) en el rango de energías 0.3-
2.1 keV, tres cámaras de rayos-X (EPIC) llamadas MOS1, MOS2 y pn, y un monitor
óptico/UV. Las cámaras EPIC cubren un campo de visión de 30’ y tienen
resolución espectral moderada (E/∆E ∼ 20 − 50). Los datos empleados para
construir las muestras empleadas en esta tesis han sido obtenidos con el detector
EPIC-pn.
Para dar respuesta a las preguntas planteadas en la sección anterior, hemos empleado
dos muestras de fuentes extragalácticas de rayos-X. Se tratan de AXIS
(An XMM-Newton International Survey) y XMS (XMM-Newton Medium Sensitivity
Survey), construidas y lideradas por el Grupo de Astronomía de Rayos-X
del Instituto de Física de Cantabria. El autor de esta tesis ha participado directamente
en ambos proyectos, realizando observaciones y reduciendo datos
ópticos y de rayos-X que han sido posteriormente utilizados para obtener los
resultados presentados en esta tesis. La muestra AXIS fue extraída de 36 observaciones
de XMM-Newton a altas latitudes galácticas (|b| ≥ 20 ◦ ) para minimizar
el número de fuentes en nuestra propia Galaxia que pudieran entrar en la muestra.
Las fuentes detectadas cubren un ángulo sólido de ∼4.8 grados cuadrados
y tienen flujos en rayos-X entre ∼ 10 −15 − 10 −12 erg cm −2 s −1 . La muestra XMS
es una submuestra limitada en flujo de 25 campos de AXIS con tiempos de exposición
típicos de ∼20 kilosegundos, y cubre en el cielo un área de en torno a
∼3 grados cuadrados. XMS forma parte de un extensivo programa de identificaciones
mediante espectroscopía óptica por lo que, como resultado del mismo,
una importante fracción (∼90%) de esta muestra se haya identificada y sus desplazamientos
al rojo medidos de forma fiable, siendo la muestra más extensa
con alto grado de completitud construida hasta la fecha.
Los estudios evolutivos de AGN requieren una gran precisión en la determinación
del desplazamiento al rojo de las fuentes. De lo contrario, los resultados
podrían estar sesgados y conducir a conclusiones erróneas. El proceso de
identificación de las fuentes conlleva un procedimiento que se puede resumir
de la siguiente forma. En primer lugar hay que tomar imágenes en el óptico
de las zonas donde se detectan fuentes de rayos-X, que posteriormente se utilizan
para buscar las posibles contrapartidas ópticas de las mismas (las fuentes
detectadas en el óptico cuya posición se encuentra próxima a la posición de
las fuentes de rayos-X). En algunos casos no es posible detectar contrapartidas
xii

ópticas, lo que implica que estas fuentes de rayos-X pueden encontrarse fuertemente
oscurecidas. En estos casos, se usan otras longitudes de onda menos sensibles
al oscurecimiento (infrarrojo cercano, infrarrojo medio) para encontrar las
posibles contrapartidas. Seguidamente se realiza espectroscopía en el óptico de
las contrapartidas seleccionadas. Cuando la densidad de fuentes es elevada es
posible hacer espectroscopía multiobjeto (tomar varios espectros de distintas
fuentes al mismo tiempo). En el caso de XMS, esto se hizo en las primeras fases
de la identificación con espectrógrafos de fibras. Posteriormente, a medida que
las contrapartidas restantes son más débiles y su densidad es menor, hay que
ir una a una mediante espectroscopía de rendija larga. Una vez reducidos los
espectros, se procede a la revisión visual de los resultados. De esta forma se
clasifican en función de su naturaleza (si presentan o no líneas de emisión, y si
éstas son anchas y estrechas - AGN de tipo 1 - o sólo estrechas - AGN de tipo
2) y se obtienen sus desplazamientos al rojo comparando la longitud de onda
observada de las líneas con su longitud de onda en reposo.
Para evaluar la contribución de nuestras fuentes al FCX necesitamos modelar la
distribución en flujo de las mismas. Cuanta mayor precisión obtengamos en los
parámetros que modelan la distribución en flujo, más precisa será nuestra estimación
de la contribución al FCX de nuestras fuentes. Además, para una mayor
precisión y cubrir un mayor rango de flujos, hemos añadido a la muestra AXIS
otras muestras más profundas y brillantes disponibles en la literatura. El procedimiento
que seguimos consta de dos pasos. En primer lugar calculamos la
distribución en flujo diferencial de las fuentes en intervalos de flujo que, esencialmente,
es el sumatorio del inverso del área efectiva de las fuentes en cada
intervalo dividido por la anchura del intervalo. A esta distribución diferencial
le ajustamos mediante una técnica de χ 2 un modelo empírico que, en este
caso, es una doble ley de potencias. Esto nos proporciona un valor inicial de los
parámetros que emplearemos como punto de inicio del siguiente paso. Como
el análisis de la distribución por intervalos puede estar sometido a sesgos (por
ejemplo, fluctuaciones debidas a unas pocas fuentes, sobre todo a flujos altos
en donde el número de fuentes es menor) hemos preferido ajustar nuestro modelo
empírico mediante un método de máxima verosimilitud, que hace uso de
todas y cada una de las fuentes disponibles. La función de verosimilitud a minimizar
tiene en cuenta no sólo la variación del área efectiva como función del
flujo, sino también las incertidumbres en el flujo de la fuente. El algoritmo de
minimización emplea como punto inicial el mejor ajuste que obtuvimos de la
xiii

distribución diferencial que, al estar próximo a la solución real, requerirá menos
iteraciones del algoritmo.
Una vez que se dispone de una medida precisa de la distribución en flujo de
las fuentes, se puede estimar la intensidad con la que éstas contribuyen al FCX,
integrando en flujo el mejor ajuste obtenido anteriormente y comparándolo con
la intensidad total del FCX, valor que se puede encontrar en la literatura.
Las fuentes de la muestra AXIS también se pueden usar para explorar la estructura
a gran escala del Universo en rayos-X. Si existe una estructura cósmica que
se encuentre presente en todos (o, al menos, en una buena parte de) los campos
observados, ésto se debe traducir en un exceso en la distribución de distancias
entre pares de fuentes con respecto de la de una distribución aleatoria. Ésta es
la definición de una función de correlación, que es uno de los medios estadísticos
que hemos empleado para medir el grado de agrupamiento de las fuentes.
Efectivamente, se pueden medir distancias angulares entre pares de fuentes y
buscar excesos en el número de pares de fuentes a una distancia angular dada
respecto al que nos daría una muestra artificial generada aleatoriamente. A
la hora de simular una muestra hay que tener en cuenta las variaciones en la
sensibilidad de la detección de fuentes reales para no obtener sobredensidades
espúreas. La función de correlación angular así medida se ajusta por χ 2 a un
modelo analítico (una ley de potencias en este caso) cuyos parámetros nos dicen
la distancia de correlación típica entre fuentes y la fuerza del agrupamiento.
Alternativamente, también hemos calculado el agrupamiento angular de las
fuentes AXIS mediante un algoritmo basado en estadística Poissoniana. Este
método compara el número esperado de pares de fuentes a distancias angulares
menores o iguales que unas observadas en ausencia de correlación con el
número total de pares de fuentes observados. De esta forma se puede obtener
la probabilidad Poissoniana integrada de obtener menos pares que los observados
para una distribución de media el número de pares aleatorios. Además
de darnos indicios acerca de la presencia o ausencia de agrupamiento angular,
éste método estima también la significancia de la detección para lo que hicimos
10000 simulaciones de muestras sintéticas sobre las que comparar los valores
observados.
No obstante, las separaciones angulares entre fuentes son una proyección en
el cielo de las auténticas separaciones espaciales entre dos fuentes que se encuentren
a distintos desplazamientos al rojo. Aún así, el agrupamiento angular
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es una herramienta poderosa para estimar la estructura a gran escala cuando
las muestras empleadas son grandes. Además, es posible desproyectar el agrupamiento
angular al espacio tridimensional si se asume una distribución de
desplazamientos al rojo. Este método se conoce como inversión de la ecuación
de Limber.
Análogamente a la función de correlación angular existe una generalización en
tres dimensiones llamada función de correlación espacial que emplea el mismo
procedimiento. Como es de esperar, en este caso se emplean distancias físicas
entre pares de fuentes de las que se conoce su desplazamiento al rojo (como es
el caso de las fuentes de la muestra XMS). El proceso de cálculo es análogo al
anterior y proporciona la distancia espacial de correlación típica entre pares de
fuentes y la fuerza del agrupamiento.
Para realizar el estudio evolutivo de los AGN presentes en la muestra XMS en
primer lugar hemos modelado la absorción intrínseca de las fuentes detectadas
en los rayos-X más energéticos (que, como hemos visto, son fuentes absorbidas
en una fracción importante) como función de la luminosidad y el desplazamiento
al rojo. Esto nos ha permitido investigar la evolución de la luminosidad
intrínseca (antes de la absorción) de estas fuentes. Para ello hemos ajustado
las observaciones a distintos modelos de evolución (evolución pura en luminosidad
y evolución tanto en la luminosidad como en la densidad comóvil de
fuentes) de la función de luminosidad de los AGN. La función de luminosidad
mide el número de fuentes por unidad de luminosidad por unidad de volumen
comóvil (o la densidad comóvil de fuentes por unidad de luminosidad).
El método empleado para hacer el ajuste es, de nuevo, un método de máxima
verosimilitud. Como hemos comentado anteriormente, éste método explota la
información disponible para cada fuente y está libre de todos los sesgos y artificios
que suelen acompañar a las estimaciones hechas por intervalos. Como en
el caso del cálculo de la distribución en flujo de las fuentes AXIS, para el estudio
de la evolución de los AGN también hemos añadido a la muestra XMS otras
muestras altamente identificadas más débiles y más brillantes para ampliar la
cobertura del plano luminosidad-desplazamiento al rojo sobre el que vamos a
realizar el estudio.
A partir del mejor modelo que describe la evolución de los AGN es posible estudiar
la historia de la acreción en el Universo. Como hemos comentado, el origen
de la emisión en rayos-X en los AGN es producida por acreción gravitatoria de
xv

materia sobre el agujero negro central. Una vez que se han corregido los posibles
efectos de la absorción, cambios en la luminosidad X de los AGN a lo largo
del tiempo cósmico implican cambios intrínsecos en la acreción de materia. De
esta forma, a partir de la función de luminosidad adoptada es posible calcular
la densidad comóvil de los AGN, la tasa de acreción volúmica y la cantidad de
materia acretada en función del tiempo.
0.3 Aportaciones originales
La investigación llevada a cabo en esta tesis ha contribuído significativamente
al conocimiento de las propiedades evolutivas de los AGN y cómo su emisión
contribuye a la emisión del fondo cósmico de rayos-X. El análisis de la distribución
en flujo de fuentes-X extragalácticas llevado a cabo en esta tesis es
uno de los más precisos hasta la fecha, gracias al tamaño de la muestra empleada,
reduciendo significativamente las incertidumbres que existían en algunos
parámetros del modelo. Además, el método para ajustar las observaciones
al modelo que hemos empleado tiene en cuenta las incertidumbres en
los flujos observados lo que incrementa la fiabilidad de los resultados.
El estudio de estructura a gran escala del Universo en rayos-X nos ha permitido
estimar el grado de agrupamiento de las fuentes. Además hemos podido cuantificar
la densidad mínima de fuentes necesaria para obtener una señal significativa
de agrupamiento. Por debajo de ella, el agrupamiento subyacente sería
indetectable aunque existiese. Adicionalmente, uno de los métodos empleados
para cuantificar la significancia en la detección del agrupamiento, basado en la
estadística Poissoniana, es original.
Finalmente, hemos estudiado la evolución de los AGN a partir de su función de
luminosidad. La muestra combinada empleada es de las mayores compiladas
hasta la fecha, lo que se ha traducido en una gran precisión en la determinación
de los parámetros evolutivos, disminuyendo las incertidumbres en varios de
ellos con respecto a otros trabajos. Además hemos llevado a cabo el estudio
evolutivo sobre una submuestra de AGN detectados en rayos-X muy duros
(energías en el rango 4.5-7.5 keV) por primera vez hasta la fecha.
xvi

0.4 Conclusiones
Los resultados más importantes de los análisis llevados a cabo sobre las fuentes
de las muestras AXIS y XMS detectadas en rayos-X blandos (energías 2 keV) son los siguientes:
1. La distribución en flujo de fuentes detectadas en rayos-X blandos (bandas
0.5-2 keV y 0.5-4.5 keV) siguen un modelo de doble ley de potencias,
presentando un cambio de pendiente a flujos ∼ 10 −14 erg cm −2 s −1 . Las
fuentes detectadas en rayos-X duros (banda 2-10 keV) también siguen este
modelo aunque hay evidencias de que puede existir un cambio de pendiente
adicional a flujos ∼ 3 × 10 −15 erg cm −2 s −1 . Es difícil asignar un
origen a esta variación (que es poco significativa) que puede ser debida a
desviaciones del modelo debido a la simplicidad del mismo (ya que estamos
intentado describir contribuciones de una superposición de distintas
poblaciones a distintos desplazamientos al rojo) o a incertidumbres en la
calibración de los datos. Los resultados obtenidos son compatibles con
otros trabajos anteriores aunque, gracias al tamaño de la muestra y la amplia
cobertura en flujo disponible, hemos reducido significativamente las
incertidumbres en los parámetros del modelo.
2. La distribución en flujo de las fuentes con espectros más duros (aquellas
que cuantitativamente emiten más rayos-X duros que blandos) no presenta
cambio de pendiente. Esto puede implicar que este tipo de fuentes
son detectadas a desplazamientos al rojo más bajos y, por lo tanto, no
muestran evolución, o ésta es muy poco intensa desde esa época hasta
el presente.
3. Hemos resuelto la intensidad de la emisión del FCX hasta las flujos más
debiles a los que tenemos acceso usando nuestra muestra combinada en
un ∼90%. La intensidad producida extrapolando nuestra distribución en
flujo a flujo cero no satura la intensidad total del FCX. Si asumimos que la
distribución en flujo vuelve a cambiar por debajo del flujo mínimo detectado
en nuestra muestra, hemos comprobado que una población de
galaxias dominante a esos flujos sería suficiente para reproducir el FCX
empleando únicamente fuentes discretas.
4. La máxima contribución fraccional al FCX en todas las bandas de energía
xvii

analizadas proviene de fuentes en torno a ∼ 10 −14 erg cm −2 s −1 (aproximadante
donde ocurre el cambio de pendiente en la distribución en flujo).
La emisión a estos flujos supone el ∼50% de la contribución total al FCX
en las bandas 0.5-2 y 2-10 keV, resaltando así la importancia de muestreos
a flujos medios como AXIS para el estudio de la evolución de la radiación
en rayos-X del Universo hasta 10 keV.
5. Hemos encontrado evidencias de agrupamiento angular a gran escala en
el Universo de rayos-X blandos (bandas 0.5-2 y 0.5-4.5 keV) con una significancia
de ∼99%-99.9%. No así para las fuentes duras, que ofrecen resultados
comparables con una distribución aleatoria. Hemos comprobado
que esto puede ser debido a la baja densidad de fuentes por campo en
esta banda, que puede diluir la presencia de agrupamiento hasta hacerlo
indetectable.
6. Dividiendo la muestra entre varias submuestras comprobamos que la señal
de agrupamiento está extendida por todo el cielo, no encontrándose limitada
a sólo unos pocos campos. Esto implica que si esta estructura tiene
un origen cosmológico, debe provenir de desplazamientos al rojo ≤1.5 (el
pico de la distribución de desplazamientos al rojo de muestras a flujos
medios).
7. Hemos usado la información espectral detallada de la que disponemos
para las fuentes duras (>2 keV) para modelar su absorción intrínseca como
función de la luminosidad y el desplazamiento al rojo. Encontramos que la
fracción de AGN absorbidos disminuye al incrementarse la luminosidad
y aumenta con el desplazamiento al rojo para las fuentes detectadas en la
banda 2-10 keV. Las fuentes más duras, detectadas en la banda 4.5-7.5 keV,
presentan también una disminución en la fracción de AGN absorbidos con
la luminosidad pero, sin embargo, no hay dependencia significativa con el
desplazamiento al rojo. Esto puede ser debido al escaso rango de desplazamientos
al rojo abarcado por esta submuestra, con la mayoría de las
fuentes a desplazamientos al rojo bajos (z < 1).
8. La evolución de los AGN no está bien descrita asumiendo que únicamente
su luminosidad evoluciona con el tiempo. Hemos comprobado que el modelo
que mejor se ajusta a las observaciones es aquel en el que existe evolución
tanto en la luminosidad como en la densidad comóvil de objetos. Gracias
al gran número de fuentes involucradas, hemos mejorado la precisión
xviii

en la determinación de los parámetros de este modelo con respecto a trabajos
anteriores. Además, hemos estudiado por primera vez la función de
luminosidad intrínseca (corrigiendo por la absorción) de las fuentes más
duras (4.5-7.5 keV), encontrando que éstas presentan una evolución significativamente
más fuerte a desplazamientos al rojo bajos que el resto de
AGN. El total de materia acretada en el Universo actual (a desplazamiento
al rojo cero) predicha por nuestro modelo coincide con la estimación de la
densidad de agujeros negros supermasivos en el Universo local hecha por
otros autores empleando otros métodos como la función de masa local de
agujeros negros.
9. En todas las bandas de energía estudiadas, los AGN más luminosos (log L X >
44) se forman antes que los menos luminosos (log L X < 44), alcanzando
un máximo en la densidad de objetos a desplazamientos al rojo de ∼1.5,
mientras que los segundos lo hacen a desplazamientos al rojo menores
(∼0.7). Esto indica que los AGN más luminosos acretaban materia más
eficientemente que los menos luminosos en las etapas tempranas del Universo,
encontrándose plenamente formados a desplazamientos al rojo de
∼1.5-2. Este comportamiento confirma que la evolución de la función de
luminosidad observada a lo largo del tiempo cósmico no está causada por
variaciones en el entorno absorbente de rayos-X, sino por variaciones intrínsecas
en la tasa de acreción de materia sobre el agujero negro supermasivo.
0.5 Futuras líneas de investigación
Aunque los resultados obtenidos en esta tesis han aportado sustanciales mejoras
al estudio de las propiedades evolutivas y de agrupamiento de los AGN,
existen aún ciertos aspectos en los que convendría profundizar.
Por un lado, aunque hemos obtenido claras evidencias de que las fuentes extragalácticas
de rayos-X a flujos medios se encuentran fuertemente agrupadas
formando estructuras cosmológicas a gran escala, no hemos podido confirmar
que esto sea cierto para fuentes detectadas en rayos-X duros. En la literatura
es fácil encontrar resultados discrepantes a este respecto, siendo la razón en la
mayor parte de los casos la baja densidad de fuentes por campo.
xix

Haciendo uso del segundo catálogo de fuentes de XMM-Newton, 2XMM 2 , el
mayor catálogo de fuentes de rayos-X hasta la fecha (2XMM es 5 veces mayor
que el anterior catálogo disponible, 1XMM 3 ) que contiene más de 250,000 fuentes
(∼150,000 detecciones únicas) detectadas sobre ∼600 grados cuadrados de cielo,
será posible determinar fuera de toda duda la presencia de agrupamiento angular
de fuentes por encima de 2 keV. Además, gracias a la superior estadística
proporcionada por 2XMM se podrán determinar los parámetros de agrupamiento
con una precisión sin precedentes, y estudiar cómo evolucionan a
distintos flujos límite poniendo de relieve las propiedades de agrupamiento de
las distintas poblaciones de fuentes dominantes a cada flujo.
Por otra parte, las propiedades cosmológicas de las fuentes detectadas en rayos-
X muy duros (en la banda 4.5-7.5 keV) que, como hemos visto, son muy eficientes
para seleccionar muestras de AGN muy poco sesgadas por la absorción,
se encuentran aún sujetas a muchas incertidumbres. En especial, la evolución
de la fracción de AGN absorbidos con el desplazamiento al rojo en esta banda
de energía no se ha podido determinar, y algunos parámetros evolutivos en
la función de luminosidad de estas fuentes requieren un estudio más detallado.
Para resolver estos aspectos es necesario mejorar la estadística de la muestra. Ya
que los AGN absorbidos tienen baja densidad angular, si se quiere disponer de
un número mayor de ellos es necesario muestrear áreas del cielo más grandes.
Correlacionando 2XMM con catálogos ya existentes en otras frecuencias como,
por ejemplo, el Sloan Digital Sky Survey (SDSS) se puede reunir suficiente información
como para ampliar la muestra a flujos altos, con una elevada cobertura
de cielo, que proporcione un número suficiente de AGN oscurecidos que permita
estudiar su evolución a desplazamientos al rojo moderados ( ∼ < 1).
¢¡£¡¥¤§¦©¨¨£¢¡£©£! "#¨£$¥¡%¥&¥ ¢¨'¥(£))#¨
2
¢¡£¡¥¤§¦©¨¨£¢¡£©£! "#¨£$¥¡%¥&¥ ¢¨+*(£))#¨
3
xx

Universidad de Cantabria
Departamento de Física Moderna
CSIC - Universidad de Cantabria
Instituto de Física de Cantabria
Evolution and large scale clustering
of a sample of extragalactic X-ray sources
A dissertation submitted in partial fulfillment of the requirements for
the degree of Doctor of Philosophy in Physics
by
Jacobo Ebrero Carrero
2008

With magic, you can turn a frog into a prince.
With science, you can turn a frog into a PhD and
you still have the frog you started with.
Terry Pratchett
In the beginning, the Universe was created.
This made a lot of people very angry and
has been widely regarded as a bad idea.
Douglas Adams. The Hitchhiker’s Guide to the Galaxy

Acknowledgements
Esta sección es, con toda probabilidad, a la que más tiempo he dedicado de
todas las componen esta tesis. La razón principal es que va a ser la más leída
de toda ella (las estadísticas así lo indican) y, mucho me temo, la única que se
entienda.
Han sido muchos años y muchas personas, por lo que es posible que me deje a
alguien en el tintero. Si es así, espero que el/los afectado/s no se lo tome/n a
mal y acepte/n el agradecimiento implícito en estas líneas.
Me gustaría empezar agradeciendo a mi director de tesis, Francisco Carrera,
todo el esfuerzo que ha puesto en que este trabajo salga adelante, sus consejos
(“más sabe el diablo por viejo que por diablo”) y, sobre todo, por su paciencia.
También quiero hacer pública mi admiración por su capacidad multi-tarea que,
en ocasiones, me ha hecho considerar seriamente la posibilidad de que sea un
replicante.
Igualmente me gustaría agradecer a Xavier Barcons la confianza depositada
y los consejos dados a lo largo de estos años (cuando conseguía parar por el
despacho, que no era todo lo a menudo que él quisiera).
Mi agradecimiento al resto de la gente del grupo (que empezó siendo grupúsculo
y ya se ha convertido en horda) de Astronomía de Rayos-X del IFCA: a
Maite Ceballos (la SUSI) por el apoyo logístico prestado (que no tiene precio
y tampoco habría páginas suficientes para agradecerlo), a mis compañeros de
fatiga Amalia y Ángel (vamos que ya os falta poco), al “infiltrado” Joserra (que
ha visto más de Cantabria en un año que yo en cuatro), a Lánder (perdona por
la puñalada trapera en el Diplomacy), a Rodrigo (por descubrirme las bondades
culinarias de Estrasburgo), y también a los ex-miembros Javier Bussons (nos vemos
en Sigüenza) y Francesca (autora de la mejor tarta de queso que he probado
en mi vida).
xxvii

Un capítulo aparte merecen mis compañeros de despacho a lo largo de estos
años. Desde aquí quiero agradecer a Ibán Cabrillo (por los consejillos informáticos
-“vale, pero antes manda un mail a la USI”- y por pasarme la serie completa
de Gárgolas), a Marcos el Castor (que creo que se lo está pasando pipa en
Cambridge), a Marcos Cruz (sí, sí, tú, el capullo maquiavélico), a Andrés (por
comentar la prensa todas la mañanas y por esas inolvidables noches de poker
-“pero... QK!!”-), al Chals (“que yo mato peña, chorbo”), y a Luis (por asistir impertérrito
a nuestros exabruptos verbales).
Quiero también extender mi agradecimiento al resto de gente del IFCA que he
tenido el placer de conocer: a Diego (por fomentar la ludopatía y el frikismo,
y por sus insondables conocimientos gastronómicos -a lo que ayuda el hecho
de que, al parecer, su estómago también es insondable-), a Chema (por... por...
bueno, por ser Chema), a Patri y a Belén (por el mus y las risas), y a la gente
del piso de abajo Ivan, Marta, Clara y Diego (por las charlas intrascendentes
delante de la máquina del café).
Desde aquí un abrazo a Emmanuel y Almudena, y como a media docena más
de personas (que no voy a enumerar porque seguro que me dejo a alguien y
entonces sí que voy a quedar mal) que me hicieron más llevaderas las estancias
en Munich, con el agravante de que eramos todos compañeros en la Complu
(va a ser verdad que el mundo es un pañuelo). También a mis amigos Sergio,
Pablo, Fede, Ana y Mónica (siempre nos queda Nochevieja).
En un lugar destacable en estos agradecimientos se encuentra toda mi familia
por el cariño y el apoyo incondicional a pesar de la incomprensión que genera
un trabajo como éste, pero muy especialmente a mis padres y a mi abuela
Chencha, y al resto de mis abuelos (que ya no están aquí pero sé que les hubiera
gustado verlo).
Finalmente, quiero agradecer a la gente de la Universidad de Leicester la posibilidad
que me han dado de trabajar unos meses con ellos, que han sido claves
para poder terminar de escribir esta tesis, y a la Spanish Armada del departamento
Silvia, Omaira, Dolores, Jenny (honoríficamente) y, proximamente, Pili
(somos más que ellos, jo, jo, jo).
A todos, muchas gracias.

xxx

Summary
Since its discovery more than 40 years ago, unveiling the origin and nature of
the cosmic X-ray background (CXB) emission has been one of the major questions
in X-ray astronomy. The deepest X-ray surveys conducted by the Chandra
and XMM-Newton imaging observatories have resolved up to a large extent
the extragalactic X-ray emission from 0.1 to 10 keV, confirming the discrete origin
of the CXB. Large campaigns of optical spectroscopic identifications of the
sources detected in these surveys have shown that dominant population of the
extragalactic X-ray sky is a mixture of obscured and unobscured Active Galactic
Nuclei (AGN).
In this work we pursue to confirm the nature and cosmic evolution of the
sources that dominate the CXB emission at medium fluxes. AGN are strong
X-ray emitters, their luminosity being several orders of magnitudes larger than
that of the host galaxy, and are believed to be powered by accretion of matter
onto a central supermassive black hole. Hard X-rays can penetrate through
large amounts of gas and dust without being significantly affected and, hence,
they provide a unique view of the central engine in obscured AGN. Given the
large sensitivity of the current X-ray observatories, it is clear that medium-deep
extragalactic X-ray surveys provide a unique tool to study the cosmic history of
accretion in the Universe.
In the work presented in this thesis we have provided further insight into the
nature and cosmic evolution of the population of AGN that dominate the CXB
emission at intermediate to faint X-ray fluxes at energies from ∼0.1 to ∼10 keV.
In order to do that we have studied the evolutionary and clustering properties
of one of the largest samples of X-ray sources analyzed up to date detected
serendipitously with XMM-Newton, the AXIS survey, and a flux-limited highlyidentified
subsample of AXIS, the XMS survey. In combination with other shallower
and deeper surveys we have constrained with unprecedent accuracy the
xxxi

sky density of extragalactic X-ray sources, resolving up to ∼90% of the CXB
emission into discrete sources and thus confirming that the bulk of the CXB
emission resides at medium X-ray fluxes ∼10 −14 erg cm −2 s −1 .
We have also estudied the large-scale structure of the X-ray Universe at medium
and faint fluxes. For that, we have undertaken two different approaches applied
to the sources of the AXIS survey. One consisted in the calculation of the
angular correlation function which measures the distribution of angular distances
between pairs of sources with respect a random distribution. On the
other hand, we applied a more formal test based on Poissonian statistics. In
both cases, we found strong evidence that AGN detected in soft (2 keV) X-
rays present only marginal clustering or no clustering at all. However, we have
demonstrated that this lack of clustering might be due to the low density of
hard sources per field rather than an intrinsic property of these sources. Additionally,
we have computed the spatial correlation function for the sources in
the XMS subsample, for which we have a very large number of accurate redshift
determinations. We did not find clustering for neither soft nor hard AGN.
This can be explained in terms of the dillution of the clustering signal across the
sky.
Another major aim of these work is to study the cosmic evolution of AGN along
cosmic time. We have carried out an evolution analysis of the sources in the
XMS survey by computing the X-ray luminosity function of these sources. In
order to have intrinsic results, not biased by absorption, we have taken into account
the intrinsic absorption column densities of the sources detected in hard
X-rays., finding that the fraction of absorbed AGN decreases with increasing
luminosity, and increases with redshift. We tested two models for the X-ray luminosity
function. A model in which there is only envolution in luminosity has
been ruled out, being more acceptable a model in which there is evolution in
both the luminosity and the comoving density of AGN. From these results we
have estimated the accretion rate density of the Universe at different epochs,
finding out that the most luminous AGN feed and grow more efficiently than
the less luminous ones, and are fully formed earlier (z ≃ 1.5 − 2).
xxxii

xxxiv

Contents
Resumen de la tesis en castellano
vii
0.1 Objetivos de la investigación . . . . . . . . . . . . . . . . . . . . . vii
0.2 Planteamiento y metodología . . . . . . . . . . . . . . . . . . . . . xi
0.3 Aportaciones originales . . . . . . . . . . . . . . . . . . . . . . . . xvi
0.4 Conclusiones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
0.5 Futuras líneas de investigación . . . . . . . . . . . . . . . . . . . . xix
Acknowledgements
xxvii
Summary
xxxi
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Brief history of X-ray Astronomy . . . . . . . . . . . . . . . . . . . 3
1.3 The Cosmic X-ray Background . . . . . . . . . . . . . . . . . . . . 6
1.4 The large-scale structure of the Universe in X-rays . . . . . . . . . 8
1.5 Active Galactic Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5.1 Emission mechanisms . . . . . . . . . . . . . . . . . . . . . 10
1.5.2 Observational properties . . . . . . . . . . . . . . . . . . . 11
1.5.3 Origin of the X-ray emission . . . . . . . . . . . . . . . . . 14
1.5.4 Classification of AGN . . . . . . . . . . . . . . . . . . . . . 15
1.5.5 The AGN model and the AGN unification picture . . . . . 17
1.6 Evolution of AGN in X-rays . . . . . . . . . . . . . . . . . . . . . . 21
xxxv

CONTENTS
1.6.1 The K-correction . . . . . . . . . . . . . . . . . . . . . . . . 21
1.6.2 Space density of AGN . . . . . . . . . . . . . . . . . . . . . 22
1.7 Modern instrumentation in X-ray astronomy . . . . . . . . . . . . 23
1.7.1 X-ray telescopes . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.7.2 Imaging X-ray detectors . . . . . . . . . . . . . . . . . . . . 24
1.7.3 The XMM-Newton observatory . . . . . . . . . . . . . . . . 27
1.8 Aims of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2 AGN surveys with XMM-Newton 33
2.1 The AXIS survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1.1 Introduction and field selection . . . . . . . . . . . . . . . . 34
2.1.2 Data processing and source selection . . . . . . . . . . . . 35
2.1.3 X-ray properties of the sources . . . . . . . . . . . . . . . . 41
2.2 The XMS survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.2 Imaging and selection of optical counterparts . . . . . . . 43
2.2.3 Identification of XMS sources . . . . . . . . . . . . . . . . . 45
2.3 Other surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.1 Chandra Deep Field . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.2 ASCA Medium Sensitivity Survey . . . . . . . . . . . . . . 51
2.3.3 XMM-Newton Bright Serendipitous Survey . . . . . . . . . 51
2.3.4 XMM-Newton Hard Bright Serendipitous Survey . . . . . 51
2.3.5 ROSAT International X-ray/Optical Survey . . . . . . . . . 52
2.3.6 ROSAT Deep Survey - Lockman Hole . . . . . . . . . . . . 52
2.3.7 ROSAT Bright Survey . . . . . . . . . . . . . . . . . . . . . 53
3 Source counts of the AXIS sources 55
3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.1 The sky areas . . . . . . . . . . . . . . . . . . . . . . . . . . 56
xxxvi

CONTENTS
3.2.2 The binned log N − log S . . . . . . . . . . . . . . . . . . . 57
3.2.3 The log N − log S model . . . . . . . . . . . . . . . . . . . . 58
3.2.4 Maximum likelihood fit method . . . . . . . . . . . . . . . 59
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 Contribution to the Cosmic X-ray Background . . . . . . . . . . . 72
3.4.1 Contribution from bright sources and stars . . . . . . . . . 72
3.4.2 Total X-ray background intensity . . . . . . . . . . . . . . . 73
3.4.3 Contribution to the CXB in different flux intervals . . . . . 74
3.4.4 Resolved and unresolved components of the CXB . . . . . 77
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4 Clustering of AXIS and XMS sources 83
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Cosmic variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3 Angular correlation function of AXIS sources . . . . . . . . . . . . 85
4.3.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3.3 Poisson statistics test . . . . . . . . . . . . . . . . . . . . . . 92
4.3.4 Angular correlation of a hardness ratio selected sample . . 99
4.3.5 Inversion of Limber’s equation . . . . . . . . . . . . . . . . 99
4.4 Spatial clustering of XMS sources . . . . . . . . . . . . . . . . . . . 105
4.4.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5 Luminosity function of XMS sources 115
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2 The N H function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.1 Binned luminosity function . . . . . . . . . . . . . . . . . . 128
xxxvii

CONTENTS
5.3.2 Analytical model . . . . . . . . . . . . . . . . . . . . . . . . 129
5.3.3 Model fitting to soft sources . . . . . . . . . . . . . . . . . . 130
5.3.4 Model fitting to hard and ultrahard sources . . . . . . . . . 131
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.4.2 Accretion history of the Universe . . . . . . . . . . . . . . . 137
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6 Summary of the results 147
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A Sensitivity maps 155
References 160
xxxviii

List of Figures
1.1 The electromagnetic window . . . . . . . . . . . . . . . . . . . . . 2
1.2 Spectrum of the extragalactic CXB . . . . . . . . . . . . . . . . . . 7
1.3 Schematic spectrum of a Type-1 AGN . . . . . . . . . . . . . . . . 12
1.4 Schematic diagram of the unified model of AGN . . . . . . . . . . 20
1.5 Light path on a Wolter-1 X-ray telescope . . . . . . . . . . . . . . . 25
1.6 Payload of the XMM-Newton observatory . . . . . . . . . . . . . . 26
1.7 Lightpath of the XMM-Newton telescopes . . . . . . . . . . . . . . 28
2.1 Examples of identified XMS sources . . . . . . . . . . . . . . . . . 49
3.1 Sky area of the AXIS survey . . . . . . . . . . . . . . . . . . . . . . 57
3.2 N(>S) 0.5-2 keV and 2-10 keV best fits . . . . . . . . . . . . . . . . 63
3.3 N(>S) 0.5-4.5 keV and 4.5-7.5 keV best fits . . . . . . . . . . . . . . 64
3.4 dN(S)/dSdΩ and best fit ratio in Soft and hard bands . . . . . . . 67
3.5 dN(S)/dSdΩ and best fit ratio in XID and Ultrahard bands . . . . 68
3.6 N(>S) for two HR selected Soft subsamples . . . . . . . . . . . . . 71
3.7 Relative contribution to the total CXB intensity . . . . . . . . . . . 76
4.1 w(θ) of AXIS in the 0.5-2 keV and 2-10 keV bands . . . . . . . . . 88
4.2 w(θ) of AXIS in the 0.5-4.5 keV and 4.5-7.5 keV bands . . . . . . . 89
4.3 1 − P µ (N θ ) versus θ for the Soft and Hard samples . . . . . . . . . 93
4.4 1 − P µ (N θ ) versus θ for the XID and Ultrahard samples . . . . . . 94
4.5 Correlation tests for a Soft/3 sample . . . . . . . . . . . . . . . . . 96
xxxix

LIST OF FIGURES
4.6 Soft 1 − P µ (N θ ) versus θ in both Galactic hemispheres . . . . . . . 98
4.7 Correlation tests for a HR selected sample . . . . . . . . . . . . . . 100
4.8 Selection function for AXIS soft and hard sources . . . . . . . . . . 103
4.9 Redshift distribution of the real and simulated XMS sources . . . 108
4.10 ξ(r) versus r of XMS sources in Soft and Hard bands . . . . . . . . 110
5.1 Intrinsic N H versus L X4.5−7.5 of XMS sources. . . . . . . . . . . . . . 118
5.2 Observed N H distributions in the hard and ultrahard bands. . . . 120
5.3 Fraction of absorbed Hard AGN as a function of L X and z . . . . . 121
5.4 Fraction of absorbed Ultrahard AGN as a function of L X and z . . 122
5.5 Luminosity-redshift plane of different X-ray surveys . . . . . . . . 126
5.6 Sky area of the survey as a function of flux . . . . . . . . . . . . . 127
5.7 X-ray luminosity function in the soft band . . . . . . . . . . . . . . 134
5.8 X-ray luminosity function in the hard band . . . . . . . . . . . . . 136
5.9 X-ray luminosity function in the ultrahard band . . . . . . . . . . 138
5.10 Comoving density of AGN . . . . . . . . . . . . . . . . . . . . . . . 139
5.11 Accretion rate density . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.12 Total accreted mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
A.1 ,§-./ vs. crpoisim for all bands . . . . . . . . . . . . . . . . . . . . . 158
xl

List of Tables
2.1 Fields of the AXIS survey . . . . . . . . . . . . . . . . . . . . . . . 39
2.1 Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2 Number of AXIS sources selected in different bands . . . . . . . . 43
2.3 Definition of the XMS samples . . . . . . . . . . . . . . . . . . . . 44
2.4 Spectroscopic facilities used to identify XMS sources . . . . . . . . 46
2.5 Identification completeness of the XMS sample . . . . . . . . . . . 47
2.6 Identification breakdown of the XMS sample . . . . . . . . . . . . 48
3.1 ML fit results to the AXIS source counts . . . . . . . . . . . . . . . 61
3.2 Fit results for HR selected Soft subsamples . . . . . . . . . . . . . 70
3.3 Cosmic X-ray Background intensities . . . . . . . . . . . . . . . . . 75
3.4 Comparison between estimated CXB intensities . . . . . . . . . . 78
4.1 Angular correlation function best χ 2 fits . . . . . . . . . . . . . . . 91
4.2 Spatial correlation lengths for the AXIS soft and hard samples . . 104
5.1 Summary of surveys used for the luminosity function . . . . . . . 125
5.2 Parameters of the X-ray luminosity function. . . . . . . . . . . . . 132
A.1 Summary of the results of the linear fits of crpoisim to ,0-.0/ . . . . 156
xli

Chapter 1
Introduction
In the last few decades, X-ray Astronomy has opened a new window to the
Universe. The capability to observe the sky at such energetic wavelengths has
allowed many astronomers to look at the most violent and obscured side of the
Universe. A X-ray photon, with an energy thousands of times that of an optical
one, can penetrate through large amounts of matter showing phenomena that
were hidden to us before.
X-ray emission can have different origins ranging from ionized plasmas at millions
of degrees to relativistic particles trapped inside strong magnetic fields,
and therefore many astronomical objects are known to be X-ray emitters. Some
of them lay inside our own Galaxy such as stars, binary systems with a compact
companion (neutron stars, black holes) or supernova remnants, but others
are extragalactic: active galactic nuclei (AGN, hereafter) or hot gas in galaxy
clusters.
The origin of the X-ray emission from the intra-cluster medium in clusters of
galaxies is thermal bremsstrahlung from a low-density, optically-thin hot (millions
of degrees) gas, whereas in the case of AGN and binary systems the radiation
comes from matter gravitationally accreting onto a compact object.
In this thesis, we will study the properties of a sample of AGN using the X-ray
data provided by the European X-ray Observatory XMM-Newton.
1

CHAPTER 1: INTRODUCTION
Figure 1.1 The electromagnetic window. The vertical axis shows the transparency of
the atmosphere for a given frequency. The higher the curve, the more opaque is the
atmosphere at that frequency.
1.1 Motivation
The atmosphere of the Earth absorbs X-rays preventing them to reach the surface
of the planet, effectively absorbing all the electromagnetic radiation coming
from space, except a small window at optical and near infrared wavelengths
and radiowaves (see figure 1.1). This has important biological implications but
it is a major problem when trying to do high-energy Astronomy unless X-ray
detectors are placed outside the atmosphere. The first steps in this field were
done through stratospheric balloons followed by rockets in the second half of
the last century.
X-ray Astronomy was born in 1962, in a rocket flight that tried to detect the
X-ray emission from the Sun reflected in the Moon. The result of this mission
was the detection of the first extra-solar X-ray source (named Sco X-1 as it was
discovered in the constellation of Scorpius) and an isotropic emission coming
from all directions in the sky ([78]). We know today that this emission is the
Cosmic X-ray Background (CXB hereafter, see section 1.3).
Observations with the modern X-ray observatories XMM-Newton and Chandra
2

CHAPTER 1: INTRODUCTION
have confirmed that the CXB emission is a composition of a miriad of individual
sources, most of them AGN. These objects are usually extremely bright in
X-rays, with luminosities in the range 10 42 − 10 48 erg s −1 accounting for an important
fraction (∼10%) of their bolometric luminosity. Variability has been observed
in the X-ray flux of many of these sources with temporal scales ranging
from days to minutes (see [179] for a review), which means that the origin of the
X-ray emission must be very close to the objects lying in their centres. Nowadays,
it is widely believed that almost all known galaxies host in their centres
a supermassive black hole (i.e. [126]) with a mass of the order of 10 6 − 10 9 M ⊙ ,
and therefore the X-ray emission is strongly linked with it, generated by gravitational
accretion.
In this process, matter falls onto a compact and massive object. Since the infalling
material possesses considerable specific angular momentum, it forms a
disk (the so-called accretion disk) around the supermassive black hole. X-ray
emission is then generated in this environment when photons gain energy by
inverse Compton scattering in the hot corona that surrounds the disk and thus
are enhanced to X-ray frequencies (see section 1.5.1).
X-rays are very penetrating and can pass through large amounts of matter that
would easily absorb optical or ultraviolet photons. This makes possible to detect
AGN through cosmological distances and to explore the Universe when it
was younger. Hence, X-rays allow us to trace the evolution of the accreting supermassive
black holes across cosmic time. Furthermore, hard X-rays are the
only ones that can escape from obscured AGN, those with intrinsic absorbing
column densities N H 10 22 cm −2 (type-2 AGN, see section 1.5.4). However,
if the absorption column density is 5 × 10 24 cm −2 , X-ray photons with energies
below 10-20 keV are also absorbed (Compton-thick objects). Recent results
seems to confirm that obscured AGN may play a key role to explain the overall
CXB emission.
1.2 Brief history of X-ray Astronomy
After the first rocket missions that probed the X-ray sky in the 1960s, it was
clear that only with instruments onboard satellites orbiting the Earth would be
possible to observe the X-ray sky. The first major advance in X-ray Astronomy
came from the launch of the mission SAS-1 (NASA), unofficially named Uhuru
3

CHAPTER 1: INTRODUCTION
(the Swahili word for Freedom) in 1970. This small satellite observed hundreds
of sources in the range of 2-20 keV, many of them in the galactic plane as they
were mainly binary systems or supernova remnants, but the rest were extragalactic
sources, homogeneously distributed on the celestial sphere. They were
mainly Seyfert galaxies (see section 1.5.4) and galaxy clusters, which meant that
most of the cosmic X-ray emission came from very far objects and therefore the
existence of very energetic physical processes was required. In addition, Uhuru
was capable of observing the sources for relatively large amounts of time (compared
with those of the rocket experiments) which led to the first discovered
variable sources.
After Uhuru the observation of the X-ray sky was continued by a series of small
satellites such as SAS-3 or OSO-8. In 1977 a new leap forward in the history
of X-ray Astronomy was given with the launch of the first of the High Energy
Astronomy Observatories (HEAO-1). Among other discoveries, HEAO-1 measured
the CXB intensity spectrum in the range 10-100 keV, showing a broad
peak at energies 40 keV. This hump was fitted to a thermal bremsstrahlung
model under the assumption of a diffuse origin for the CXB ([146]). However,
when the satellite COBE measured the cosmic microwave background with the
instrument FIRAS in 1992, its emission spectrum perfectly fitted with a black
body spectrum showing no traces of Compton scattered microwave photons
by hot electrons ([152]). This meant that the diffuse origin hypothesis for the
CXB had to be abandoned.
Although the instruments onboard HEAO-1 had an improved sensitivity with
respect the previous missions, it was not until 1978 with HEAO-2 (renamed Einstein
afterwards) that a modern X-ray telescope was finally put into orbit. The
construction and installation of the four nested mirrors in the satellite was a
major technological challenge for the epoch. It could focus X-ray photons with
energies between 0.25 and 4 keV with an angular resolution of several arcseconds.
Einstein detected over 5000 sources and performed the first deep imaging
observations (to a limiting flux of ∼ 2 × 10 −14 erg cm −2 s −1 ) that resolved 25%
of the CXB in the 1-3 keV band into discrete sources ([77], [91], [96], [186]).
The first important European mission was Exosat, which was launched in 1983
and was operative until 1986. Its very eccentric orbit with an orbital period
of 90 hours, allowed to observe the same source for some days and therefore to
study in detail their variability. In fact, the most remarkable discovery achieved
4

CHAPTER 1: INTRODUCTION
by this mission was the existence of quasiperiodic oscillations in the X-ray spectrum
of binary systems.
In 1990 was launched the mission Rosat, a collaboration between Germany, the
United States and the United Kingdom. It operated in the range 0.1-2.4 keV
and, compared with Exosat, increased its sensitivity and field of view (the area
of the sky visible from a telescope). The prime task of Rosat was to carry out an
all-sky survey, something that had not been done since HEAO-1, which yielded
to a catalogue of ∼ 77000 sources. Besides, Rosat performed a deep observation
in the Lockman Hole region resolving up to ∼ 90% of the CXB into discrete
sources down to a flux limit of ∼ 10 −15 erg cm −2 s −1 ([98], [102]) in that energy
band.
The Japanese Space Agency participated actively in the investigation of the X-
ray sky in the 1980s with a couple of two small missions (Tenma, Ginga) but it
was in 1993 with Asca when they fully gave a technological leap forward. This
satellite could observe in a range of energies spanning from 0.5 to 10 keV while
retaining a great effective area. The X-ray detectors placed onboard were based
on the CCD technology (see section 1.7.2) for the first time. Asca carried out
some medium/deep surveys in the 2-10 keV band down to limiting fluxes of
∼ 5 × 10 −14 erg cm −2 s −1 that resolved ∼ 35% of the CXB in this energy band
([69], [74], [226]). These results showed that there was a hidden population
of AGN with harder spectra than the AGN detected at lower energies, many of
them turned out to be X-ray absorbed AGN at low redshifts. This meant that the
unresolved fraction of the CXB at harder energies could be due to a population
of undetected obscured AGN. In addition, the gravitationally redshifted Fe K α
fluorescence emission line was observed with better sensitivity and spectral
resolution (which was first discovered by Ginga) thus proving the existence of
matter moving at relativistic velocities around a supermassive black hole.
In 1996, the Italian Space Agency in collaboration with the Dutch Space Agency
launched the BeppoSAX satellite. Among its achievements was to survey a region
of the sky down to fluxes of ∼ 5 × 10 −14 erg cm −2 s −1 in the 5-10 keV band
resolving ∼ 20 − 30% of the CXB ([40]) and the observation of highly-absorbed
Compton-thick AGN.
The most powerful X-ray observatories up to now, Chandra (NASA) and XMM-
Newton (ESA), were both launched in 1999 and are still operative. Their designs
are very different: Chandra has an unprecedent angular resolution that makes
5

CHAPTER 1: INTRODUCTION
it ideal for imaging, whereas XMM-Newton possesses a larger effective area
(sensitivity) that is better for X-ray spectroscopy. Both of them have reached
limiting fluxes up to ∼ 100 times fainter than the precedent observatories. For
instance, Chandra reached ∼ 2 × 10 −16 erg cm −2 s −1 in the ultra-deep surveys
Chandra Deep Field North (CDF-N, [28]) and South (CDF-S, [79], [194]) resolving
up to a ∼ 90% of the CXB in the 2-8 keV band ([33], [80], [115], [156], [163],
[219]). These surveys have been used in this thesis to complement our X-ray
data (see section 2.3). On the other hand, XMM-Newton reached a 0.5-2 keV
limiting flux of ∼ 5 × 10 −16 erg cm −2 s −1 in the Cosmos survey ([134]) and the
Lockman Hole region ([101]). However, at energies above 10 keV, where the
bulk of the CXB is emitted, only a tiny fraction of it has been resolved into discrete
sources, probably heavily obscured AGN that remain undetected until a
new generation of X-ray telescopes is developed.
Since 1999, when XMM-Newton began to operate, each of its pointings have
provided between ∼ 30 − 150 serendipitous sources, most of them newly detected.
The 1XMM catalogue was released in 2003 and contained all the sources
(∼ 33, 000 in total, ∼ 28, 000 unique sources) detected by XMM-Newton before
May 2002. In 2007, the XMM-Newton Survey Science Center (SSC) 1 released the
2XMM catalogue, the largest X-ray catalogue ever made, comprising ∼ 250, 000
sources, ∼ 150, 000 of them unique 2 .
1.3 The Cosmic X-ray Background
The X-ray sky is dominated by a diffuse radiation of cosmic origin. Since its discovery
(see section 1.2) the hypothetical origin of the CXB has been a challenge
for the X-ray astronomers.
The CXB spans from ∼ 0.1 keV to several keV (see Fig. 1.2) and the contribution
at different energies has different origins. For instance, at very soft energies,
0.1-0.3 keV, the main contribution comes from thermal emission from a local
hot plasma (with T ∼ 10 6 K) known as the Local Hot Bubble. A second contributor
is the thin plasma in the halo of our Galaxy ([153]). From 0.5 to 1 keV
there is contribution to the CXB emission from both the Galactic hot plasma
and extragalactic discrete sources. Above ∼3 keV the CXB is highly isotropic
¢¡£¡¥¤§¦©¨¨£¢¡£©£! "#¨
1
2 A fraction of the sources has been detected more than once because of the overlapping in XMM-
Newton’s observations.
6

CHAPTER 1: INTRODUCTION
Figure 1.2 Spectrum of the extragalactic X-ray background from 0.2 to 400 keV measured
by different missions (taken from [82])
(once the weak Galactic component and the dipolar field caused by the motion
of the Galaxy have been conveniently taken into account) and it is known to
have a extragalactic origin, due to the integrated emission of unresolved discrete
sources.
None of the missions and experiments that have measured the CXB spectrum to
date have found significant deviations in the spectral shape from Γ ∼ 1.4 over
the ∼3-10 keV band. However, the values obtained for its intensity (usually
parameterized as the intensity at 1 keV in units of photons keV −1 cm −2 s −1
sr −1 ) have been significantly different (sometimes even among measurements
taken with the same instrument) with variations that can be as large as ∼40%,
which makes the value of the normalization of the CXB rather uncertain.
It is expected that the discrete nature of the CXB induces a cosmic variance in
the measured value of the CXB intensity. The discrete nature of the CXB produces
confusion noise, caused by unresolved sources in the images ([11], [202]).
All measurements, except the one carried out by HEAO-1, were obtained from
observations over small solid angles (below ∼1 deg 2 ). [14] showed that confusion
noise can account for variations in the measured intensity of the CXB
of ∼10% for solid angles below 1 deg 2 . When cosmic variance is taken into
7

CHAPTER 1: INTRODUCTION
account measurements within the same mission but different instruments are
brought to consistency. However, they also found that cosmic variance alone
cannot acount for the observed discrepancies between missions, and hence significant
instrumental cross-calibration uncertainties between different instruments
must still be present ([52]).
1.4 The large-scale structure of the Universe in X-rays
In the last decades there has been substantial advances in the study and understanding
of the cosmic structure of the Universe and the large-scale matter
distribution (see [214] for a review). New generations of galaxy surveys, such as
the 2-degree Field Galaxy Survey ([39]) or the Sloan Digital Sky Survey (SDSS,
[243]), have quantified the distribution of galaxies in the local Universe. These
wide-angle galaxy surveys have shown the existence of large-scale structure in
the form of filaments around voids with extensions of ∼20-30 h −1 Mpc or forming
superstructures like the ’Great Wall’ ([73]). Such structures have been found
up to distances of z ≃ 0.2. However, the study of these structures at higher redshifts
requires the involvement of AGN which, thanks to their large bolometric
luminosities (see section 1.5), can be detected at cosmological distances. Since
strong X-ray emission is a typical feature of AGN activity and it is less likely
to be affected by absorption, X-ray surveys provide the most efficient mean of
investigating the large-scale structure at high redshifts.
The standard way of describing the clustering of galaxies, clusters of galaxies
and AGN in statistical cosmology have been, for many years, the correlation
functions. They were first suggested in the 1960s by [218] to study the spatial
clustering of galaxies in the near Universe. Nonetheless, the major boost for the
correlation functions as a tool to measure large-scale clustering came up in the
1970s, with the works of P. J. E. Peebles, along with several colleagues. They
carried out a programme to extract estimates of the correlation functions from
the Lick galaxy catalogue and other data sets (see [174] and references therein).
The correlation functions set up a description of the clustering properties of a
set of points distributed in space, although useful results can also be obtained
for two-dimensional distributions of positions on the celestial sphere. A number
of works have used the correlation functions of X-ray selected AGN trying
to trace the underlying cosmic large-scale structure ([24], [18], [38], [84], [159],
8

CHAPTER 1: INTRODUCTION
[161], [242]), although the significancies on the measurements vary and the results
show very large uncertainties in some cases. In addition, other authors
have found similar results for X-ray selected clusters of galaxies (e.g. [206]),
whose clustering properties have been claimed to be linked with that of AGN
([47], [35], [34]) and therefore with the processes of formation of galaxies and
supermassive black holes.
1.5 Active Galactic Nuclei
Active Galactic Nuclei (AGN) were first discovered in the 1940s as galaxies
characterized by the extreme brightness of their centres. The luminosity of
the centre can range from tens to thousands of times that of the underlying
host galaxy, which is completely outshone, appearing in the optical images as
a bright and variable point source when the AGN is distant. The suggested
activity of the central regions of these galaxies led to the term Active Galactic
Nuclei. These objects are the most luminous persistent sources known in the
Universe (gamma ray bursts can be brighter by a few orders of magnitude but
they only last a few seconds). Their bolometric luminosities span a broad range
of values, from 10 42 to 10 48 erg s −1 for the most luminous AGN often known
as quasars. This term was originally applied to radio-loud objects (quasi-stellar
radio source), while QSO was used to radio-quiet objects. More recently, the
term quasar has been frequently used to refer to all luminous AGN, although
we now know that many properties are similar for both low and high luminosity
objects.
With the improvement of sensitivity of X-ray detectors, it has been possible to
detect activity in an increasing number of non-active galaxies, somehow blurring
the division between active and non-active galaxies. There is observational
evidence that supermassive black holes are hosted in the centres of most, if
not all, galaxies (i.e. [126]), including the Milky Way. It is customary in X-ray
astronomy to classify a galaxy as active if its X-ray luminosity is higher than
∼10 42 erg s −1 since nothing but gravitational accretion of matter can produce
such luminosities.
9

CHAPTER 1: INTRODUCTION
1.5.1 Emission mechanisms
The mechanisms that are believed to produce the observed emission in AGN at
different wavelengths can be summarized as follows:
1. Thermal black body emission: A black body is defined as a body in thermal
equilibrium with its surroundings that is both a perfect absorber and a
perfect emitter of radiation. None of the radiation that reaches a black
body is reflected. Real objects are not perfect black bodies, but the black
body approximation works reasonably well in many cases. The emission
spectrum of a black body depends only on its temperature.
Thermal radiation by the gas present in the accretion disk has been traditionally
used as an explanation to the optical/UV continuum emission in
AGN. AGN accretion disks are typically cool (∼10 5 - 10 6 K) producing relatively
soft spectra in the optical/UV energy range. Black body emission
coming from dust heated by the optical/UV radiation field is believed to
be responsible for the mid-/far-IR emission in radio-quiet AGN.
2. Inverse Compton scattering: Photons can interchange energy by interactions
with charged particles, a process known as Compton scattering. The scattering
cross-section of nuclei is much smaller than that of the electrons
and therefore Compton scattering by nuclei can be neglected. If the electrons
are relativistic, photons may gain energy from the electrons and the
process is known as Inverse Compton scattering. The spectrum of the
scattered radiation depends on the electron energy distribution. Inverse
Compton scattering is believed to be responsible for the broad band continuum
observed in the X-ray spectra of radio-quiet AGN.
3. Synchrotron radiation: Electromagnetic radiation produced by relativistic
charged particles accelerated in an external magnetic field is known as
synchrotron radiation.
Assuming a non-thermal particle distribution with a power law energy
spectrum, the emitted spectrum is another power law with an energy index
α (F ν ∝ ν −α ) that is related to the power law of the particle spectrum.
It is believed that synchrotron radiation from a population of relativistic
electrons located in jets is responsible for the radio emission in radio-loud
AGN. However, it is very unlikely that synchrotron radiation is an impor-
10

CHAPTER 1: INTRODUCTION
tant contributor to the high energy spectra of AGN, excepting the small
fraction of radio-loud AGN.
4. Bremsstrahlung (free-free emission): Bremsstrahlung (which is the German
word for ’braking radiation’) is related to emission produced in hot dense
ionized plasma. It is produced when free electrons lose energy and therefore
emit electromagnetic radiation when they are accelerated by the electromagnetic
field of the ions. As free electrons can have a very large range
of energies, the emission has a thermal continuum distribution. If the material
contains metals, there are might also be very intense emission lines
superimposed to this continuum.
The emission mechanism on clusters of galaxies is believed to be bremsstrahlung
from hot (∼10 8 K), low-density (∼10 −3 atoms cm −3 ) gas.
1.5.2 Observational properties
The broadband emission of AGN is very different to that of normal galaxies,
and spans the entire electromagnetic spectrum from radio to gamma rays (unless
stated otherwise, all energies mentioned in this section are rest-frame energies):
1. Radio emission: Only ∼10% of optically and X-ray selected AGN are strong
radio emitters, and the emission in radio rarely contributes more than
∼1% to the AGN bolometric luminosity. The spectrum of AGN at radio
wavelengths is a power law, and the origin of the radio emission is
believed to be synchrotron radiation emitted in outflows of relativistic
charged particles along the poles of a rotating supermassive black hole
(see section 1.5.1).
2. Infrared emission: The IR continuum of AGN rise following a power law
from the optical to the FIR/submm wavelengths. The IR broad band
spectrum can be well reproduced by a model in which a significant fraction
of the nuclear emission is reprocessed by warm molecular gas that
surrounds the active nucleus and the broad line region (see section 1.5.5)
with an axisymmetric torus-like structure ([87], [181], [182]). The gas absorbs
the optical/UV/X-ray radiation and thermally reprocesses it into
the rest-frame mid- and far-IR range. Obscuration in a moderately thick
11

CHAPTER 1: INTRODUCTION
Figure 1.3 Schematic spectrum of a type-1 AGN (black solid line) along with the most
relevant spectral components (taken from [191]).
gas (optical depth from 10 to 300 in the UV) and at maximum distance
to the black hole of tens to hundreds of parsecs, gives a good description
of the broadband IR spectrum of AGN ([88]). This scenario has gained
strong observational support as some observations of the Hubble Space
Telescope to the active galaxy NGC 4261 have resolved a torus structure
([68]).
3. Optical/UV emission: The optical/UV continuum emission of AGN is dominated
by a broad hump known as the Big Blue Bump (BBB), which peaks
at ∼1000 Å. The BBB is usually interpreted as thermal emission from the
accreting matter in the innermost regions of the AGN. The optical/UV
spectrum of Type-1 AGN (see section 1.5.4) also shows strong broad permitted
lines and narrow permitted and forbidden emission lines superimposed
to the continuum.
4. X-ray emission: AGN are very luminous X-ray sources. As a first approximation,
the X-ray spectrum of AGN from ∼1 to ∼100 keV is continuumdominated,
and is well described by a single power law with a typical
slope of ∼1.9. At low-energy gamma rays the spectrum of AGN is also
well reproduced by a power law albeit with a steeper slope. If the signal-
12

CHAPTER 1: INTRODUCTION
to-noise ratio of the X-ray spectrum is good enough, other prominent features
are observed (see Figure 1.3). The most common spectral features
are:
• Photoelectric absorption: The strongest feature in the 0.1-100 keV spectrum
of a significant fraction of AGN is a photoelectric cut-off of the
intrinsic power law at low energies due to absorption by a cold or
partially ionized material in the line of sight to the nucleus. Photoelectric
absorption by our own Galaxy modifies the X-ray spectrum
below 0.6 keV. On the other hand, local absorption lines have been
detected in the X-ray spectrum of bright AGN, which are believed to
be caused by hot plasma (10 5 - 10 7 K) in the so-called Warm-Hot Intergalactic
Medium (WHIM). Apart from this, 50% of Seyfert 1 galaxies
(see section 1.5.4) show X-ray absorption by highly ionized gas by
the intense nuclear UV/X-ray radiation (warm absorber, [76], [189]).
These absorption edges usually appear blueshifted, showing velocities
of the order of a few hundreds km s −1 thus suggesting that the
absorbing material is moving away the central source at these velocities
([120], [121]).
• Soft excess: At low energies (below ∼2 keV) the emission of a significant
fraction (∼30%) of AGN shows a strong soft component superimposed
over the hard X-ray continuum with a peak of emission in
the Extreme UV ([223]), known as the soft excess ([235]). This emission
was first reported by [8] in 1985, but the origin of the spectral
component is not clear. It has been often interpreted as direct thermal
emission from the hot innermost region of the accretion disk ([8], [46],
[132], [185], [195]) and therefore as the high-energy tail extension of
the BBB. However, the typical measured temperatures (>500 eV) are
too high to explain it as thermal emission from the accretion disk. Alternative
models for this emission are reflection of hard X-rays by cold
dense gas ([94]) or, more recently, by ionized absorption of the primary
continuum by a relativistic wind moving at several thousands
km s −1 ([81]).
• Fluorescent Fe K α emission: Emission lines at rest-frame energies ∼6.4 -
6.7 keV are common in high quality X-ray spectra of AGN. Since iron
is the most abundant heavy element, the observed line emission in X-
13

CHAPTER 1: INTRODUCTION
rays has been attributed to iron fluorescence. Fe K α emission has been
detected in both absorbed and unabsorbed AGN ([162], [164], [184]).
The material responsible for the line emission in absorbed objects is
likely to be the molecular torus responsible for the X-ray absorption.
In unobscured AGN the emission originates in optically thick material
out of the line of sight.
• Compton reflection hump: A broad bump above the power law continuum
is observed in many AGN over the ∼7 - 60 keV rest-frame
energy range, peaking at ∼30 keV ([165]). This spectral feature is often
explained as reflection of the hard X-ray photons in the accretion
disk or the molecular torus (i.e. [75], [93], [136]).
• Exponential cut-off : At energies of several tens to hundreds of keV an
exponential cut-off has been obverved in the BeppoSAX spectra of a
few AGN ([92], [166], [176], [177]). This cut-off indicates the presence
of a thermal hot corona around the accretion disk.
1.5.3 Origin of the X-ray emission
In this section we will summarize some of the properties already discussed in
order to put them in the context of the origin of the X-ray emission of AGN. We
know that AGN are cosmological sources that, because of their large bolometric
luminosities, can be detected at very large distances. The large emissivity
of these objects puts very strong constraints on the emission mechanisms that
powers them (see section 1.5.1). It is commonly accepted that the source of energy
of AGN is the conversion into radiation of gravitational energy of accretting
matter in the region surrounding a supermassive central black hole with
masses in the range ∼10 6 - 10 10 M ⊙ . The efficiency of the proccess can be of
the order of ∼10%, much higher than any other source of energy (for instance,
nuclear fusion, the power source in stars, has an efficiency of ∼0.7%).
In spite of this commonly accepted scenario, the details on how X-rays are produced
are still not clear and remain as one of the most challenging problems in
AGN physics. As seen in section 1.5.2, an optically thick accretion disk is not
hot enough to form the soft excess emission often seen in the spectrum of AGN
and therefore it cannot produce the higher X-ray emission observed.
The best model to date for the primary X-ray emission above 1 keV in AGN is
14

CHAPTER 1: INTRODUCTION
Compton up-scattering of optical/UV photons emitted thermally in the accretion
disk by an optically thin hot plasma of thermal electrons that surrounds the
accretion disk, which is modelled as a Comptonizing corona. Comptonization
leads to a power law spectral shape that reproduces well the observed continuum
emission of AGN in X-rays ([46], [94], [95], [133], [196]).
In the simplest geometry of the Comptonization model, half of the X-ray radiation
is emitted towards the observer while the other half is directed to the accretion
disk, where it is absorbed and re-emitted as optical/UV photons that enter
again the corona thus cooling the hot electrons. Hence, the spectral slope of the
X-ray power law depends on the temperature and optical depth of the Comptonizing
plasma. Heating and cooling processes are coupled so the Comptonizing
models predict a narrow range of power law shapes, which is in agreement
with the observations that have found rather small dispersions on the X-ray
continuum of AGN (∆Γ ∼0.2, [149]).
Thermal models for the corona predict a high energy cut-off at energies that depend
on the temperature of the Comptonizing plasma. This has already been
observed in the BeppoSAX spectra of a number of AGN (see section 1.5.2), giving
strong support to the thermal models.
1.5.4 Classification of AGN
The different observational properties of AGN have been described in previous
sections, which have been commonly used to classify AGN into different
groups. The scheme adopted for this work is based on their emission properties
at optical/UV wavelengths. AGN are often classified using a secondary scheme
based on their emission properties at radio wavelengths (radio-loudness).
AGN are classified according to their optical/UV spectral properties, falling
into the following categories:
• Broad Line AGN (Type-1 AGN): The optical spectrum of a Type-1 AGN
shows strong highly ionized broad permitted lines and hydrogen lines,
although HeI, HeII and FeII lines are also frequently detected with typical
widths of 2000-10000 km s −1 . Because of this, these objects are often
referred as Broad Line AGN (BLAGN). They cover a broad range of redshifts
and are the dominant population at bright fluxes ([217]). Most AGN
in this group do not show signs of obscuration at neither X-ray nor optical
15

CHAPTER 1: INTRODUCTION
wavelengths. Some observational evidences ([149]), however, point out
that ∼10% of the sources in this group have X-ray absorption, although
with low absorbing column densities (below 10 22 cm −2 ).
The radio-quiet objects in this class are usually subdivided into Seyfert 1
galaxies, when they have luminosities below 10 44 erg s −1 (and are therefore
seen nearby), and QSO, when they have luminosities above 10 44 erg
s −1 (which appear as point-like sources in both X-ray and optical images).
• Narrow Line AGN (Type-2 AGN): These sources have optical continua with
superimposed permitted and forbidden lines, being all the observed lines
narrow (widths ≤1500 km s −1 ). Their optical spectral continuum is dominated
by starlight and therefore has very weak non-thermal optical/UV
continuum, with little evidence for the optical/UV bump typical of Type-
1 AGN. The X-ray spectrum of a Type-2 AGN usually shows signatures
of X-ray absorption, with a wide range of absorbing column densities but
systematically higher than those of Type-1 AGN. Hence, they are fainter
soft sources, detected at z ≤ 1.5 in current X-ray surveys ([12]).
Like in the Type-1 category, Type-2 radio-quiet AGN are classified as Seyfert
2 galaxies at low luminosities and as Type-2 QSO at high luminosities. A
general name used for all galaxies which only show narrow emission lines
in their optical/UV spectrum is Narrow Emission Line Galaxies (NELG,
[162]), which includes Seyfert 2 galaxies, LINERs, starburst galaxies and
Type-2 QSO.
• Other categories: A small number of AGN are characterized by the absence
of emission lines in their optical/UV spectrum. The radio-loud sources in
this group include BL Lacertae (BL Lac) objects, Optically Violently Variable
Quasars (OVV), Highly Polarized Quasars (HPQ) and Core Dominated
Quasars (CDQ). All of them are characterized by rapid variability
in flux at very short time scales and are generally termed as blazars.
One of the most surprising findings of the Chandra and XMM-Newton
medium-deep surveys was the discovery of X-ray luminous sources (≥
10 42 erg s −1 ) in the nuclei of optically normal galaxies ([15], [41], [79],
[114], [163]). These sources, which present an optical spectrum typical of
an absorption line galaxy (ALG), have been given a variety of names such
as Optically Dull Galaxies ([63]), Passive Galaxies ([90]), X-ray Bright Optically
Normal Galaxies (XBONG, [41]) or Elusive Active Galactic Nuclei
16

CHAPTER 1: INTRODUCTION
([142]). It is uncertain why we do not see AGN signatures in the optical
spectra of these sources, although a possible explanation is the combination
of absorption, faint nuclear emision with respect to the host galaxy,
and an inadequate set-up and atmospheric conditions during the spectroscopic
observations ([208]). Additionally, some of these sources show absorbed
X-ray spectra with column densities higher than 10 24 cm −2 ([142])
which suggests that these sources indeed host an AGN and that the peculiar
optical and X-ray properties are related to heavy obscuration.
A secondary classification of AGN classify them into two broad categories according
to their radio-loudness, defined as:
( )
f5
R L = log
f B
(1.5.1)
where f 5 is the radio flux at 5 GHz and f B is the optical flux on the B band,
centred at 4400 Å. Those objects with R L ≥ 10 are labeled as radio-loud AGN
whereas the rest are radio-quiet AGN. The optical/UV emission line spectra of
both classes of objects are very similar ([200]), although radio-loud AGN appear
to have systematically flatter X-ray spectral slopes than the radio-quiet objects
([210], [235]). Radio-loud AGN constitute a small fraction (5-10%) of the optical
and X-ray selected AGN population.
The radio-loud Type-1 AGN are named Broad Line Radio Galaxies at low luminosities,
and Radio Loud Quasars (RLQ) at high luminosities. Radio-loud Type-
2 AGN are usually termed Narrow Line Radio Galaxies (NLRG), and are subdivided
into two categories according to their morphological type: the low luminosity
Fanaroff-Riley 1 radio galaxies (FRI) and the high luminosity Fanaroff-
Riley 2 radio galaxies (FRII, [67]). Radio emission in FRI objects is found to be
core dominated and show weak optical emission, while the FRII objects show
strong optical emission and their radio emission is lobe dominated.
1.5.5 The AGN model and the AGN unification picture
The large diversity of observational properties of AGN makes the detailed understanding
of the underlying physic very complex. However, the approximate
structure of AGN is believed to be as illustrated in Figure 1.4 and it is widely
accepted that all active galaxies are constituted by the following ingredients:
17

CHAPTER 1: INTRODUCTION
1. A supermassive black hole (10 6 - 10 10 M ⊙ ) accreting matter at the centre.
2. The accreting material posseses significant angular momentum and therefore
the accretion cannot be radial thus forming a planar disk of optically
thick plasma (accretion disk, see section 3.1) that surrounds the black
hole ([209]). The accreting matter is probably heated by magnetic and/or
viscous processes to temperatures of the order of 10 5 - 10 6 K and emits
thermally in the optical/UV and, probably, soft X-rays. The characteristic
radius of an active nucleus is generally parametrized in terms of
the radius of a non-rotating Schwarzschild black hole, R S = 2GM/c 2 ∼
3 × 10 5 M/M ⊙ cm. For a black hole of mass 10 8 M ⊙ , R S = 10 14 cm or 1
light-hour.
3. A quasi-spherical cloud of hot optically thin plasma surrounds (or perhaps
it is mixed with) the inner parts of the accretion disk. The hot electrons
Compton up-scatter the thermal photons emitted in the accretion disk to
hard energy X-rays. This results in the non-thermal power law spectrum
observed at X-rays in AGN.
4. At distances of about 100 light-days from the central engine are located
clouds of high density (10 7 - 10 10 cm −3 ) gas moving at high velocity (thousands
of km s −1 ), which are responsible for the strong highly ionized
Doppler-broadened optical/UV emission lines observed in the spectrum
of many AGN. This is known as the Broad Line Region (BLR).
5. Further out, at distances of parsecs or a few light-years from the nucleus,
there is a region of thick cold material of gas and dust with a toroidal geometry
in a similar plane as the accretion disk ([127], [181], [182]). The
torus absorbs and scatters the nuclear radiation and partially covers the
central engine, blocking the BLR and the accretion disk to certain lines of
sight. It is not clear whether the torus geometry depends on the luminosity,
but the apparent lack of cross-correlation of the amount of absorption
with the host galaxy inclination angle (even for AGN of the same optical
type), suggests that its orientation must be random with respect to the host
galaxy ([143]).
6. At distances ranging from a few tens of parsecs to kiloparsecs are lowvelocity
clouds of gas excited by the ionizing nuclear radiation emitted
along the polar axis of the torus. This is known as the Narrow Line Region
18

CHAPTER 1: INTRODUCTION
(NLR) and is responsible for the narrow optical/UV emission lines and,
as it lies outside the region affected by the high column density, they only
suffer from moderate dust obscuration. The detection of strong forbidden
narrow lines implies that the density of the material in the NLR cannot
exceed the critical density for collisional de-excitation and must be of the
order of ∼10 4 cm −3 or less.
7. Powerful relativistic radio jets and ionization cones flow from the central
black hole and can extend up to tens of kiloparsecs. They are symmetric
with respect to the black hole and propagate in both directions along the
axis perpendicular to the accretion disk. They are best seen in radio wavelengths
thanks to synchrotron emission, but it is unclear how common are
these jets in AGN.
Unification models try to unify all different classes of AGN with only a few parameters
giving rise to the whole observed variety of properties. The basis of
the unification schemes is that all AGN have intrinsically the same mechanism
(they are powered by accretion onto a supermassive black hole) and their different
observational properties are mostly due to the anisotropic distribution of
obscuring matter. Unification models were firstly invoked to explain the results
of spectropolarimetric observations that detected broad line components in the
optical/UV spectrum of Seyfert 2 galaxies ([6]). Further support to a unified
model theory came with the detection of broad permitted emission lines in the
near-IR unpolarized spectra of optically Type-2 AGN and no broad lines features
in the polarized spectra, as the absorption is less effective in the IR than
in the optical band ([86], [192], [199]).
In this context the different observational properties of Type-1 and Type-2 AGN
are mainly due to different orientation angles from which the obscuring matter
is observed. The absorbing matter would be located at intermediate distances
between the BLR and the NLR, but it would not be completely blocking the
nuclear region. The simplest geometry that describes the obscuring matter is a
torus ([5], [228]), the clouds of the BLR, or material associated with the accretion
disk ([111]). The sources in which we can directly see the nuclear emission and
the BLR will therefore have unabsorbed X-ray spectra and would be optically
classified as Type-1 AGN. The sources in which the obscured matter intercepts
the line of sight of the observer, the central engine and the BLR will be hidden.
These sources would therefore have an absorbed X-ray spectrum and will be
19

CHAPTER 1: INTRODUCTION
Figure 1.4 Schematic diagram of the unified model of AGN (image credit: NASA). The
torus is not at scale.
20

CHAPTER 1: INTRODUCTION
optically classified as Type-2 AGN (see Figure 1.4).
Unification schemes provide a simple description of the most general properties
of AGN. X-ray observations show that Type-2 AGN are systematically weaker
in the soft X-ray band than Type-1 AGN, as expected if their nuclear emission
is obscured. However, the number of observational results that cannot be explained
by the standard unified model are increasing rapidly. X-ray surveys are
finding that not all X-ray obscured AGN have Type-2 optical spectra, and that
not all Type-1 AGN are X-ray unobscured (e.g. [149], [150]).
1.6 Evolution of AGN in X-rays
1.6.1 The K-correction
The luminosities of extragalactic objects such as AGN have to be corrected for
their redshift, so that all luminosities are studied over the same emitted band
(we would have different emitted bands for different redshifts otherwise).
Formally, this can be expressed as:
L = L obs × K corr (z) (1.6.1)
where L obs is the luminosity in the observer bandpass and L is the luminosity
over the same bandpass in the frame of reference of the emitting object. For an
object with a power law spectrum (typical of AGN), the K-correction is:
K corr (z) = (1 + z) α−1 (1.6.2)
where α is the energy index defined in section 1.5.1. The K-correction is unity
(and therefore has no effect at all) when α = 1. In any other cases, neglecting
the K-correction would lead to spurious luminosity evolution with redshift.
In this work, the spectral index of most AGN is known and therefore we have
applied the K-correction for individual AGN. However, in some cases in which
we do not know the spectral index for every single source in a sample we have
applied an average K-correction.
21

CHAPTER 1: INTRODUCTION
1.6.2 Space density of AGN
As we have seen before, AGN can be detected at cosmological distances thanks
to their large luminosity and hence they are of great interest to study the Universe
at earlier epochs. However, all observations have a limiting flux for detection,
such that an object with a flux below this limit cannot be distinguished
from the background. The limiting luminosity for detection varies with distance
so that we end up seeing different populations of AGN at different redshifts.
The luminosity function enables us to represent what is observed in
terms of different distances and luminosities, and is thus defined as the number
of objects detected per unit comoving volume per unit luminosity. In general,
the luminosity function will be a function of both luminosity and redshift. The
comoving volume is the volume that a region of space would have if it were
observed at the present epoch. Hence, the comoving volume is independent
of the expansion of the Universe and therefore there is no density evolution of
objects caused by this cosmological expansion.
Evolution in the comoving space density or luminsity of AGN is seen as a
change in the luminosity function. This can be described in different forms:
• Pure Luminosity Evolution (PLE): In PLE, the number of AGN per unit
comoving volume remains constant while the luminosity of each AGN
evolves, at a rate that is the same for AGN of all luminosities. In the
framework of a PLE model, the luminosity function retains its shape at all
redshifts and depends only on the evolution law and the luminosity function
at zero redshift. It has been a fairly succesful model for the evolution
of AGN at radio ([56], [169], [198]), optical ([27], [26], [106], [107], [108],
[205]) and X-ray ([51], [25], [118], [171]) wavelengths, although deviations
from this model have been seen at high redshifts and overproductions of
the X-ray background have been reported ([157], [224]).
• Pure Density Evolution (PDE): In PDE, the number of AGN per unit comoving
volume is assumed to evolve while the distribution of luminosities remains
constant. This model has failed to fit the current observations well
since it clearly overpredicts the measured cosmic X-ray background (e.g.
[99], [157], [224]) and therefore has been ruled out as a possible description
of the evolution of AGN.
• Luminosity-dependent Density Evolution (LDDE): In LDDE, both the num-
22

CHAPTER 1: INTRODUCTION
ber of AGN per unit comoving volume and the luminosity of each AGN
are assumed to evolve. This model, although more complicated than the
previous ones, it is now widely accepted since it reproduces well the observations
in both optical (e.g. [236]) and X-ray ([157], [104], [224], [130],
[211]) wavelengths.
1.7 Modern instrumentation in X-ray astronomy
The sources that dominate the CXB are faint, with typical fluxes of ∼10 −14 erg
cm −2 s −1 (see sections 1.3 and 3.4) and therefore large area detectors with very
high efficiency are required to study them. The rocket that first discovered the
X-ray background in 1962 carried a small detector, a Geiger counter, with very
low spectral resolution and no imaging capabilities (see section 1.2). The first
X-ray orbiting observatories used mechanical collimators to limit the field of
view covered by the detectors. This provided rough angular resolutions (of
the order of several degrees) which significantly limited the sensitivity of the
observations because of the confusion of the faintest sources.
Since then there have been major advances in instrumentation in X-ray astronomy,
the most important one being the introduction fo X-ray imaging optics
(the Einstein observatory in the 1970s).
Proportional counter detectors have been extensively used in several missions
for many decades, until the advent of high resolution solid state detectors (charge
coupled devices, CCDs), which were first used in the Japanese ASCA observatory
and were able to produce X-ray images with photons of up to 10 keV. The
spectral resolution of CCD detectors is one order of magnitude better to that of
proportional counters and are now used in all modern X-ray observatories.
1.7.1 X-ray telescopes
Focusing X-ray photons is an extremely difficult task. Unlike standard reflecting
telescopes, in which photons are directed almost perpendicular to the surface
of the reflector and then collected in the focal plane, X-ray telescopes cannot
make use of normal incidence as it leads to the absorption and scattering of
X-ray photons due to their high energy.
X-ray photons can only be focused in grazing incidence at very small angles.
23

CHAPTER 1: INTRODUCTION
The reflection angle is ∼1 degree for ∼1 keV X-rays and standard reflection
metals such as Au, Pt, Ir or Ni.
The German physicist Hans Wolter showed in 1952 that a system formed by
two reflectors (a paraboloid followed by a co-axial hyperboloid) can focus X-
rays. This system, known as Wolter-1 configuration, is frequently used in X-ray
astronomy (for instance, in the XMM-Newton X-ray telescopes). The light path
in a Wolter-1 configuration is shown in Figure 1.5.
The critical angle for reflection depends inversely on the energy of the incident
photons (reflection is more difficult at higher energies) and increases with the
density of free electrons in the reflecting material. Shorter focal length telescopes
focus mostly soft X-rays, while to focus harder photons longer focal
lengths (which implies longer telescopes) are needed. The effective area of the
telescope is therefore a function of the energy of the incident photons but also
of the off-axis angle (distance to the centre of the optical system or optical axis):
the fraction os incident photons reaching the focal plane decreases with the offaxis
angle. This effect is known as vignetting and it is observed as a decline of
the effective area of the X-ray telescopes at larger off-axis angles.
In grazing incidence the effective area of the mirror seen by an incoming photon
is very small, and therefore a large number of mirrors are usually nested in
order to increase significantly the collecting area of the telescope.
1.7.2 Imaging X-ray detectors
A variety of non-dispersive detectors have been used in X-ray astronomy, including
Position Sensitive Proportional Counters (PSPC), Micro Channel Plates
(MCP), Micro-calorimeters, or Charge Coupled Devices (CCD). PSPCs, for instance,
were the detectors onboard the Einstein and ROSAT observatories.
CCDs were used in the ASCA observatory and are also onboard of the Chandra
and XMM-Newton observatories. CCDs are imaging arrays of pixels (charge
collecting units or capacitors) with low noise and good energy resolution. When
a X-ray photon hits a capacitor, the semiconductor material of the CCD produces
multiple electron-hole pairs via the photoelectric effect. Optical photons
can only release a few electron-hole pairs and hence need to be accumulated
in order to collect enough signal through longer exposures. However, a X-ray
photon is able to produce hundreds of thousands of pairs which, in principle,
24

CHAPTER 1: INTRODUCTION
Figure 1.5 Light path on a Wolter-1 X-ray telescope (image credit: ESA).
make possible to measure the energy of each photon individually. CCD detectors
work as photon counting devices in X-ray astronomy.
The charge carried by the cloud of electrons is proportional to the energy of the
incident photon. To read the signal, the charge is transferred along the surface
of the semiconductor from the capacitor hit by the X-ray photon to neighbouring
capacitors. The last capacitor in the array will transfer then its charge to an
amplifier that converts the charge into voltage, that can be recorded, making
possible to recover the position and energy of the incident photon.
The charge collected in a CCD is recovered in successive read-outs that limit
the time resolution of the observations to a few seconds. CCDs can be operated
in different observing modes, although to improve the time resolution of the
observatories it is necessary to reduce the read-out time of the CCD which is
only achievable by reducing the read-out area and hence the field of view. The
next generation of CCDs for X-ray astronomy will be based on Active Pixel
Sensors in which each pixel is read individually.
25

CHAPTER 1: INTRODUCTION
Figure 1.6 Payload of the XMM-Newton observatory (image credit: ESA).
26

CHAPTER 1: INTRODUCTION
1.7.3 The XMM-Newton observatory
Most of the data used in this thesis have been obtained with the X-ray detectors
onboard the XMM-Newton observatory 3 , which was the second cornerstone of
the Horizon 2000 science programme of the European Space Agency (ESA). It
was launched on the 10th of December of 1999 on an Ariane 504 rocket from
Kourou, French Guyana. The satellite is in a 48-hour elliptical orbit allowing
continuous monitoring of selected targets up to about 40 hours.
XMM-Newton carries six science instruments. Three co-aligned X-ray telescopes
(each with 58 nested Wolter-1 type mirrors) focus X-rays into the CCD cameras
at the focal plane ([117], see Figure 1.6). The telescopes have the largest effective
area achieved so far, 3 to 10 times higher at 1 and 7 keV that that of Chandra, respectively.
The light path of the X-ray telescopes aboard XMM-Newton is shown
in Figure 1.7.
The maximum effective area of the XMM-Newton mirrors is 0.15 m 2 at 1 keV
and 0.05 m 2 at 5 keV. Each telescope has its own Point Spread Function (PSF,
the distribution of light of a point-like source in the focal plane), which varies
little with energy in the 0.1-4 keV range but has a strong dependence on the
off-axis angle.
On the focal plane of each telescope there is an European Photon Imaging Camera
(EPIC) instrument. XMM-Newton carries two different technologies of CCD
detectors: two of the cameras contain 7 individual MOS (Metal-Oxide Semiconductor)
front-illuminated CCD arrays (600 × 600 pixel each, [222]) referred
to as MOS1 and MOS2 cameras, respectively, while the last detector contains
12 pn (p-n junction) back-illuminated CCDs (64 × 200 pixel each, [216]) and is
referred to as pn camera, which was specially developed for XMM-Newton.
The EPIC cameras can perform imaging over a 30 arcmin diameter field of view
(2.5 times that of Chandra), and are sensitive to photons with energies from 0.1
to 15 keV providing moderate energy resolution (E/∆E ∼ 20 − 50). Because
of the small sizes of the pixels in the EPIC cameras (1.1 and 4.1 arcsec in the
MOS and pn, respectively), the angular resolution is determined by the PSF of
their mirror modules. The FWHM of the PSF is 6 arcsec, allowing to obtain
X-ray source positions with accuracies of ∼1-3 arcsec, while Chandra achieves a
positional accuracy of 0.3-1 arcsec. X-ray source confusion in XMM-Newton is
3 ¢¡£¡¥¤§¦©¨¨1¥¢2¥354¡ 27

CHAPTER 1: INTRODUCTION
Figure 1.7 Lightpath of the XMM-Newton telescopes (image credit: ESA). Left panel:
Without grating assembly. Right panel: With grating assembly.
not significant for observations with exposures ≤100-200 ks.
The EPIC cameras can be operated in various observing modes ([122], [123],
[128]). The EPIC CCDs are sensitive to X-rays but also to IR, visible and UV
photons. In order to reduce the contamination of the observations each EPIC
camera is equipped with three aluminized optical blocking systems with different
thicknesses (named thick, medium and thin filters). It is also possible to
perform observations in an open position (with no filter at all) or in a closed
position (only for internal calibration purposes).
The telescopes with MOS cameras in their focal planes have a grating assembly
(RGA, [54]) that diverts part (∼40%) of the incoming photons to a Reflection
Grating Spectrometer (RGS). About 44% of the incoming light reaches the MOS
cameras, while the remaining ∼16% is absorbed by the supporting structures
of the RGA. The RGS instruments perform high resolution dispersive spectroscopy
(resolving power E/∆E ∼ 200 − 800) of bright sources in the soft
energy band.
1.8 Aims of the thesis
In the previous sections we have briefly summarized our current understanding
of the nature of the cosmic X-ray background and AGN emission. We have
tried to highlight the importance of studying the X-ray emission of AGN since
it is originated in the innermost regions of these objects, close the central supermassive
black hole. We know that AGN dominate the overall CXB emission
and that they are detectable at very large distances. Hence, X-ray surveys of
28

CHAPTER 1: INTRODUCTION
AGN are essential to investigate the large-scale structure of the Universe and
to provide an accurate look at the evolution of the central engine that powers
these sources along cosmic time.
The aim of the work presented in this thesis is to give insight to the evolutionary
and clustering properties of a medium-deep sample of AGN, and to evaluate
the importance of the contribution of this population of AGN to the cosmic
X-ray background.
The medium-flux X-ray surveys presented in this work in Chapter 2 are especially
suitable to estimate the intensity of the CXB. Since its origin seems to
be the integrated emission of discrete individual sources we can estimate the
resolved fraction of the CXB integrating the sky density of the sources in our
samples over their flux range. However, the contribution from sources brighter
and fainter than ours, although small, is not negligible. We could obtain a
much more accurate estimation spanning a broader flux range, but to do that
we would need to know the sky density distribution of sources at those fluxes
in detail. The sky density or source counts are dependent on the cosmological
properties of the sources involved and can be described by an empirical model
(which is a function of the X-ray flux). Adding wide-area bright surveys and
deep faint surveys to our medium sample would allow us to constrain the parameters
of such model with unprecedent accuracy and therefore determine the
contribution of these sources to the total intensity of the CXB. Such analysis is
presented in Chapter 3.
Similarly, this kind of surveys (medium-deep moderately wide area) are potentially
useful to explore the underlying cosmic structure of the X-ray Universe
since they achieve both high angular density and width. If there exists a cosmological
structure in the X-ray sky, we would be able to detect it either through
the cosmic variance in the number of sources per field or the distribution of
the angular separations between pairs of sources. This can be estimated using
a variety of mathematical tools that rely on Poissonian statistics and the correlation
functions introduced in section 1.4. This subject will be investigated in
Chapter 4.
As we have seen in the previous sections, the origin of the X-ray emission of
AGN is located in the proximity of the accreting central black hole. Changes in
the accretion rate of matter onto the black hole would therefore lead to changes
in the X-ray luminosity of the object. Since AGN can be detected through enor-
29

CHAPTER 1: INTRODUCTION
mous distances, we can measure their intrinsic luminosity at different epochs of
the Universe and hence estimate how it is related to the accretion rate of matter
at those epochs. It is believed that the evolution observed in the luminosity of
AGN is directly linked to intrinsic changes in the matter inflow, which tell us
how the supermassive black hole grew and fed in the early stages of the Universe.
However, according to the unified model of AGN we have described
before, Type-2 AGN are more likely to be observed at high energies (> 2 keV)
since only hard X-rays are capable of passing through the molecular torus that
enshrouds the central engine of the AGN. Hence, this absorption has to be taken
into account in order to obtain unbiased intrinsic luminosities. In Chapter 5 we
will address this subject as well as the possible evolutionary models for AGN.
Specifically, the issues we have investigated in this thesis are:
1. To study the flux distribution of sources detected in soft and hard X-rays at
medium fluxes. This distribution depends on the cosmological properties
of the sources and can be described by an empirical model. We have used
this model to estimate the contribution of the sources to the total CXB
intensity. At what fluxes do the dominant sources of the CXB contribute
most?
2. To explore the underlying cosmic structure of the X-ray Universe. It is
known that local galaxies (redshifts up to ∼0.2) cluster forming large-scale
structures (filaments and voids). AGN are at cosmological distances and
hence they will allow us to investigate whether these structures were already
present in the early Universe and to quantify the strength of the
clustering.
3. To study the behaviour of the fraction of absorbed AGN at different X-
ray luminosities and redshifts and to model the intrinsic absorption of the
AGN as a function of these parameters. Accordingly to the unified model,
it is more probable to detect Type-2 AGN in hard X-rays since only this
radiation can pass through the molecular torus around the central black
hole. Does the fraction of obscured AGN depend on the luminosity? Were
there more absorbed AGN in the early Universe?
4. To investigate the evolution of AGN at different epochs of the Universe.
Were they more luminous in the past? Has the density of AGN changed
with time? There is evidence of this, so we intend to quantify better these
30

CHAPTER 1: INTRODUCTION
subjects making use of the available absorption information. We can convolve
an absorption model with evolutionary models in order to obtain
intrinsic results for the sources. Has the accretion rate of matter changed
with time? At what epoch of the Universe were AGN fully formed?
We have addressed these points throughout this thesis and the results are discussed
and summarized in Chapter 6.
31

Chapter 2
AGN surveys with XMM-Newton
As discussed in Chapter 1, X-ray source populations studies are essential to understand
their X-ray emission and cosmic evolution, especially those related to
AGN. However, in order to have good enough statistics, these studies need to
collect a moderately large number of objects. Moreover, it is difficult (if not impossible)
for a single survey to gather simultaneously a wide sky coverage and
high sensitivity to detect very faint sources. It is hence imperative to combine
wide field shallow surveys with deep pencil-beam surveys so as to carry out
accurate population and evolutionary studies such as those conducted in this
thesis.
In this chapter we will discuss the X-ray extragalactic surveys that have been
used throughout this thesis. The surveys that compose the core of this work
are the AXIS survey ([13], [38], see section 2.1) and the XMS survey ([12], see
section 2.2). The project involving the construction of both surveys and the
development of the tools needed for that purpose has been led by the X-ray
Group at the Instituto de Física de Cantabria 1 . The author of this thesis has
been actively involved in the development of these surveys by participating in
observation runs and reducing optical and X-ray data.
AXIS and XMS are medium-depth samples, which means that the sources inside
of them have the bulk of their X-ray emission at medium fluxes. The dominant
population at these fluxes are AGN, whose clustering and evolutionary
properties are going to be investigated in this thesis as they are critical issues to
understand the accretion history of Universe across cosmic time.
Important as they are, the AXIS and XMS samples alone cannot fulfill the cov-
1 ¢¡£¡¥¤§¦©¨¨64 +7389¥! 4+34§¢¥¨ ∼ £:¢¨ 33

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
erage and depth requirements described above to conduct this work. We have
combined them with a variety of surveys (some of them deeper, other shallower)
in all energy bands under study. The properties of these samples are described
in section 2.3 and they were chosen so they were complementary to
AXIS and XMS in order to obtain results of unprecedent accuracy in the population
(see Chapter 3) and evolutionary (see Chapter 5) studies carried out in
this thesis.
2.1 The AXIS survey
2.1.1 Introduction and field selection
Thanks to its large collecting area and sensitivity, in each XMM-Newton pointing
∼30-150 serendipitous sources are detected, most of them being entirely
new detections. In 1996, three years before the launch of XMM-Newton, the
XMM-Newton Survey Science Centre (SSC) 2 was appointed by ESA to develop
the software analysis system, the pipelines to process all the XMM-Newton data
and the scientific exploitation of the XMM-Newton’s serendipitous sky surveys.
The SSC is a consortium of ten european institutions which has, among other responsabilities,
the task of following-up and identifying the XMM-Newton serendipitous
sources (XID programme, [234]). The XID programme has two components:
• Core programme: Its aim is to obtain the identifications from a well-defined
sample of X-ray sources. This strategy involves a high galactic latitude and
a low galactic latitud samples. The high latitude sample consists of three
large enough subsamples of sources with fluxes ≥ 10 −13 erg cm −2 s −1
(bright sample), ≥ 10 −14 erg cm −2 s −1 (medium sample), and ≥ 10 −15 erg
cm −2 s −1 (faint sample).
• Imaging programme: Deep optical and infrared imaging of a larger fraction
of objects in order to obtain optical magnitudes and colors necessary for
statistical identifications of the sources.
AXIS (An XMM-Newton International Survey, [13], [38]) is a medium X-ray survey
that constitutes the backbone of the SSC XID programme by providing es-
2 ¢¡£¡¥¤§¦©¨¨£¢¡£©£! " 34

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
sential resources for the exploitation of the XMM-Newton serendipitous survey.
In total, 36 XMM-Newton observations were selected for optical follow-up of
X-ray sources within the AXIS programme. The selected fields (listed in Table
2.1) had high galactic latitude (|b| > 20 ◦ ) to avoid contamination coming
from Galactic sources. They had total exposure times above 15 ks and bright
or extended targets were excluded, except for the A1837 and A399 fields. Some
of the fields ended up with exposure times below 15 ks after discarding observation
intervals with high background rates, and others were added to expand
the solid angle for bright X-ray sources. All of them have been used for the
study of the source counts (see Chapter 3) and for cosmic variance and angular
clustering analysis (two fields were removed in this latter case: HD111812 and
HD117555, see section 4.3 for details).
Of the original 36 fields, 27 were selected for optical follow-up of X-ray sources
at medium fluxes. Two of them (A2690 and MS2137) were excluded later from
the identification programme because of their low Declination, which prevented
them from being observed from the Calar Alto Observatory (Spain) 3 . The remaining
25 fields constitute the XMS sample ([12], see section 2.2).
2.1.2 Data processing and source selection
The Observation Data Files (ODF) of the data used in this thesis were processed
in the SSC Pipeline Processing Facility at the University of Leicester (UK), using
the same Science Analysis System (SAS, [71]) used for the processing of the
1XMM catalogue 4 , except for the field Mkn205 which was processed with the
slightly different SAS version 5.3.3. The field PHL1092 was never reprocessed
originally and a set of data from the XMM-Newton Science Archive reprocessed
with SAS version 5.4.0 was used for this work. The difference between the SAS
versions used in the field Mkn205 and the rest of the fields was the possibility
of including sources with negative count rates while using the source detection
task (;7=7?§;2@1;BAC@
) in the latter version. This was allowed to avoid a bias in the
total count rates of sources that were undetected in one or more energy bands.
However, since negative count rates do not have physical meaning and can
¢¡£¡¥¤§¦©¨¨0 9
3
4 The First XMM-Newton Serendipitous Source Catalogue (1XMM) was released in 2003 and contains
source detections from 585 XMM Newton EPIC observations made between March 1 st 2000 and May
5 th 2002. It comprises over 28000 individual X-ray sources with a median 0.5-12 keV flux of ∼ 3 × 10 −14 erg
cm −2 s −1 .
35

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
cause numerical problems in certain cases, negative count rates for this work
have all been set to zero as well as the detection likelihood of the source.
The SAS products provide X-ray source lists (created ;D

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
(sizes and positions are also listed in Table 2.1) as well as rectangular regions
around Out Of Time (OOT) regions 5 .
Two sets of fields were partially overlapping: G133-69pos_2 and G133-69pos_1
on one hand and SDS-1b, SDS-2 and SDS-3 on the other. The portion of the
second field (and also the third in the case of the latter set) overlapping with the
first field was masked so as to not having in the final lists duplicated sources
and an overestimation of the total sky coverage of the survey.
In the analysis carried out in this thesis we have used the following energy
bands:
• Soft: 0.5-2 keV
• Hard: 2-10 keV
• XID: 0.5-4.5 keV
• Ultrahard: 4.5-7.5 keV
The Soft, XID and Ultrahard bands are identical to the standard SAS (before
version 6.9) bands 2, 9 and 4, respectively 6 . The hard band is a combination of
the standard SAS (before version 6.9) bands 3, 4 and 5, which corresponds to
counts in the range 0.5-12 keV. However, all hard band fluxes in this work have
been calculated in the range 2-10 keV.
The detection likelihood in the hard band (L 345 ) was obtained from the detection
likelihoods in bands 3, 4 and 5 (L 3 , L 4 and L 5 , respectively) using the following
expression:
L 345 = −log(1 − Q( 5 2 , L′ 3 + L′ 4 + L′ 5 )) (2.1.1)
where L
i ′ is obtained from: L i = −log(1 − Q( 3 2 , L′ i )) (2.1.2)
and Q(a, x) is the incomplete gamma function (see ;7=7?§;2@1;BAC@
documentation).
5 Bright band that extends from the target to the pn chip reading edge, due to the photons arriving at
the detector while it was being read out.
6 These bands correspond to SAS version 6.9 or earlier. New energy bands were defined during the
2XMM catalogue processing: former band 2 was splitted into two bands (0.5-1 and 1-2 keV), while former
bands 4 and 5 were merged into a single band (4.5-12 keV).
37

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
detection likeli-
In total, there were 2560 accepted sources with ;D=7?§;@B;BAC@
an
hood ≥10 (the default value) in at least one band.
The final selection of sources in each band was done using their detection likelihood
and the corresponding sensitivity map (see Appendix A for details) at
their sky position. We have chosen a detection confidence limit of 5-σ which
corresponds to L = 15 in the band under consideration. In addition, we have
also imposed that the source has a count rate equal or larger than the value of
the sensitivity map at that sky position in order to ensure that the detection is
reliable. This way, less than 5% of the sources in the soft band, ∼10% of the
sources in the XID and ultrahard bands, and ∼20% of the sources in the hard
band with L ≥ 15 were excluded.
The total of distinct sources that fulfill all the criteria mentioned above in at least
one band is 1433. The number of sources in each band are listed in Table 2.2.
For the analysis done in this thesis we have used only sources detected in the
corresponfing bands, unless otherwise stated. It has to be noted, however, that
once a source has been detected in at least one band it can be considered a real
source and therefore its counts in other bands can be used, even if the source
has a count rate smaller than the detection threshold in those bands.
In order to estimate the number of spurious detections in the survey, it is firstly
needed to calculate the number of independent source detection boxes. The
;D=2?§;2@B;BAD@ task uses an input list ;2KHG7L?§;@B;BAC@ from which is a sliding-box algorithm
using a square 5 × 5 pixels detection cell. Each pixel side has 4 arcsec, so
the individual detection cell has an area of 5 × 5 × (4”) 2 =400 arcsec 2 . Since the
total area of the survey is ∼4.8 deg 2 (see section 3.2.1), or about 155520 independent
detection cells, and that the probability of a false detection at the 5-σ
level is 0.000057, the number of spurious detections is 9 in each detection band.
This is less than 1% in the soft and XID bands, about 2% in the hard band, and
almost 10% in the ultrahard band.
38

39
Table 2.1: Fields of the AXIS survey.
Target name OBS_ID R.A. Dec Texp Filter N H,Gal R.A. Dec. R OOT R.A. Dec. R’
(J2000) (J2000) (s) (10 20 cm −2 ) (J2000) (J2000) (”) (”) (J2000) (J2000) (”)
A2690 0125310101 00:00:30.30 −25:07:30.00 21586.7 Medium 1.84 00:00:21.2 −25:08:12.18 20 0 - - 0
Cl0016+1609 a 0111000101 00:18:33.00 +16:26:18.00 29149.3 Medium 4.07 00:18:33.2 +16:26:07.97 148 0 - - 0
G133-69pos_2 a 0112650501 01:04:00.00 −06:42:00.00 18080.0 Thin 5.19 - - 0 0 - - 0
G133-69Pos_1 a 0112650401 01:04:24.00 −06:24:00.00 20000.0 Thin 5.20 - - 0 0 - - 0
PHL1092 0110890501 01:39:56.00 +06:19:21.00 16180.0 Medium 4.12 01:39:55.8 +06:19:19.67 88 40 01:40:09.0 +06:23:27.67 68
SDS-1b a,d 0112371001 02:18:00.00 −05:00:00.00 43040.0 Thin 2.47 - - 0 0 - - 0
SDS-3 a,d 0112371501 02:18:48.00 −04:39:00.00 14927.9 Thin 2.54 - - 0 0 - - 0
SDS-2 a,d 0112370301 02:19:36.00 −05:00:00.00 40673.0 Thin 2.54 - - 0 0 - - 0
A399 a,c 0112260201 02:58:25.00 +13:18:00.00 14298.7 Thin 11.10 02:57:50.2 +13:03:20.88 272 0 - - 0
Mkn3 a,c 0111220201 06:15:36.30 +71:02:04.90 44506.1 Medium 8.82 06:15:36.6 +71:02:15.95 76 32 - - 0
MS0737.9+7441 a,e 0123100201 07:44:04.50 +74:33:49.50 20209.3 Thin 3.51 07:44:04.3 +74:33:54.56 120 40 - - 0
S5 0836+71 a 0112620101 08:41:24.00 +70:53:40.70 25057.3 Medium 2.98 08:41:24.3 +70:53:41.06 160 52 - - 0
PG0844+349 0103660201 08:47:42.30 +34:45:04.90 9783.5 Medium 3.28 08:47:42.9 +34:45:03.27 200 40 - - 0
Cl0939+4713 a 0106460101 09:43:00.10 +46:59:29.90 43690.0 Thin 1.24 09:43:01.8 +46:59:44.37 160 0 - - 0
B21028+31 a 0102040301 10:30:59.10 +31:02:56.00 23236.0 Thin 1.94 10:30:59.3 +31:02:56.08 140 72 - - 0
B21128+31 a 0102040201 11:31:09.40 +31:14:07.00 13799.8 Thin 2.00 11:31:09.6 +31:14:06.02 140 44 - - 0
Mkn205 a,e 0124110101 12:21:44.00 +75:18:37.00 17199.6 Medium 3.02 12:21:43.8 +75:18:39.08 140 36 - - 0
MS1229.2+6430 a,e 0124900101 12:31:32.32 +64:14:21.00 28700.0 Thin 1.98 12:31:31.2 +64:14:18.06 140 40 - - 0
HD111812 b 0008220201 12:50:42.56 +27:26:07.70 37338.8 Thick 0.90 12:51:42.6 +27:32:23.27 168 40 - - 0
NGC4968 0002940101 13:07:06.10 −23:40:43.00 4898.7 Medium 9.14 13:07:06.3 −23:40:33.23 40 0 - - 0
NGC5044 0037950101 13:15:24.10 −16:23:06.00 20030.0 Medium 5.03 13:15:24.2 −16:23:08.53 340 0 - - 0
IC883 0093640401 13:20:35.51 +34:08:20.50 15849.4 Medium 0.99 13:20:35.4 +34:08:21.37 48 0 13:20:54.4 +33:55:17.26 104
HD117555 a,b 0100240201 13:30:47.10 +24:13:58.00 33225.4 Medium 1.16 13:30:47.8 +24:13:51.07 160 40 - - 0
F278 0061940101 13:31:52.37 +11:16:48.70 4648.3 Thin 1.93 13:31:52.4 +11:16:43.88 48 0 - - 0
A1837 a 0109910101 14:01:34.68 −11:07:37.20 45361.3 Thin 4.38 14:01:36.5 −11:07:43.14 440 0 - - 0
UZLib a 0100240801 15:32:23.00 −08:32:05.00 23391.2 Medium 8.97 15:32:23.4 −08:32:05.32 140 40 - - 0
FieldVI 0067340601 16:07:13.50 +08:04:42.00 9634.0 Medium 4.00 - - 0 0 - - 0
PKS2126-15 a 0103060101 21:29:12.20 −15:38:41.00 16150.0 Medium 5.00 21:29:12.1 −15:38:40.44 120 40 - - 0
PKS2135-14 a, f 0092850201 21:37:45.45 −14:32:55.40 28484.3 Medium 4.70 21:37:45.1 −14:32:55.22 120 44 - - 0
CHAPTER 2: AGN SURVEYS WITH XMM-Newton

R
R
OQP
ONM
40
Table 2.1: Continued.
Target name OBS_ID R.A. Dec Texp Filter N H,Gal R.A. Dec. R OOT R.A. Dec. R’
(J2000) (J2000) (s) (10 20 cm −2 ) (J2000) (J2000) (”) (”) (J2000) (J2000) (”)
MS2137.3-2353 0008830101 21:40:15.00 −23:39:41.00 9880.0 Thin 3.50 21:40:15.1 −23:39:39.32 140 48 - - 0
PB5062 a 0012440301 22:05:09.90 −01:55:18.10 28340.9 Thin 6.17 22:05:10.3 −01:55:20.38 140 40 - - 0
LBQS2212-1759 a 0106660101 22:15:31.67 −17:44:05.00 90892.5 Thin 2.39 - - 0 0 - - 0
PHL5200 a 0100440101 22:28:30.40 −05:18:55.00 43278.5 Thick 5.26 22:28:30.4 −05:18:53.12 16 0 - - 0
IRAS22491-1808 a 0081340901 22:51:49.49 −17:52:23.20 19867.2 Medium 2.71 22:51:49.4 −17:52:25.02 32 0 - - 0
EQPeg a 0112880301 23:31:50.00 +19:56:17.00 12200.0 Thick 4.25 23:31:52.7 +19:56:18.46 160 48 - - 0
HD223460 0100241001 23:49:41.00 +36:25:33.00 6699.0 Thick 8.25 23:49:40.8 +36:25:32.56 172 40 23:50:02.0 +36:25:36.36 116
Columns: (1) Target name, (2) XMM-Newton OBS_ID number, (3)(4) Right Ascension and Declination of the field centre, (5)(6) Clean exposure time and filter used in the pn camera, (7) Galactic
column density in the direction of the field ([55]),(8)(9)(10) Centre and radius of the circular exclusion area for the target, where applicable, (11) Width of the OOT exclusion area, (12)(13)(14)
Centre and radius of an additional exclusion area around bright/extended sources.
a Fields belonging to the XMS
b Fields excluded from the angular correlation studies
c
astrometric correction failed in these fields
d In common with SXDS ([227])
e In common with HELLAS2XMM ([10])
CHAPTER 2: AGN SURVEYS WITH XMM-Newton
f Same area as one ChaMP field ([124])

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
2.1.3 X-ray properties of the sources
We have fitted the count rates of the sources in several bands to those expected
from a power-law spectrum in order to study their spectral characteristics. The
model has a slope Γ and Galactic Hydrogen column density N H obtained from
21 cm radio measurements ([55], see Table 2.1). Obviously not all the sources
have their spectrum well represented by a power law (for instance, stars and
galaxy clusters show thermal spectra) but for the purpose of calculating fluxes
in the same bands as those in which the fit is performed this is an accurate and
simple model.
We have calculated the expected count rates for different values of Γ ranging
from -10 to 10 in steps of 0.5, linearly interpolating for intermediate values,
using LSIF1;1A
([7]) with the on-axis redistribution matrix files and effective areas
for each field generated by the SAS TJUV§;7W task . The count rates obtained from
are already corrected from vignetting, so the effective areas were
generated disabling the vignetting and PSF corrections in TJ0UV§;7W .
;D=2?§;2@B;BAD@
The fluxes obtained for bands 2 to 5 (in the case of band 5 the flux was calculated
in the range 7.5-10 keV) were also calculated for the same Γ values but
setting N H to zero, i.e. they were calculated ’before the atmosphere’. We have
also checked that the chosen step size in Γ does not significatively affect the
calculations by repeating the spectral fits in a single field with a step of 0.001,
finding that the differences in the slopes were smaller than the uncertainties.
Spectral fits were performed in bands 2 and 3 for the soft and XID fluxes, and
in bands 3, 4 and 5 for the hard and ultrahard fluxes. The average count rates
of our sources in the XID and hard bands were 0.0095 and 0.0032, respectively,
which give (for a typical exposure time of 15 ks) an average of more than 10
counts per bin thus ensuring the validity of Gaussian statistics. The best fit
Γ and flux were calculated by minimising the χ 2 between the observed and
expected count rates. The minimisation was done in Γ, setting the flux from the
normalisation that minimised the χ 2 in the corresponding band. 1-σ error bars
for Γ and flux were obtained from the values which produced ∆χ 2 = 1 from the
minimum. In most cases these error bars were assymetric but we have used a
symetric error bar obtained from the average of the upper and lower error bars
for the weighted Γ and the source counts study (see section 3). In some cases the
fitted slopes are very steep (|Γ| ∼ 10): this corresponds to sources with positive
count rates in only one of the fitted bands, which forces the power law to the
41

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
steepest allowed slope.
In Table 2.2 are shown the weighted average Γ of the detected sources in each of
the fitted bands as well as the number of sources used in the averages excluding
those sources with |Γ| > 9 (typically

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
Table 2.2 Number of sources selected in different bands N, weighted average slopes
〈Γ〉 and errors (taking into account both the error bars in the individual Γ and the
dispersion around the mean), and number of observed sources used in the average
N ave . The soft, hard, XID and ultra-hard bands are as defined in the text. “Soft and
hard” refers to sources selected simultaneously in the soft and hard bands, “Only soft”
refers to sources selected in the soft band but not in the hard band, and “Only hard”
refers to sources selected in the hard band and not in the soft band.
0.5-2 keV 2-10 keV
Selection N N ave 〈Γ〉 N ave 〈Γ〉
Soft 1267 1239 1.811 ± 0.015 1145 1.53 ± 0.02
Hard 397 397 1.76 ± 0.03 394 1.55 ± 0.03
XID 1359 1335 1.773 ± 0.016 1244 1.47 ± 0.02
Ultrahard 91 91 1.80 ± 0.06 91 1.50 ± 0.07
Soft and hard 345 345 1.79 ± 0.03 342 1.67 ± 0.03
Only soft 922 894 1.878 ± 0.017 803 1.04 ± 0.04
Only hard 52 52 −0.29 ± 0.08 52 0.53 ± 0.12
The identification completeness of the sample in the different energy bands is
listed in Table 2.5 and it largely exceeds 90% in the soft and XID bands, and is
around 85% in the hard and ultrahard bands.
2.2.2 Imaging and selection of optical counterparts
Target fields were mainly observed with the Wide Field Camera (WFC) on the
2.5 m Isaac Newton Telescope (INT) since this instrument practically covers all
the field of view of EPIC if it is optimally centered. These observations were
awarded via the AXIS programme and other programmes devoted to image
the XMM-Newton target fields in the optical. All the XMS target fields were
imaged using the Sloan Digital Sky Survey (SDSS) 7 filters g ′ , r ′ and i ′ .
Exposure times were adjusted to be deep enough in order to have an optical
counterpart for most of the X-ray sources in the r ′ and i ′ filters. The chosen
times were 600 seconds for the g ′ and r ′ filters, and 1200 seconds for the i ′ filter,
which produced an image with a limiting magnitude down to r ′ ∼ 23 − 24 for
7 ¢¡£¡¥¤§¦©¨¨0X92©%& 43

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
Table 2.3 Definition of the XMS samples: the first column is the sample energy band,
the second is the flux limit, the third is the number of sources in the sample, the next
four columns give the number of sources belonging to any pair of two samples, and
the last column is the number of sources only present in the corresponding sample.
Overlap
Sample Flux limit N Soft Hard XID UH Only
(10 −14 cgs)
Soft 1.5 210 210 111 209 50 1
Hard 3.3 159 111 159 128 62 20
XID 2.0 284 209 128 284 57 56
Ultrahard 0.7 a 70 50 62 57 70 2
a This band is not artificially flux limited and this value corresponds
to the flux of the faintest detected source.
a seeing of ∼1-1.5 ′′ ([13]). Under bright moon observing conditions, the times
were doubled and only the reddest filters were used. The WFC images were
reduced using the standard reduction pipeline (see the Cambridge Astronomy
Survey Unit -CASU- site 8 ).
The photometric calibration of the WFC images was also done in the standard
way, observing photometric standard stars at different airmasses during the
same nights in which the XMM-Newton target fields were imaged, and fitting an
extinction curve for each optical band afterwards. In a number of target fields
and for some of the bands the scattering in the extinction curve showed that
the observations were carried out under non-photometric conditions. In those
cases, the calibration was done on one band, typically r ′ , and then colour corrections
were applied to propagate the improved photometry to other bands. To
do that, two sets of complementary photometrically calibrated data were used:
the SDSS-Data Release 5, which was used on 6 XMM-Newton fields, and the
Carlsberg Meridian Catalogue (CMC) 9 astrometric survey in the r ′ band, which
was applied to 19 fields. Details on the calibration procedure can be found in
[12].
The astrometric calibration of the WFC was performed using the CASU pro-
8 8¢5 ¢
∼ "#¨ ¢¡£¡¥¤§¦©¨¨0¡¥1¢2Y
9 ¢¡£¡¥¤§¦©¨¨¥£95 +36¢¡¥5B¢2! £"+¨¥5¨ 44

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
cedures. The astrometric reference for the optical images was the APM Catalogue
10 . The astrometry of the XMM-Newton source positions was registered
against the USNO-A2 source catalogue (same as AXIS, see section 2.1). Since
the optical astrometry refers to a different astrometric system, there could be
artificial mismatches. A test that was done measuring the USNO-APM shifts
in each XMM-Newton field by cross-correlating both source catalogues in the
corresponding region, showed that the shifts were systematic but less than the
statistical accuracy in the X-ray source positions (∼0.5 arcsec against 0.6 arcsec
averaged over the entire XMS sample, respectively).
2.2.3 Identification of XMS sources
The search for candidate counterpartes of the X-ray sources was done using the
r ′ WFC images, for which optical source lists were generated using the CASU
standard procedures. The optical counterparts were searched in these lists and
the candidates must be within 5-σ (90% confidence level) of the X-ray source position
or within 5 arcsec from that position (this last criterion was added to accommodate
any residual systematics in the astrometric calibration of the EPIC
X-ray images).
As a result of this, most sources in the XMS ended up having a single counterpart
with only a few exceptions. In the few cases in which the X-ray source
position fell in a gap between CCDs in the WFC images, the counterpart was
found considering other optical imaging data, mainly the USNO-A2 catalogue
or complementary imaging data. Also, for a number of sources (∼80), there
was more than a single candidate counterpart fulfilling the proximity criteria.
In most of these cases (∼90%), the closest candidate to the X-ray source position
was also the brightest and therefore that was the adopted counterpart.
Given the brightness (r ′

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
Table 2.4 Spectroscopic facilities used to identify XMS sources. The first column lists the
ground-based facility; the second, the instrument used, and the last four columns the
spectral range, slit width, spectral resolution and type of the instrument, respectively.
Telescope Instrument Spectral Slit width Spectral Comments
range (Å) (arcsec) resolution a (Å)
WHT/ORM WYFFOS 3900-7100 2.7 b 7 Fibre
WHT/ORM WYFFOS 3900-7100 1.6 b 6 Fibre
WHT/ORM ISIS 3500-8500 1.2-2.0 3.0-3.3 Long slit
TNG/ORM DOLORES 3500-8000 1.0-1.5 14-15 Long slit
NOT/ORM ALFOSC 4000-9000 1.0-1.5 4 Long slit
3.5m/CAHA MOSCA 3300-10000 1.0-1.7 24 Long slit
UT1/ESO FORS2 4400-10000 1.0 6-12 Long slit
a Measured from unsaturated arc lines; b Width of individual fibres
X-ray surveys such as the SXDS ([227]) or the HBS ([50]), which means that
the vast majority of the XMS sources required optical spectroscopy in order to
identify them.
Optical spectroscopy was conducted in a number of ground-based optical facilities
(see Table 2.4). Due to the low surface density of the XMS sources
(∼100 deg −2 ), the use of multiobject slit-mask spectrographs was not very efficient.
In some cases, a fibre spectrometer (WYFFOS) was used to carry out
the identifications, but only for sources brighter than r ′ ∼20.5 mag due to the
problems to substract the sky light that enters the fiber along with the light
coming from the target and, therefore, the strategy that best fitted the optical
magnitude distribution of the sample was long-slit spectroscopy. A number of
these instruments were used in a variety of ground-based telescopes with apertures
ranging from 2.5 m to 8.2 m (see Table 2.4). The spectra thus obtained are
reliable only for identification purposes based on broad/narrow emission lines
and absorption bands, but not for calculating line fluxes or line ratios. The identification
completenesses achieved in each band are listed in Table 2.5. It can be
seen that the high completitudes, in particular in the soft and XID bands, make
the XMS sample specially suitable for cosmic evolution works (see Chapter 5).
The identification breakdown of the XMS sample in several bands is summarised
in Table 2.6, and the different source types are based on those of [13]. Extra-
46

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
Table 2.5 Identification completeness of the XMS sample. The first column is the sample
energy band, the second column N is the total number of sources in that band, the third
column N id is the total number of espectroscopically identified sources, and the fourth
column is the fraction of identified sources.
Sample N N id Fraction (%)
Soft 210 202 96
Hard 159 134 84
XID 284 263 93
Ultrahard 70 60 86
galactic sources showing broad emission lines (velocity widths 1500 km s −1 )
are classified as Broad Line Active Galactic Nuclei (BLAGN, see section 1.5.4).
Those showing only narrow emission lines are termed Narrow Emission Line
Galaxy (NELG). Those with galaxy spectra without obvious emission lines are
plainly classified as Galaxy (Gal) although there are two exceptions: two sources
falling in this category were already catalogued as BL Lac objects and we have
thus mantained this classification, and if a qualitative inspection of the optical
images shows evidences of galaxy concentration, the source is classified as a
Galaxy Cluster (Clus). Finally, all X-ray sources with an stellar espectrum with
or without coronal activity are labeled as Star/AC.
This classification is functional but it has some limitations. For instance, in those
sources labeled as NELG no line diagnosis was carried out to check whether the
source hosts an AGN or not. This is due to the relatively broad range spanned
by these sources and the rather narrow wavelength coverage of the optical spectra
(in particular for the fibres) the number of lines detected is small and the
typical diagnostic lines drop out the spectrum with redshift. Moreover, the
quality of the spectrum is not good enough to detected very weak lines needed
for these diagnostics. In principle the sources classified here as NELG could be
a mixture of type-2 AGN and star-forming galaxies but, given their high X-ray
luminosities, we have concluded that most of them are indeed AGN-powered
sources.
Other limitation arise in the case of galaxy clusters. Only two sources were clas-
47

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
Table 2.6 Identification breakdown of the XMS sample. The first column is the type of
source (see text for the definitions), the next four columns are the number of sources in
each category for the Soft, XID, Hard and Ultrahard bands, respectively. In parenthesis
is the fraction of objects in each class with respect to the total of sources in that band.
Type Soft XID Hard Ultrahard
Total 210 284 159 70
BLAGN 149 (71%) 191 (67%) 83 (52%) 39 (56%)
NELG 27 (13%) 39 (14%) 35 (22%) 16 (23%)
Gal/Clus 9 (4%) 11 (4%) 11 (7%) 3 (4%)
Star/AC 15 (7%) 20 (7%) 3 (2%) 0 (0%)
BL Lac 2 (1%) 2 (1%) 2 (1%) 2 (3%)
Un-ID 8 (4%) 21 (7%) 25 (16%) 10 (14%)
sified as such and this low number is caused by a bias in the detection and classification
method. The detection method was designed for point-like sources
and therefore it could be missing a certain number of extended X-ray sources.
Furthermore, the presence of a cluster of galaxies could not be very obvious on
the optical images and the source might have been misclassified as galaxy with
or without emission lines.
Redshifts have been estimated by matching the most prominent features in
emission or absorption to characteristic line wavelengths displaced at different
redshifts. In some cases, template spectra for AGN and galaxies with a
range of spectroscopic classes were used to assist when no prominent features
were found in the spectra. Some examples of spectra and identifications of XMS
sources are shown in Figure 2.1.
2.3 Other surveys
In this section we will overview all the additional surveys we have made use of
throughout this work in order to complement AXIS (see Chapter 3) and XMS
(see Chapter 5).
48

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
GUIspec z=1.958
GUIspec z=0.238
Flux (cgs/Å)
2×10 −17 4×10 −17 6×10 −17
SiIV CIV
OIV
NIV]
[NIII]
CIII]
MgII
Flux (cgs/Å)
0 5×10 −17 10 −16 1.5×10 −16
[OII]
[OII]
H−edge
He
CaIIK
CaIIH
Hd
CHG
CHG
Hg
CHG [OIII]
Hb
[OIII]
[OIII]
MgI
MgI
MgI
HeI
NaI
NaI
Flux (cgs/Å)
0 2×10 −16 4×10 −16 6×10 −16
4000 5000 6000 7000 8000 9000
Wavelength (Å)
He CHG
CaIIK CHG Hg
CaIIHHd CHG
GUIspec z=0.301
4000 5000 6000 7000 8000
Wavelength (Å)
Hb
MgI
MgI
MgI
NaI
NaI
Flux (cgs/Å)
0 10 −15 2×10 −15 3×10 −15
4500 5000 5500 6000 6500 7000
Wavelength (Å)
He CHG
CaIIK CHG Hg
CaIIHdCHG
Hb
MgI
MgI
MgI
GUIspec z=0.0
NaI
NaI
4000 5000 6000 7000 8000
Wavelength (Å)
Ha
Figure 2.1 Examples of identified XMS sources. Top left: Broad Line AGN (BLAGN);
Top right: Narrow Emission Line Galaxy (NELG); Bottom left: Galaxy; Bottom right:
Star/Active Corona. Overplotted are the most prominent features detected in the spectra.
49

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
2.3.1 Chandra Deep Field
The deepest survey in the soft and hard bands so far is the Chandra Deep Field
North (CDF-N, [19]), obtained from a total exposure of 2 Ms in a Northern
hemisphere location. In a complementary effort in the Southern hemisphere,
the Chandra Deep Field South (CDF-S, [79], [194]) obtained a total exposure
time of 1 Ms. The source counts of both samples are widely discussed in [19].
There are a total of 442 soft and 313 hard sources in the CDF-N, and 282 soft
and 186 hard sources in the CDF-S, covering an area on the sky of ∼0.125 deg 2
and ∼0.108 deg 2 , respectively.
Recent Chandra calibrations have increased the estimate of the ACIS instrument
effective area above 2 keV. We have used the utilities available in the Chandra
calibration database to compare data from Cycle 8 to those from Cycle 5. It
turned out that above 2 keV the relation between the effective areas from both
Cycles is reasonably flat and can be well approximated to a constant factor of
about 12%. This increase in the 2-8 keV fluxes is unlikely to be caused by the
increasing contamination in the optical blocking filter since the latter only manifests
itself below 1 keV.
All the CDF-N and CDF-S hard fluxes and their corresponding errors, which
were taken from [19] and belonged to Cycle 5, were therefore decreased by a
12% factor. Moreover, when comparing the sky areas calculated individually
for each source with those calculated from interpolating the sky area of the full
survey, the faintest sources in both CDF samples showed large discrepancies
up to several orders of magnitude. In the study of the source counts of X-ray
sources (see Chapter 3) we make use of a model of the sky area for the full
survey (see 3.2.4), so we have thus decided not to use soft sources fainter than
3 and 7 × 10 −17 erg cm −2 s −1 in the CDF-N and CDF-S, respectively.
For the X-ray luminosity function analysis in Chapter 5 we have only used the
CDF-S sample, since this is the survey with the most secure identifications (up
to ∼60%). The optical imaging strategy and optical counterparts catalogue can
be found in [80], while the spectroscopic identifications have been taken from
[217]. In both cases the ground-based facilities used were the FORS1 and FORS2
instruments at the VLT. The redshifts of the unconclusive identifications and
unidentified sources have been taken from photometric redshift estimations of
[246]. These estimations make use of 12-band data in near ultraviolet, optical,
infrared and X-rays along with sets of power law models for type-1 AGN
50

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
and various templates of galaxies and have been calculated using two parallel
models: HyperZ ([21]) and the Bayesian Model BPZ ([20]). The photometric
redshift estimations were checked against the secure spectroscopic identifications
in [217] and the COMBO-17 survey ([237], [239], [238]) to ensure their
reliability, matching well that of both surveys.
2.3.2 ASCA Medium Sensitivity Survey
The ASCA Medium Sensitivity Survey (AMSS, [225]) is one of the largest high
galactic latitude, broad band, X-ray surveys to date. It includes 606 sources in
the 2-10 keV band over an sky area of 278 deg 2 with hard band fluxes spanning
between 10 −13 and 10 −11 erg cm −2 s −1 , which have been used in Chapter 3.
For the X-ray luminosity function (Chapter 5), we have used a flux-limited subsample
of the AMSS in the northern sky (AMSSn). The flux limit of this subsample
is 3 × 10 −13 erg cm −2 s −1 in the 2-10 keV band, and all but one of the 87
hard X-ray selected sources have been optically identified, covering an area of
∼68 deg 2 . Details on the imaging and spectroscopic identifications procedures
can be found in [1].
2.3.3 XMM-Newton Bright Serendipitous Survey
The XMM-Newton Bright Serendipitous Survey (BSS, [50]) is a bright sample
of XMM-Newton high galactic latitude sources down to a flux of 7 × 10 −14 erg
cm −2 s −1 in the 0.5-4.5 keV band, with an uniform coverage of ∼28 deg 2 above
that flux. This ideally complements the AXIS survey since it is selected exactly
in the same energy band (XID) with the same X-ray observatory (but with a
different detector: EPIC-MOS2 instead of the EPIC-pn used for AXIS), and it
is both wider and shallower. For our source counts calculation purposes (see
Chapter 3) we have used a total of 389 sources from this survey, including those
identified as stars that have been excluded from the analysis performed in [50].
2.3.4 XMM-Newton Hard Bright Serendipitous Survey
Similarly to the BSS, the XMM-Newton Hard Bright Serendipitous Survey (HBSS,
[50]) is a sample of sources at high galactic latitudes detected in the 4.5-7.5 keV
band down to the same flux limit (7 × 10 −14 erg cm −2 s −1 ), with a flat sky cov-
51

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
erage of ∼25 deg 2 . The sample contains 67 sources that have been used to
complement the AXIS and XMS samples in the ultrahard band.
All of these sources but two have been spectroscopically identified, as reported
in [48], with 62 of them being AGN. Along with the redshifts, information on
the intrinsic absorption column densities are also provided in [48] which allow
us to model the absorption of these hard sources (most of them are likely to
be type-2 AGN) and convolve it with the X-ray luminosity function in order to
obtain a purely observation-based evolution model for these objects (see section
5.2).
2.3.5 ROSAT International X-ray/Optical Survey
The ROSAT International X-ray/Optical Survey (RIXOS, [147]) is a medium
sensitivity survey of high galactic latitude sources. The sample contains 401
sources divided in two subsamples: 64 ROSAT fields with 296 sources down to
a flux limit of 3 × 10 −14 erg cm −2 s −1 (known as RIXOS3), plus 18 further fields
containing 105 sources down to a flux limit of 8 × 10 −14 erg cm −2 s −1 in the
0.5-2 keV (RIXOS8).
RIXOS3 covers 15.77 deg 2 in the sky while RIXOS8 covers 4.44 deg 2 , to a total
survey area of ∼20.2 deg 2 . The RIXOS3 subsample has been spectroscopically
identified in a 94%, and the RIXOS8 subsample has been completely identified
which makes the full sample ideal for evolution studies in the soft band.
2.3.6 ROSAT Deep Survey - Lockman Hole
The ROSAT Deep Survey (RDS, [102]) collects all the observations performed
by ROSAT in the period 1990-1997 in the direction of the Lockman Hole, which
is one of the areas of the sky with a minimum of the Galactic Hydrogen column
density ([138]). This sample comprises 50 sources down to a flux limit of
5.5 × 10 −15 erg cm −2 s −1 in the 0.5-2 keV band, with an sky coverage of about
∼0.3 deg 2 . All but four of the 50 sources that compose the RDS have been spectroscopically
identified ([204]), the vast majority of them being AGN. This deep
pencil-beam sample ideally complements the XMS soft sample and hence it has
been used in the calculations done in Chapter 5.
52

CHAPTER 2: AGN SURVEYS WITH XMM-Newton
2.3.7 ROSAT Bright Survey
The ROSAT Bright Survey (RBS, [70], [207]) aimed to identify the brightest
∼2000 sources detected in the ROSAT All-Sky Survey (RASS, [232]) at high
galactic latitudes, excluding the Magellanic Clouds and the Virgo cluster, with
PSPC count rates above 0.2 s −1 . This sample cointains bright sources (flux limit
∼ 2.5 × 10 −12 erg cm −2 s −1 in the 0.5-2 keV band) with redshifts mainly below
1 and a total sky coverage of ∼20300 deg 2 . We have selected a subsample of
∼600 objects that have been completely identified via spectroscopic observations,
most of them being AGN, plus a strong population of galaxy clusters.
53

Chapter 3
Source counts of the AXIS sources
3.1 Motivation
The X-ray Background ([78], see section 1.3) is a record of the accretion power
history of the Universe [66], and seeking its origin and composition has been a
cornerstone in the modern X-ray Astronomy [64]. As a consequence of the diverse
studies on the the Cosmic X-ray Background (CXB hereafter) carried out
in the last decades, it is now widely accepted that the CXB emission arises from
the integrated emission of discrete extragalactic sources. At soft X-rays (0.5-
2 keV) most of the CXB ( 90%) has been resolved into individual sources using
deep pencil-beam surveys ([137],[19],[80]), with smaller resolved fractions
at higher energies. Most of these resolved sources are obscured and unobscured
AGN, while the normal galaxies population only contributes significantly at the
faintest fluxes [113]. Models of the CXB combining obscured and unobscured
AGN populations have reproduced successfully the CXB spectrum. However,
although it has been widely confirmed that the evolution of the X-ray luminosity
is well described by a luminosity-dependent density evolution (see Chapter
5 for details) it is not clear whether the fraction of obscured AGN depends on
the luminosity ([224],[104]), redshift ([220]), both ([130]) or even none of them
([57]).
The fainter sources from deep pencil-beam surveys do not contribute much
to the CXB intensity and it is often difficult to study them individually both
optically and in X-rays. Wide shallow surveys over a large portion of the sky
detect minority populations and allow studies on individual sources but again
scarcely contributing to the CXB.
55

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Medium depth wide band surveys which combine many sources with a relatively
wide sky coverage ([103],[38],[12]) are potentially useful to solve the CXB
problem, since almost 50% of the CXB below 10 keV comes from sources at intermediate
fluxes ([64]) and the X-ray spectrum of many of them can be studied
individually ([149]).
In this chapter we will calculate the sky density or source counts of the AXIS
sources (see 2.1), since these distributions are dependent on the cosmological
properties of the source populations that configure the CXB emission. Accurately
constraining the shape of the source counts is essential to determine the
contribution from discrete sources to the CXB. This chapter is structured as follows:
in section 3.2 we will explain the method used in the source counts calculation,
the results will be discussed in section 3.3 and, finally, in section 3.4 we
will calculate and discuss the contribution of the sources to the total CXB intensity
using the obtained source counts results. For simplicity, in this chapter we
will use cgs as a shorthand for the cgs system units for the flux: erg cm −2 s −1 .
3.2 Method
In this section we will explain the method used to calculate the sky density
of the detected sources in the AXIS survey as a function of flux (log N − log S
relations) in four energy bands: Soft (0.5-2 keV), Hard (2-10 keV), XID (0.5-
4.5 keV) and Ultrahard (4.5-7.5 keV).
3.2.1 The sky areas
In order to compute the log N − log S we need to determine the sky area over
which we are sensitive for a given flux. This can be obtained by summing the
sky area corresponding to the values of the sensitivity maps that are below that
flux. As the conversion between count rate and flux depends on the spectral
shape, for each band i we have calculated the sky area values at each flux for
each spectral slope Ω i (S, Γ). To do this, we have converted S to count rate using
Γ and the response matrices in each field of the survey and then summed the
area for which the corresponding sensitivity map is below that rate. The overall
sky area thus obtained is just the sum of the areas found in each field.
Therefore, the sky area in each band i for each source j would be Ω ji = Ω i (S ji , Γ ji ),
56

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Figure 3.1 Sky area of the AXIS survey as a function of flux for different energy bands
where the fluxes S ji and the slopes Γ ji are those explained in section 2.1.
But we are interested in obtaining sky areas independent of the spectral shape
Ω i (S). This can be calculated by weighting Ω i (S, Γ) with the number of detected
sources in each (S, Γ) bin. This spectrally averaged areas are the sky
coverage of our survey (taking into account the excluded areas), summing a
maximum value of 4.8 deg 2 (see Fig. 3.1).
3.2.2 The binned log N − log S
The number of sources per unit flux and unit sky area at a given flux S is called
differential log N − log S. A binned estimate for it can be built by summing the
inverse of the Ω ji for the sources in each flux bin and then dividing that number
by the width of the bin:
dN
dSdΩ = ∑ j 1/Ω ji
∆S
(3.2.1)
The errors are calculated by dividing the above value by the square root of the
number of sources in each bin. We have chosen to have a minimum number of
sources per bin for reasons that will be explained below. This means that the
bin width is determined by the flux of the first source in the bin and the flux
57

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
of the first source in the next bin, which can make all of them to have different
widths in principle. The width of the last bin would be undefined then, but we
have dropped the brightest source of each sample and used its flux as the upper
bound for this bin when we compute the binned log N − log S.
The number of sources per unit sky area with fluxes higher than a given flux
N(> S) is the integral log N − log S. In this work, each bin contains 15 sources
(except the last one which can contain up to 29 sources) in order to avoid some
features that arise due to fluctuations caused by a few sources, especially at
bright fluxes where the number of sources is low. The N(> S) is built by just
summing the inverse of Ω ji for all sources with fluxes above the lower limit of
each bin:
N(> S) = ∑
j
1
Ω ji
(3.2.2)
The errors are calculated by dividing the N(> S) by the square root of the
number of sources with fluxes equal or greater than the lower limit of the bin.
It may happen that sources below the survey’s flux limit are promoted into
the survey due to statistical fluctuations in their fluxes. Analogously, the faint
sources placed just above the flux limit could drop out of the survey but, as
there are many more faint sources than bright ones, the former have more probabilities
of being promoted than the latter of being demoted. This leads to a net
increase in the source counts at very faint fluxes, thus re-steepening the curve.
This effect is known as the Eddington bias ([58]) and can be observed in the
AXIS Ultrahard source counts (see Fig. 3.3 bottom panel).
3.2.3 The log N − log S model
In previous works it has been shown that a log N − log S is well represented
by a double power law with a steep slope at bright fluxes and a flatter slope
at faint fluxes ([225],[19],[160],[10],[102],[32]). Therefore, we have adopted the
following model for the differential log N − log S:
⎧ ( ) ⎫
⎪⎨
−Γd
K SSb ⎪⎬
dN(S)
dSdΩ = Sb
; S ≤ S b
( )
⎪ −Γu (3.2.3)
⎩ K SSb
S
; S > S
⎪
b
b
⎭
58

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
This model has four independent parameters: the normalisation K, the break
flux at which the change in the slope occurs S b , the slope at bright fluxes Γ u ,
and the slope at faint fluxes Γ d . When there are no significant changes in the
slope because the flux limit of our survey is too close to (or above) the break
flux and there are insufficent sources to perform the fit, we have used a single
power law model in which we have fixed S b ≡ 10 −14 cgs and used a single
slope leaving only two independent variables, K and Γ:
dN(S)
dSdΩ =
K ( ) S −Γ
10 −14 10 −14 (3.2.4)
The integral log N − log S (number of sources above a flux S per unit sky area)
form is thus:
N(> S) =
∫ ∞
S
dS dN(S)
dSdΩ
(3.2.5)
and, therefore, the expected number of sources with fluxes between S min and
S max assuming a given log N − log S is:
N(S min ≤ S ≤ S max ) =
∫ Smax
S min
dS dN(S) Ω(S) (3.2.6)
dSdΩ
3.2.4 Maximum likelihood fit method
We have fitted our data to the models described in section 3.2.3 using a Maximum
Likelihood method that takes into account the uncertainties in the fluxes
of the sources, and the dependence of the sky areas with the flux.
More formally, the expression to be minimised is:
L = −2
(
N sample N∑
)
∑ log(P i (S j )) − 2 log(P λi (N))
i=1 j=1
(3.2.7)
where P i (S j ) is the probability of finding a source with flux S j in the sample i:
P i (S j ) =
∫ S ′ max
S min
′
exp
dS dN(S)
dSdΩ Ω i(S)
59
λ
( )
−(S j −S) 2
2σ
j
2 √
2πσj
(3.2.8)

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
and P λi (N) is the Poissonian probability of finding N sources in a sample i when
the expected number of sources is λ i (equivalent to equation 3.2.6):
P λi (N) = e−λ iλ N i
N!
(3.2.9)
λ i =
∫ Smax
S min
dS dN(S)
dSdΩ Ω i(S) (3.2.10)
This likelihood expression takes into account not only the variation of sky area
in a sample i with the flux, Ω i (S) but also the uncertainty in the flux of the
source σ j ([173]) via the exponential term in the numerator of equation 3.2.8,
assuming that the error around the measured flux value follows a Gaussian
distribution. Since the tails of a Gaussian decrease very quickly, we have used
S ′ min = max(S j − 4σ j , S min ) and S ′ max = min(S j + 4σ j , S max ) as the integration
limits. Additionally, with this method we also consider the normalisation K as
a free parameter; since it appears both in the numerator and the denominator
of equation 3.2.8, we have included the second term in equation 3.2.7 to have
it taken into account. This approach is fully equivalent to that described by
[145] to determine the luminosity function parameters of a complete sample of
AGN (see section 5.3 for details) and, essentially, it takes into account the full
distribution of sources in the Ω(S) plane.
The 1-σ uncertainties in the log N − log S parameters are estimated from the
range of values of each parameter around the minimum L min that make ∆L =
1. The procedure is as follows: the parameter of interest is fixed to a value
close to the best-fit value and we let the rest of the parameters vary until a new
minimum is found. This is repeated for several values of the parameter until
the new minimum L new
min
satisfies Lnew
min = L min + 1.
60

61
Table 3.1 Maximum likelihood fit results to the log N − log S in different bands and using different samples: the first column is the band
used, the second is the power-law slope above the flux break, the third is the slope below that break, the fourth is the flux break, the fifth is
the normalisation, the last six columns indicate the number of sources from each sample used in the fit.
N used /N tot
Band Γ u Γ d S b K AXIS BSS HBS CDF-N CD F-S AMSS
(10 −14 cg s) (deg −2 )
Soft 2.39 +0.06
−0.06
1.69 +0.07
−0.06
1.15 +0.16
−0.13
123.4 +18.8
−17.1
1267/1267
Soft f 2.38 +0.14
−0.09
1.56 +0.01
−0.01
1.02 +0.14
−0.17
141.4 +42.1
−7.3
1267/1267 429/442 a 269/282 b
Hard 2.72 +0.07
−0.08
- 1.00 684.4 +74.1
−84.0
348/397 c
Hard 2.03 +0.12
−0.11
1.00 +0.11
−0.12
0.30 +0.07
−0.05
1086.6 +134.3
−146.5
313/313
Hard 2.51 +0.50
−0.28
0.89 +0.12
−0.12
0.72 +0.11
−0.10
743.7 +109.6
−105.6
186/186
Hard 2.12 +0.13
−0.01
1.10 +0.01
−0.01
0.44 +0.04
−0.01
799.1 +226.8
−8.4
313/313 186/186
Hard 2.66 +0.08
−0.05
1.20 +0.01
−0.01
1.00 +0.08
−0.01
611.5 +49.1
−34.3
397/397 313/313 186/186
Hard 2.58 +0.02
−0.02
- 1.00 606.5 +46.8
−46.3
348/397 c 606/606
Hard 2.53 +0.25
−0.18
1.18 +0.14
−0.08
0.92 +0.66
−0.19
607.8 +366.4
−208.1
313/313 186/186 606/606
Hard f 2.58 +0.17
−0.02
1.30 +0.01
−0.01
1.17 +0.01
−0.05
485.3 +10.1
−24.3
397/397 313/313 186/186 606/606
XID 2.46 +0.11
−0.07
1.29 +0.09
−0.18
1.45 +0.16
−0.26
212.2 +47.4
−22.8
1359/1359
XID f 2.54 +0.03
−0.04
1.35 +0.06
−0.25
1.64 +0.13
−0.28
193.0 +33.1
−15.8
1359/1359 389/389
Ultrahard 2.59 +0.09
−0.05
- 1.00 95.0 +11.1
−12.8
84/89 f
Ultrahard f 2.62 +0.10
−0.10
- 1.00 102.2 +20.0
−21.1
84/89 d 58/65 e
a S min,CDF−N = 3 × 10 −17 cgs; b S min,CDF−S = 6 × 10 −17 cgs; c S min,AXIS = 1.5 × 10 −14 cgs; d S min,AXIS = 10 −14 cgs; e S max,HBS = 2.5 × 10 −13 cgs;
CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
f
Best fit used for contribution to CXB

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
3.3 Results
In order to span a wider range of fluxes and hence to achieve greater accuracy
in the source counts parameters determination, we have combined the AXIS
sample with other shallower and deeper surveys in all the energy bands under
study (see 2.3 for details on them). In the Soft and Hard band we have added
both Chandra Deep Field surveys ([19], [80], [79]) which give us coverage at faint
fluxes. In addition, in the Hard band we have also added the AMSS ([225])
survey which helps us to constrain better the slope at the bright end of the
log N − log S. In both XID and Ultrahard bands we have combined the AXIS
sources with those of the BSS and HBSS ([50]) in their respective energy bands.
Adding these samples will help us to better constrain the shape of the log N −
log S at both bright and faint ends and hence diminishing the uncertainties in
the source counts parameters.
The results of the Maximum Likelihood fits to various single and combined
surveys in different energy bands are summarized in table 3.1. The flux interval
used in the fit is S min = 10 −17 and S max = 10 −12 unless stated otherwise. This
numbers have been chosen to span the observed fluxes of the sources, but the
results are not very dependent on them since the sky area drops abruptly at low
fluxes and the sky density of bright sources is very small. The best fit curves
are plotted along with the observed integral log N − log S in figures 3.2 and 3.3.
For each energy band in Table 3.1 we have performed several fits. In the first
two rows we have fitted the AXIS sources alone, using a fixed spectral index to
calculate fluxes and sky areas (first row) or the best fit spectral index for each
source (second row). In the former case, the spectral slopes were Γ = 1.8 in
the Soft and XID bands and Γ = 1.7 in the Hard and Ultrahard bands. It can
be seen that the results of the fit are mutually compatible within the error bars,
although the uncertainties in the parameters are larger when we fix the spectral
index (especially in the XID and Ultrahard bands). These differences in the bestfit
log N − log S parameters between both methods can be (partly) explained in
terms of the uncertainties in the fitted fluxes of the sources. When the photon
index for the power law slope of the spectrum of the source is obtained via their
spectral fitting, the uncertainties in the fitted fluxes thus obtained are smaller
than those calculated using a fixed spectral slope. In light of this, we have thus
used the spectral fitted slopes to compute the fluxes and count rates for the
AXIS sources.
62

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Figure 3.2 Integral log N − log S in different bands (Top panel: Soft, Bottom panel: Hard),
along with our best fits and some previus results
63

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Figure 3.3 Integral log N − log S in different bands (Top panel: XID, Bottom panel: Ultrahard),
along with our best fits
64

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
The absolute value of the likelihood, unlike the χ 2 , is not an indicator of the
goodness of the fit. Although there appears to be a good agreement between
the data and the best fit model in Figs. 3.2 and 3.3 this is only a qualitative impression.
We have therefore plotted the ratio between the binned differential
log N − log S and the best fit model so that any significative deviations from
unit would arise (see Figs. 3.4 and 3.5). Overplotted is the 1-σ uncertainty interval
calculated as follows: for each flux it has been calculated the differential
log N − log S in the corners of the hypercube defined by the 1-σ errors of the
best fit parameters and then taken the minimum and maximum values.
The agreement with the CDF samples is very good in general. In the Soft band,
the combined AXIS-CDF fit is in excellent agreement with the slope provided
by [19] (which is what we expected since at faint fluxes the only contribution to
the log N − log S comes from the CDF sources) whereas the AXIS-only fit has
a steeper slope below the flux break. However, it is compatible with the AXIS-
CDF Γ d slope at

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
them to rise and drop above and below this flux respectively thus explaining
the bump seen in Fig. 3.4.
When we fit only the CDF and AMSS samples we can reproduce the overall
behavior of the log N − log S since the former constrain the Γ d value at faint
fluxes and the AMSS constrains the Γ u value at bright fluxes. Hence, the best fit
parameters between CDF+AMSS and AXIS+CDF+AMSS are consistent within

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Figure 3.4 Ratio between the differential log N − log S and the best fit model in different
bands (Top panel: Soft, Bottom panel: Hard). The dashed bowtie is the 1-σ uncertainty in
the log N − log S
67

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Figure 3.5 Ratio between the differential log N − log S and the best fit model in different
bands (Top panel: XID, Bottom panel: Ultrahard). The dashed bowtie is the 1-σ
uncertainty in the log N − log S
68

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
when we consider all sources (the Maximum Likelihood method is very insensitive
to a few discrepant points). The AXIS-only and AXIS-HBS fits are
very similar and compatible within −0.2 and HR < −0.2, respectively).
To construct the log N − log S it would formally be necessary to recalculate
the effective area of these subsamples but when we used our method (see
69

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Table 3.2 Maximum likelihood fit results to the log N − log S in the Soft band for two
HR selected subsamples. The first column is the band used, the second is the powerlaw
slope above the flux break, the third is the slope below that break, the fourth is the
flux break, the fifth is the normalisation, and the sixth column indicate the number of
sources from each sample used in the fit.
N used /N tot
Band Γ u Γ d S b K AXIS
(10 −14 cg s) (deg −2 )
Soft HR < −0.2 2.33 +0.04
−0.04
1.69 +0.03
−0.04
1.40 +0.20
−0.10
88.7 +5.9
−7.9
1058/1058
Soft HR > −0.2 2.77 +0.07
−0.06
- 1.00 16.9 +0.05
−0.06
209/209
section 3.2.1), it produced gaps in those flux bins which have been depleted of
sources after the splitting of the sample. Since it is extremely difficult to deal
with this problem when the area varies rapidly with the flux (see Fig. 3.1), we
decided to use as a first approximation the Soft Ω(S) for both subsamples. A
similar approach has been used in [125] where they use the corresponding area
curve for each energy band under study.
It can be seen in Fig. 3.6 that the source counts of Soft sources with HR < −0.2
clearly still follows a broken power law model, while for the HR > −0.2 sources
it is a simple power law. The best fit parameters are listed in table 3.2. Those
for the softest sources (HR < −0.2) are fully compatible, well within the 1-σ
errors, with the best fit parameters obtained for the Soft AXIS-only sample (see
table 3.1). This is reasonable, since the AXIS Soft sources with HR < −0.2 are
over 83% of the total Soft sample. However, the Soft HR > −0.2 subsample
best fit parameters are more similar to those obtained for the hard AXIS-only
sample.
In [125] they found similar results using a discriminating value of HR = 0 for
all energy bands in the Chandra Multiwavelength Project (ChaMP). They demostrated
that the missing break is not due to small number statistics, since
the HR < 0 sources largely outnumbered the HR > 0 sources, by performing
simulations in randomly selected subsets of the HR < 0 sample with the same
number of sources as the HR > 0 subsample. They calculated the log N − log S
for these subsets finding that, in spite of the reduced statistics, they all showed
a detectable break. A possible explanation for this behavior is that spectrally
70

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
N(>S) (sources/deg 2 )
10 100
10 −15 10 −14 10 −13
S 0.5−2 keV
(cgs)
N(>S) (sources/deg 2 )
10 100
10 −15 10 −14 10 −13
S 0.5−2 keV
(cgs)
Figure 3.6 Integral log N − log S for two HR selected 0.5-2 keV AXIS subsamples (Top
panel: HR < −0.2, Bottom panel: HR > −0.2). The solid line is the best fit curve.
71

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
hard sources (HR > −0.2), which are likely to be obscured, are detected predominantly
at relatively close redshifts and hence do not show the break flux in
the source counts that is an observable effect of cosmological evolution ([97]).
3.4 Contribution to the Cosmic X-ray Background
Now that we have accurately determined the parameter of the source counts
we can estimate the intensity contributed by sources in different flux intervals
using:
I(S min ≤ S ≤ S max ) =
∫ Smax
S min
dSS dN(S)
dSdΩ
(3.4.1)
We are interested here in comparing the total intensity contributed by resolved
sources with the total CXB intensity. Before that, we need to estimate both the
contribution from bright sources and the total CXB intensity.
3.4.1 Contribution from bright sources and stars
Since the surveys we are using in this section to calculate the log N − log S
clearly lack bright sources we must first estimate which would be their contribution
to the CXB, which is small but not negligible.
In the Soft band we have followed the same method as [160] summing the soft
fluxes of the sources in the RBS ([207], see section 2.3) higher than 10 −11 cgs,
and dividing by the area covered by the survey. In the Hard band we have
used the sources in the HEAO-1 A2 survey [180], which is complete down to
3.1 × 10 −11 cgs. For the Ultrahard band we have taken the values from the
Hard band converting both the flux limit and the intensities to 4.5-7.5 keV using
a power law with slope Γ = 1.7. The XID band is a bit more problematic since
it is partly in the Soft band and partly in the Hard band. Here we have just
estimated the 2-4.5 keV flux limit and intensities from the Hard band the same
way as before and then added them to the Soft band values.
Moreover, we need to estimate the contribution from galactic stars down to our
fainter flux limit so that we can substract it from our source intensities, since
we are pursuing to determine the resolved fraction of the extragalactic CXB.
We have taken the estimations from [19] of the fraction of stars contributing
72

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
to the CXB and their total CXB intensities, obtaining the following values for
stars: 0.19 +0.05
−0.04 × 10−12 cgs deg −2 and 0.36 +0.34
−0.19 × 10−12 cgs deg −2 in the Soft and
Hard bands, respectively. For the XID band, assuming that most of the contribution
from stars comes from high fluxes ([19]) and that the stars at such high
fluxes have a low temperature thermal spectrum ([50]), we have tried to determine
the XID band contribution from the Soft band assuming a T = 0.5 MK

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
of these values to the Soft band using spectral shape described above provides
a result of (7.46 ± 0.09) × 10 −12 cgs deg −2 and (7.78 ± 0.06) × 10 −12 cgs deg −2 ,
respectively, which are again fully compatible with our adopted value of (7.5 ±
0.4) × 10 −12 cgs deg −2 .
More recently, there has been a re-estimation of the total CXB intensity in the
1-2 keV and 2-8 keV bands using Chandra CDF data and contributions from
bright sources ([109]). They have measured the unresolved CXB by extracting
spectra of the sky and then removing all point-like and extended sources detected
in the CDF. Their total CXB intensity estimation comes from the sum of
the unresolved components and the contributions from the CDF sources and
from brighter sources for which they have used the source counts derived in
[230] and [231], with different spectral slopes at different fluxes. Their 1-2 keV
CXB intensity is thus (4.6 ± 0.3) × 10 −12 cgs deg −2 , quite similar to our value.
3.4.3 Contribution to the CXB in different flux intervals
Our calculated CXB intensities for the observed flux intervals along with the
XRB intensities from [160] are shown in Table 3.3.
In Fig. 3.7 is plotted the relative contribution of two flux intervals per decade
to the total CXB intensity for the four energy bands under study assuming our
best fit log N − log S. It can be seen that the maximum contribution comes from
fluxes around ∼ 10 −14 cgs, where the break in the source counts is. The contribution
from the bins one decade around this value are close to the 50% of the
total CXB intensity in the Soft and Hard bands. In the Ultrahard band, we are
not deep enough to detect the break, although using the 5-10 keV source counts
from [101] and [194] it could be possible that a break just below ∼ 10 −14 cgs
exists.
The extrapolation of the Soft and Hard bands log N − log S to zero flux using
our best fit model does not saturate the CXB intensity (Table 3.3), although in
the Soft band the total CXB intensity is within the intensities spanned by the
uncertainties in the best fit parameters. However, the possibility of a new dominant
population at fainter fluxes remains open, especially in the Hard band.
Assuming that the fraction of truly diffuse CXB is negligible (in [156] is shown
that the source counts in the Soft band grows down to at least 7 × 10 −18 cgs) it is
possible to estimate the slope needed to saturate the CXB at zero flux supposing
74

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Table 3.3 Intensity in different bands from different origins and flux intervals. The first
column indicates the band, the second gives the origin of the intensity, the third and
fourth columns list the flux interval, the fifth column total intensity from that interval,
the sixth column shows the fraction of the XRB intensity contributed by sources in that
interval.
Band Origin S min S max I(S min ≤ S ≤ S min ) f XRB
(cgs) (cgs) (10 −12 cgs deg −2 )
Soft Best fit AXIS+CDF log N − log S 0 3 × 10 −17 0.25 0.03
Soft Best fit AXIS+CDF log N − log S 3 × 10 −17 2 × 10 −13 5.60 0.75
Soft Best fit AXIS+CDF log N − log S 3 × 10 −17 10 −11 6.54 0.87
Soft RBS sources a 10 −11 0.20 0.03
Soft Total resolved 3 × 10 −17 6.55 e 0.87
Soft XRB b 7.5 ± 0.4
Hard Best fit AXIS+CDF+AMSS log N − log S 0 3 × 10 −16 0.62 0.03
Hard Best fit AXIS+CDF+AMSS log N − log S 3 × 10 −16 1 × 10 −11 17.08 0.85
Hard Best fit AXIS+CDF+AMSS log N − log S 3 × 10 −16 3.1 × 10 −11 17.18 0.85
Hard HEAO-1 A4 sources c 3.1 × 10 −11 0.43 0.02
Hard Total resolved 3 × 10 −16 17.25 e 0.85
Hard XRB b 20.2 ± 1.1
XID Best fit AXIS+BSS log N − log S 3 × 10 −15 10 −12 8.48 0.56
XID Best fit AXIS+BSS log N − log S 3 × 10 −15 2.38 × 10 −11 9.00 0.59
XID Bright sources d 2.38 × 10 −11 0.39 0.02
XID Total resolved 3 × 10 −15 9.20 e 0.60
XID XRB d 15.3 ± 0.6
Ultrahard Best fit AXIS+HBS log N − log S 9 × 10 −15 2 × 10 −13 1.50 0.21
Ultrahard Best fit AXIS+HBS log N − log S 9 × 10 −15 1.05 × 10 −11 1.74 0.24
Ultrahard Bright sources d 1.05 × 10 −11 0.15 0.02
Ultrahard Total resolved 9 × 10 −11 1.79 e 0.25
Ultrahard XRB d 7.2 ± 0.4
a Schwope et al. ([207])
b Moretti et al. ([160])
c Piccinotti et al. ([180])
d
See text
e After subtracting the stellar contribution (see Section 3.4.1)
75

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Figure 3.7 Relative contribution to the total X-ray Background intensity from equally
spaced logarithmic flux intervals using the best fit models in each band: Soft (solid),
Hard (dashed), XID (dot-dashed) and Ultrahard (dotted).
the log N − log S steepens below the minimum flux studied here. We find out
that these slopes are 1.85 and 1.84 in the Soft and Hard bands, respectively. If
we compare these values to the observed slopes of the separate source counts of
AGN and galaxies in the CDF field ([19]) only the absorbed AGN with an slope
of ∼1.62 are close to saturate the soft CXB (the rest of AGN estimates have values
in the range 1.2-1.5), whereas the galaxies could do so with any estimate
(slopes ranging from 2.1 to 2.7) if we assume they grow at the same rate below
the resolved fluxes. In the Hard band the situation is quite similar, being the
absorbed AGN the only AGN population capable of saturating the hard CXB
(slope ∼1.95, against slopes ∼1.5 for the rest of AGN) while the galaxies, having
slopes ranging 3-3.5, could satisfy this condition at any estimate. Even if a
higher intensity of the CXB is assumed ([109]) this conclusion is still valid since
that would need a steeper source counts slope to saturate the CXB.
In any case, it has been made clear that the maximum contribution to the CXB
comes from sources at fluxes around ∼ 10 −14 cgs at all energy bands (including,
probably, the Ultrahard band) and hence medium flux surveys with limiting
fluxes close to this value, like AXIS, are essential to understand the evolution of
76

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
the X-ray emission in the Universe at these energies. Sources at fainter fluxes or
being heavily absorbed are very important for the overall energy content of the
CXB ([85]), but they reside at harder X-ray energies where the resolved fraction
is much smaller ([240]).
3.4.4 Resolved and unresolved components of the CXB
A direct comparation between the results in [109] and our results conveys a
certain uncertainty since the energy bands under consideration are different
(0.5-2 keV versus 1-2 keV in the Soft band, 2-10 keV versus 2-8 keV in the Hard
band). For the conversions between these bands we have assumed a power law
model with photon indices of 1.5 for the unresolved component (fitted by [109]
to the unresolved CXB spectrum), 1.43 for the resolved faint sources (again, fitted
by [109] to the summed spectrum of resolved sources) and 2 for the resolved
sources brighter than ∼ 10 −14 cgs ([149]).
Also, in [109] they have excluded the areas around the sources catalogued in
[4] from their study of the unresolved CXB, with flux limits of 2.5 × 10 −17 cgs
in the 0.5-2 keV and 1.4 × 10 −16 cgs in the 2-8 keV and therefore they define as
unresolved any intensity coming from fluxes below those limits or from a truly
diffuse component. Additionally, in the 2-8 keV band, the sources in [4] were
also the basis of the work in [19], and we have seen in sections 3.3 and 2.3 that
the fluxes need to be decreased by ∼12% due to changes in Chandra calibrations.
Assuming all these corrections and a spectral slope of 1.43, the flux limit in the
2-10 keV band becomes 1.6 × 10 −16 cgs.
In table 3.4, there is a comparison between the intensities from [109] and the
results of this and previous works in the 0.5-2 keV, 1-2 keV and 2-10 keV bands.
The error bars in our estimates of the intensities have been derived from the
errors in the log N − log S best fit parameters. For the extrapolation to zero flux,
the errors have been calculated using the values spanned by the uncertainties
in the best fit parameters as explained in section 3.3.
The most remarkable difference is that the total soft CXB intensities are barely
compatible at the ∼1-σ level, whereas at 1-2 keV they are compatible at 0.16-σ
(see section 3.4.2). This discrepance is caused by the way the 0.5-2 keV intensities
have been estimated. Our 0.5-2 keV value is an extrapolation from the
1-2 keV total CXB intensity in [160] assuming Γ = 1.4, while in [109] they use
77

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Table 3.4 Comparison between the estimated X-ray intensities from [109] and this and
previous works, from different origins and flux intervals. The first two columns indicate
the flux limits between which has been estimated the intensity. If the first one is
missing the intensity is calculated from zero flux, while if the second one is missing,
the intensity is calculated to infinity. The third column is the intensity from [109], and
the fourth column the intensity from this work (or previous ones as indicated).
0.5-2 keV
Flux limits
Intensity
(cgs) (10 −12 cgs deg −2 )
[109] Here
2.5 × 10 −17 1.8 ± 0.3 0.23 ± 0.09 a
2.5 × 10 −17 5.0 × 10 −15 2.4 ± 0.4 2.2 ± 0.4 a
5.0 × 10 −15 1.0 × 10 −11 4.2 ± 0.3 4.4 ± 1.4
1.0 × 10 −11 - 0.2 b
Total 8.4 ± 0.6 7.5 ± 0.4 c
Total resolved 6.6 ± 0.5 6.6 ± 1.7 e
Fraction resolved 0.79 ± 0.07 0.88 ± 0.23
1-2 keV
Flux limits
Intensity
(cgs) (10 −12 cgs deg −2 )
[109] Here
1.5 × 10 −17 1.0 ± 0.1 0.13 ± 0.05 a
1.5 × 10 −17 3.0 × 10 −15 1.5 ± 0.3 1.3 ± 0.2 a
3.0 × 10 −15 0.5 × 10 −11 2.1 ± 0.1 2.2 ± 0.7
0.5 × 10 −11 - 0.1 b
Total 4.6 ± 0.3 4.5 ± 0.2 c
Total resolved 3.6 ± 0.2 3.7 ± 0.7 e
Fraction resolved 0.78 ± 0.07 0.81 ± 0.16
2-10 keV
Flux limits
Intensity
(cgs) (10 −12 cgs deg −2 )
[109] Here
1.6 × 10 −16 4.2 ± 2.1 0.40 ± 0.04 a
1.6 × 10 −16 1.6 × 10 −14 9.5 ± 1.3 9.3 ± 0.4 a
1.6 × 10 −14 1.0 × 10 −11 7.0 ± 0.4 7.9 ± 1.5
1.0 × 10 −11 3.1 × 10 −11 - 0.09 ± 0.06
3.1 × 10 −11 - 0.4 d
Total 20.7 ± 2.5 20.2 ± 1.1 c
Total resolved 16.5 ± 1.3 17.3 ± 1.7 e
Fraction resolved 0.80 ± 0.11 0.86 ± 0.10
a Extrapolating our best fit log N − log S; b Schwope et al. ([207]); c Moretti et al. ([160]); d Piccinotti et al. ([180]); e After
subtracting the stellar contribution
78

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
different contributions with different photon indices. Since the contribution
from the brightest sources is almost half of the total and their slopes are steeper,
the effective spectral slope in the conversion of the CXB intensity in [109] from
1-2 keV to 0.5-2 keV is Γ ∼ 1.72, steeper tan our value of 1.4, and hence providing
a much larger contribution in the 0.5-1 keV interval. The resolved contribution
in [109] also increases in the Soft band with respect to the 1-2 keV band, but
the resolved fraction only increases slightly because of the very similar effective
spectral slopes of the resolved component and the CXB intensity. On the contrary,
our resolved component is very similar to that of [109], but our assumed
CXB intensity in the Soft band has a flatter spectral shape, resulting in a smaller
resolved fraction but still compatible within the errors.
Furthermore, we have converted our resolved contributions from the Soft band
to the 1-2 keV band using different spectral slopes for different flux intervals
(as explained at the beginning of this section), and hence the differences in the
resolved components and the resolved fraction with respect to those of [109]
are very small (see table 3.4) and well within the errors.
So, to summarize, the differences in the Soft band in the total CXB intensity are
around ∼1-σ and mostly due to the different effective spectral shape assumed
for the total CXB intensity between [109] and most of the previous works. On
the contrary, the resolved intensities are very similar both in [109] and in this
work.
Assuming the Γ = 1.4 CXB spectral shape below 1 keV, where its real shape
is unknown, is an important source of uncertainty. Supposing that the CXB
spectrum below 1 keV steepens with a power law shape, a slope Γ ∼ 2.2 would
be needed to produce the estimate of the 0.5-2 keV CXB intensity from [109]
from their 1-2 keV intensity. Given that the typical slope of the faintest sources
detected and of the unresolved component in the Soft band are around Γ ∼
1.5, the uncertainty in the spectral shape below 1 keV cannot fully explain the
difference in the CXB intensities discussed above.
In the Hard band there is full agreement in the total CXB intensity as well as in
the resolved component, where our estimate is slightly higher but well within
the 1-σ errors. Our estimate of the bright source contribution in the Hard band
is quite robust since the AMSS sources cover the same region of the log N −
log S parameter space.
Extrapolating the log N − log S to zero flux we cannot saturate the unresolved
79

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
component so either there is a diffuse component, or the source counts has to
steepen again somewhere below the current flux limits.
3.5 Summary
In this chapter we have performed a maximum likelihood fit to a broken power
law model for the log N − log S in four different energy bands: Soft (0.5-2 keV),
Hard (2-10 keV), XID (0.5-4.5 keV) and Ultrahard (4.5-7.5 keV). The results of
the fit are summarized in table 3.3. We have found that fits to the source counts
using fixed spectral slopes produce similar results to those using the spectral
slopes of the individual sources, but with larger error bars.
The source counts in the Soft, Hard and XID bands present breaks at fluxes
around ∼ 10 −14 cgs. A detailed examination of the ratios between the data and
the best fit to this model do not show significant differences in the Soft and XID
bands, whereas in the Hard band there seems to be some evidence of another
break at ∼ 3 × 10 −15 cgs and several changes of slope. This only happens in the
Hard band so it is difficult to tell whether is due to the simplicity of the model
(that has to take into account several contributions from different populations at
different redshifts) or to calibration uncertainties. The best fit model parameter
values obtained are compatible with previous smaller and similar surveys, but
the combination of large number of sources and wide flux coverage in this work
produce smaller uncertainties in the fitted parameters. The source counts of
two HR selected subsamples in the Soft band reveals that the spectrally hard
sources (those with HR > −0.2) show no flux break in their log N − log S. This
may imply that such hard sources are detected at relatively low redshifts and
therefore they show no evolution.
We have also used our best fit log N − log S to calculate both the total resolved
fraction of the Cosmic X-ray Background (including the contribution from bright
sources, table 3.3) and the relative contribution in different flux bins to the total
CXB (see Fig.3.7). We have used the estimates of the average CXB intensity in
the Soft and Hard bands from [160] and converted them to the XID and Ultrahard
bands using a power law spectrum with Γ = 1.4.
The total resolved fraction down to the lowest fluxes of our combined sample
reaches 88% in the Soft band and 86% in the Hard band (where we have been
able to reach deep fluxes usin pencil beam surveys [19]), but it is only 60% in
80

CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
the XID band and 25% in the Ultrahard band. The total intensity produced
extrapolating our log N − log S to zero flux does not saturate the CXB intensity.
Assuming that another flux break occurs just below our detected minimum
fluxes, we have estimated the minimum slope needed to reproduce the CXB
with only discrete sources obtaining values of 1.85 in the Soft band and 1.84 in
the Hard band. If we compare these values with those of the galaxy and AGN
source counts from the CDF ([19]), we find that galaxies could easily provide
this steepening and, among the AGN population, only the absorbed ones could
do so as well.
The maximum fractional contribution to the CXB in the Soft, Hard and XID
bands comes from sources within a decade around ∼ 10 −14 cgs (where the
break in the source counts power law approximately occurs). This is almost
50% of the total contribution in the Soft and Hard bands, which means that
medium deep surveys such as AXIS are essential to understand the evolution
of the X-ray emission in the Universe up to 10 keV.
A recent re-estimation of the Soft and Hard CXB intensities using CDF data
[109] finds lower resolved fractions of the CXB than in this work. We have
shown that the difference in our results in the Soft band, where it is highest, is
only at the ∼1-σ level and that it is due to the different ways in which the CXB
intensity is calculated. In [109] they add different contributions at different
fluxes, which produces an effective slope Γ ∼ 1.8 which is much steeper than
the CXB spectral slope Γ = 1.4 that we have assumed.
81

Chapter 4
Clustering of AXIS and XMS sources
4.1 Motivation
The dominant population at medium and low X-ray fluxes are AGN, which are
known to cluster strongly ([242], [84], [161], [37]).
To detect source clustering it is needed a survey that is both deep (to achieve
high angular density) and wide (to prevent a single structure to bias the overall
average). To achieve both requirements simultaneously is almost impossible,
so some sort of compromise between them must be reached. The AXIS sample
comprises 36 fields outside the Galactic plane (see section 2.1) and has a relatively
high source density (about 35 sources per field in the Soft and XID bands).
This will allow us to compute the angular correlation function of AXIS sources
and to translate the results into spatial clustering inverting Limber’s equation
([175], see section 4.3.5) knowing the luminosity function of the populations
involved.
Several studies have investigated the angular clustering in the Soft and Hard
bands on different scales ranging from tens or hundreds of arcsecs to degrees,
with varying success. For instance, angular clustering have been detected in the
Soft band ([72], [18], [3], [229]) with different values at the clustering strength.
Angular clustering in the hard band has evaded detection in some cases ([72],
[187]), but not in others ([241], [17]) where clustering strengths are found to
be marginally compatible with the observed spatial clustering of optically and
X-ray selected AGN.
The spatial correlation function provides useful information on how extragalac-
83

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
tic X-ray sources cluster forming physical structures of cosmological origin although
it is more expensive in terms of resources than the angular correlation
function because it needs highly complete surveys (which require hundreds of
secure redshift identications obtained via ground-based espectroscopy). Many
works have reported spatial clustering using this method with different significancies
in the strength if the signal ([242], [84], [161], [45]) at all energy bands.
Since the XMS sample has identification completenesses over 95% in the Soft
band and about ∼85% in the Hard band, it would allow us to test these results
using its sources.
This chapter is structured as follows: in sections 4.2 and 4.3 we will study the
cosmic variance and the angular clustering of the AXIS sources, while in section
4.4, we will investigate the spatial clustering of XMS sources. Throughout
this chapter we will assume H 0 = 70 km s −1 Mpc −1 and a flat Universe framework
with Ω M = 0.3 and Ω Λ = 0.7 ([213]).
4.2 Cosmic variance
The simplest test for source clustering is to compare the actual number of sources
detected in each field N k , with the number of expected sources λ k from the best
fit log N − log S (see Chapter 3) and the sky area of each individual field Ω k .
This procedure is similar to the traditional counts-in-cells method. In principle,
if one field (or a few fields) were looking through strong cosmic structures
the number of sources detected should be significantly different from the expected
number of sources for a random, uniform distribution as measured by
the overall log N − log S.
The statistical tools we have used to measure the deviation from such a random
uniform distribution are the cumulative Poisson distributions:
P λk (≥ N k ) =
∞
∑
l=N k
P λk (l); N k > λ k (4.2.1)
P λk (≤ N k ) =
N k
∑ P λk (l); N k < λ k (4.2.2)
l=0
where P λ (l) is the Poisson probability of detecting l sources when the expected
number of sources is λ. The cumulative distributions above give the probability
84

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
of finding ≥ N k (eq. 4.2.1) or ≤ N k (eq. 4.2.2) sources when the expected number
from the source counts is λ k . This method is similar to the one used in [37],
which uses P λ (l) instead of the cumulative probabilities, being our approach a
more conservative estimate to determine the likelihood of finding a number of
sources in a field which is different from the expected value.
Then, the maximum likelihood for the whole sample is:
L ′ = −2 ∑ ln P λk (≥ N k ) − 2 ∑ ln P (≤ N λk ′ k ′) (4.2.3)
k
k ′
where k runs over the fields for which N k > λ k and k ′ runs over the fields for
which N ′ k < λ′ k .
We have compared the observed L’ values in each band with 10000 simulated
values using the values of λ k and Poisson statistics. The number of simulations
with likelihood values above the observed ones were 1388, 4580, 778 and 4958
for the Soft, Hard, XID and ultrahard bands, respectively. As it can be seen, we
found nothing significant in both the hard and ultrahard bands. However, in
the Soft and XID bands we have found some deviations below or at about the
90% significance level. These results are not conclusive at all but indicate that,
at least in the Soft and XID bands, a more detailed study of clustering may be
worthwhile.
4.3 Angular correlation function of AXIS sources
If cosmic structure is present in all (or most) fields, a test that measures significant
deviations from the mean number of sources in each field from some
overall average will not provide any significant results, as seen in section 4.2.
Instead, we should look for evidence of sources tending to appear together in
the sky with respect to an unclustered source distribution.
4.3.1 Method
According to [174], the angular two-point correlation function of objects distribution
w(θ) determines the joint probability of finding two objects in two small
angular regions δΩ 1 and δΩ 2 separated at an angular distance θ with respect to
85

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
that expected from a random distribution:
δP = n 2 δΩ 1 δΩ 2 [1 + w(θ)] (4.3.1)
where n is the mean sky density of objects in the sky. If w(θ) = 0 the distribution
is homogeneous.
The angular separation is a projection in the sky of the real spatial separation
between two sources at different redshifts thus hiding the underlying spatial
clustering (which needs accurate redshifts for a very high fraction of the sources
to be properly measured). The spatial clustering, however, can be estimated
by deprojecting the computed angular correlation function assuming a given
redshift distribution for the sources (which can be either empirically measured
or derived from a luminosity function model) via the inversion of Limber’s
equation (see section 4.3.5). The angular correlation function is, nevertheless,
a powerful approach given the large sizes of the two-dimensional extragalactic
surveys.
There are several methods to measure the angular correlation function, most
of them based on the idea of looking for an excess number of source pairs at a
given angular separation θ with respect to a simulated random homogeneous
sample ([131], [59]). Among all the proposed estimators for w(θ), we have chosen
the one proposed by [59]:
w(θ) = f DD
DR − 1 (4.3.2)
where DD is the number of actual pairs of sources with an angular separation
θ, and DR is the number of pairs having one real and one simulated source at
the same angular separation, while f is a normalisation constant that takes into
account the different numbers of real and simulated sources. The error bars are
given by ([174]):
√
1 + w(θ)
∆w(θ) =
(4.3.3)
DR
To produce the random source sample we tried to follow as closely as possible
the real distribution of the source detection sensitivity of the survey so that we
can provide an accurate random sky against which to judge the presence or absence
of significative overdensities at different angular separations. To do this,
86

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
we have used bootstrap simulations in the following manner. First, we have
formed a pool of real sources with detection likelihoods higher than 15 (see section
2.1) in the band under study, regardless of having their count rates above or
below the sensitivity map of the corresponding field at the source position (see
Appendix A). Then, keeping the number of simulated sources equal to the real
number of sources in each field N k , we have randomly extracted sources from
this pool keeping their count rates and distances to the optical axis of the X-ray
telescope but randomising the azimuthal angle around it. If the source had a
count rate above the sensitivity map of the field under consideration at its new
position (X, Y), the source was kept in the simulated sample. Otherwise, a new
source is randomly extracted from the pool until N k valid simulated sources are
found. This way, we are able to mimic the decline of the source detection sensitivity
with the off-axis angle in the simulated sample. The number of random
samples used in this calculations N sim have been chosen so as to give a total of
about one million simulated sources in each band.
With this in mind, the normalisation constant f in equation 4.3.2 is:
f = ∑ k N k (N k − 1)
2N sim ∑ k N 2 k
(4.3.4)
where N k is the number of sources in field k and N sim is the number of simulations.
4.3.2 Results
We have applied the method described in section 4.3.1 to the AXIS sample for
each energy band discussed in this thesis: Soft (0.5-2 keV), Hard (2-10 keV), XID
(0.5-4.5 keV) and Ultrahard (4.5-7.5 keV).
The values of w(θ) calculated using equation 4.3.2 in each band are shown in
Figs. 4.1 and 4.2. These values are corrected from the so-called integral constraint,
which is a bias in the correlation function that occurs when a positive
correlation is present at angular scales comparable to the individual field size.
When this happens, the estimate of the mean surface density of objects from
the survey is too high, thus generating a negative bias in the angular correla-
87

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.1 w(θ) versus θ (Top panel: Soft, Bottom panel: Hard). Solid dots are the integral
constraint-corrected observed values. Solid triangles are the estimated values of the
integral constraint, displaced to the left for clarity. The solid line is the best χ 2 fit to our
data.
88

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.2 w(θ) versus θ (Top panel: XID, Bottom panel: Ultrahard). Solid dots are the
integral constraint-corrected observed values. Solid triangles are the estimated values
of the integral constraint, displaced to the left for clarity. The solid line is the best χ 2 fit
to our data. The panels have different scales on their Y-axis.
89

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
tion function [17]. Formally, the integral constraint can be estimated by:
W =
∫ ∫
dΩ1 dΩ 1 w(θ)
∫ ∫
dΩ1 dΩ 2
(4.3.5)
where the integral is carried out over the whole area of the survey. However,
given the complicated dependence of the sensitivity with the area of our survey,
we decided to evaluate the integral constraint empirically. To do that, we
calculated the angular correlation function that would have been detected in
the absence of correlation w IC (θ) via the average of N sim simulated realisations
of w(θ), where the real data were replaced by random samples simulated independently
using the method described in section 4.3.1. The w IC (θ) points at
each angular scale are overplotted as triangles in Figs. 4.1 and 4.2, and have
been used to increase the corresponding w(θ), convolving the error bars using
Gaussian statistics.
Our first results to the full sample resulted in a ∼3-σ significant bump at scales
about 200 arcsec, which was also present in the simulations but at lower significance.
The origin of this bump turned out to be in only two fields: HD 111812
and HD 117555. Both fields have stellar clusters in their field of view ([60])
and, since we are only interested in the extragalactic large-scale structure, we
have opted to exclude these two fields from all subsequent angular clustering
analysis.
The observed w(θ) values can be fit to a power law model in the form:
w(θ) =
( θ
θ 0
) −γ
(4.3.6)
The best χ 2 fits to this model are overplotted in Figs. 4.1 and 4.2. The best
fit parameters are listed in table 4.1 along with the significance of the detection
from an F-test, comparing the χ 2 value of a power law model a w(θ) = 0,
no-clustering model. The F-test suggests significant correlation at the ∼99%
confidence level in the Soft and XID bands, whereas no significant clustering
detection is seen the the Hard and Ultrahard bands.
In [72], they find significant angular correlation in the XMM-LSS sample ([183])
in the Soft band with a similar slope γ = 1.2 ± 0.2, and a lower correlation
length θ 0 = 7 ± 3 arcsec, but compatible with ours within ∼1-σ. In [229] find
γ = 0.7 ± 0.3 and θ 0 = 4 ± 3 arcsec, again a lower correlation length than in our
90

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Table 4.1 Information on the simulations for the angular correlation function together
with fit results: Band is the band where the sources were selected, N pool is the number
of sources in the pool used for the bootstrap simulation (see section 4.3.1), N is number
of sources selected in the real sample, N sim is the number of simulations, χ 2 0
is the value
of the χ 2 fit when using a no clustering model, χ 2 is the best fit value for a power-law
model (see Eq. 4.3.6) with the best fit parameters and their 1-σ uncertainty intervals
given by the last two columns, N bin is the number of bins used in the fit and P(F) is the
F-test probability that the improvement in the fit is significant (the smaller the P(F) the
higher the significance). The second row in each band corresponds to the best fit fixing
γ to the “canonical” value 0.8.
Band N pool N N sim χ 2 0
χ 2 N bin P(F) θ 0 (“) γ
Soft 1177 1131 1000 17.10 5.10 10 0.0079 19 +7
−8
1.2 +0.3
−0.2
7.80 10 0.0096 6 +2
−2
≡ 0.8
Hard 415 351 2500 8.47 7.33 10 0.5622 12 +20
−12
1.1 +2.8
−2.3
7.47 10 0.3017 4 +5
−4
≡ 0.8
XID 1301 1218 1000 16.00 5.30 10 0.0120 19 +7
−8
1.3 +0.4
−0.3
8.80 10 0.0238 4 +2
−2
≡ 0.8
Ultrahard 88 77 10000 1.97 1.87 10 0.8119 0.7 a 0.22 a
1.90 10 0.5759 8 +26
−8
≡ 0.8
HR 250 225 10000 3.60 1.10 10 0.0087 42 +8
−12
3.9 +2.5
−1.3
3.22 10 0.3165 5 +9
−5
≡ 0.8
Soft/3 392 380 2500 14.28 10.42 10 0.2835 35 +11
−18
1.7 +1.0
−0.6
12.53 10 0.2912 7 +7
−6
≡ 0.8
a
Parameter unconstrained by the fit
91

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
results but compatible within less than 1-σ with our γ ≡ 0 result. On the other
hand, in [18] is also found significant angular correlation in the Soft band but
with a higher correlation length θ 0 = 10.4 ± 1.9 arcsec with the canonical slope
γ = 0.8, compatible with our results at about the 2-σ level. Using the RASS-
BSC survey ([232]), [3] have also found significant correlation in this band, but
at much higher angular distances (∼ 8 ◦ ).
In the Hard band there are no evidences of correlation in [72] (413 sources) and
[187] (205 sources). However, there is very strong (> 4σ) clustering detected by
[17] (171 sources) with γ = 1.2 ± 0.3 and θ 0 = 49 +16
−25
arcsec. There is also clustering
detected at similar significance by [241] with γ ≡ 0.8 and θ 0 = 40 ± 11 arcsec
(278 sources). These results are somewhat surprising, since the sample in [17]
is less than a half of the sample in [72] and similar to the one in [187], while
the sample in [241] is also smaller than the [72] sample. Our angular correlation
length is compatible with [17] and [187] results within 1-σ, but not with the
correlation length obtained by [241]. Nevertheless, the F-test on our correlation
function and a Poissonian statistics test (see section 4.3.3) indicates that no significant
clustering have been detected in this band. Our best fit results are again
intermediate between the results obtained by [17] and [241] on one hand, and
[72] and [187] on the other.
4.3.3 Poisson statistics test
Each bin in w(θ) contains information from many pairs, probably involving the
same real and simulated sources many times. The underlying independent bins
hypothesis in the χ 2 test may not be applicable in this case. To solve this problem
and check the significance of the correlation we have applied a test using
Poisson statistics ([37]) to compare the expected number of pairs at angular distances
smaller or equal than each individual observed distance in the absence
of correlation:
DR(θ
µ = ∑
′ )
f
θ ′

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.3 1 − P µ (N θ ) versus θ (Top panel: Soft, Bottom panel: Hard). The median (50%),
99% and 99.9% levels from random simulations are also shown. The Y-axis scaling is
different in each panel for clarity.
93

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.4 1 − P µ (N θ ) versus θ (Top panel: XID, Bottom panel: Ultrahard). The median
(50%), 99% and 99.9% levels from random simulations are also shown. The Y-axis
scaling is different in each panel for clarity.
94

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
This way we can calculate the integrated Poisson probability of obtaining < N θ
pairs for a distribution of mean µ:
P µ (< N θ ) ≡
N θ −1
N θ −1
µ
∑ P µ (N) = ∑
N e −µ
N!
N=0
N=0
(4.3.9)
This way we can use the quantity 1 − P µ (N θ ) as an estimator of the significance
of the clustering detection. A plot of 1 − P µ (N θ ) versus the angular distance θ
is shown in Figures 4.3 and 4.4 for each band. We have estimated the signal
in the absence of correlation in a similar way in order to quantify the integral
constraint (see section 4.3.2) but replacing the real data by randomly placed
sources. For each sample we have performed 10000 simulations in this way.
We have thus determined the distribution of the expected value of 1 − P µ (N θ )
for each angular scale if the sources were not correlated. We also show in Figures
4.3 and 4.4 the mean and 99% and 99.9% percentiles of those distributions
for each angular distance.
The simulations show clearly that the detection significance is actually lower
than the value given by purely Poisson statistics when there are more than 1000
sources, as it can be seen in the Soft and XID bands where the 99% percentile
is about the 3-σ level, whereas in the Hard and Ultrahard samples the 99%
percentile is closer to the standard Poisson position, although showing large
excursions.
As we can see from the percentile values obtained from the simulations, we
have found a >99% (and mostly

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.5 Top panel: w(θ) versus θ. Symbols are the same as in Fig. 4.1. Bottom panel:
1 − P µ (N θ ) versus θ for a random selection of one third of the Soft sources. The median
(50%), 99% and 99.9% levels from random simulations are also shown.
96

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
band sample. When we repeated both correlation tests to this sample, we found
that the clear correlation signal observed in the full Soft sample dissapeared
(see Table 4.1, sixth row, and Figure 4.5). We also repeated this test keeping at
random a half and two thirds of the Soft sources, finding correlation at the 99%
significance level only in the last case. Hence we conclude that clustering in the
Hard and Ultrahard bands may be at least as strong as in the Soft band, but our
relatively low number of sources prevent us from detecting it, which would
be consistent with the results of [84] who did not find significant differences
between the clustering properties of soft and hard X-ray selected sources in the
CDF.
The significant clustering found for the P µ (N θ ) test in the Soft band corresponds
to a broad bump between ∼150 and ∼700 arcsecs, with secondary peaks at
∼300, ∼400 and ∼650 arcsecs, the first two reaching 99.9% significancies (see
Figure 4.3, top panel). These peaks also appear in the XID band (see Figure 4.4,
top panel). While the increase in the number of real pairs that produce the
broad bump is very gradual, the narrow peaks must correspond to significant
increases in relatively narrow ranges of angular distances. To investigate
whether these peaks come from a small number of fields in particular, we divided
the Soft sample between the fields in the northern and southern Galactic
hemispheres respectively. We performed the 1 − P µ (N θ ) test on these regions
(see Figure 4.6) finding that, despite the lower significance of the results due to
the lower number of sources, the broad bump and the peaks are still present
in both hemispheres as well as the ∼300 arcsec peak. The peak at ∼400 arcsecs
appears predominantly in the northern hemisphere while the peak at ∼650 arcsecs
is much more significant in the southern hemisphere.
We have repeated analysis excluding the two fields with obvious cluster emission
(A1837 and A399) from the northern and southern Galactic hemispheres,
respectively, but there were no significant changes in the strength or the position
of the peaks. Additionally, we have performed this test one more time on a
sample composed of the 7 deeper fields (exposure time over 40 ks, ∼400 sources)
and in the remaining 27 fields (∼800 sources) to see whether the signal is introduced
by a few deep fields. We found strong correlation only in the latter case
and hence the signal must be relatively widespread over the survey area. This
means that if it has cosmic origin, it must be generated by sources at z ≤ 1.5,
which is the peak of the redshift distribution of medium-depth X-ray surveys
([12]).
97

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.6 1 − P µ (N θ ) versus θ for the soft fields in the northern Galactic hemisphere
(top panel) and southern Galactic hemisphere (bottom panel). The median (50%), 99% and
99.9% levels from random simulations are also shown. The Y-axis scaling is different in
each panel for clarity.
98

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
4.3.4 Angular correlation of a hardness ratio selected sample
The low significance or even the absence of the clustering signal detected in the
hard band is a surprising result since it is known that most of the sources at the
fluxes of our sources are AGN ([12]), which are known to be strongly clustered
when selected both in X-rays ([161], [242]) and optically ([44]). Additionally,
obscured AGN are more common in hard X-ray selected samples ([30], [50],
[12]). However, we have just seen in section 4.3.3 that the significance of the
clustering signal depends strongly on the density of sources in the fields under
study. If the source density is too low, the signal might be dilluted and therefore
we obtain results compatible with a no-clustering scenario, even if angular
clustering is present.
Furthermore, in [72] is shown that, in spite of the absence of significant angular
clustering in their hard sample, when they selected the sources with the hardest
spectrum (using their hardness ratio as a discriminator) the significance of
the detection increased to 2-3σ. To select this sample, they had to reduce the
significance of the detection threshold so as to increase the number of sources
available to perform the analysis.
Since this could be a potentially interesting result, we have performed a similar
analysis defining the same hardness ratio HR = (H − S)/(H + S) where H and
S are the 2-12 keV and 0.5-2 keV count rates, respectively. We have selected the
sources in either the Soft and Hard band which have HR ≥ −0.2 (same as in
section 3.3).
The F-test indicate correlation at >99% confidence level (see Table 4.1, fifth
row), but when we perform the Poisson 1 − P µ (N θ ) method no clustering is
detected at any angular scale (see Figure 4.7), with the data consistent with
the median of the random simulations. We cannot thus confirm the results obtained
in [72], in spite of having a slightly larger sample of sources (250 versus
209 in [72]). Moreover, this would be in agreement with the results of [242],
who could not find any dependence on the shape of the source spectra in their
spatial clustering analysis.
4.3.5 Inversion of Limber’s equation
The two-dimensional angular correlation function is a projection in the sky of
the real three-dimensional spatial correlation function ξ(r) along the line of
99

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.7 Top panel: w(θ) versus θ. Symbols are the same as in Fig. 4.1. Bottom panel:
1 − P µ (N θ ) versus θ for a HR selected sample (HR ≥ −0.2). The median (50%), 99%
and 99.9% levels from random simulations are also shown.
100

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
sight, where r is the physical separation between sources.
We can model the spatial correlation function as ([53]):
ξ(r, z) =
( r
r 0
) −γ
(1 + z) −(3+ɛ) (4.3.10)
where ɛ parametrizes the type of clustering evolution. For instance, if ɛ =
γ − 3, the clustering is constant in comoving coordinates, which means that the
amplitude of the correlation function remains fixed with redshift in comoving
coordinates as the pair of sources expands together with the Universe. On the
other hand, if ɛ = −3 the clustering is constant in physical coordinates ([53]).
The angular amplitude θ 0 can be related to the spatial amplitude r 0 by inverting
Limber’s integral equation ([175]). In the case of a spatially flat Universe,
Limber’s equation can be expressed as ([18]):
w(θ) = 2
∫ ∞
0
∫ ∞
0 D4 C φ2 (D c )ξ(r, z)dD c du
(∫ ∞
0 D2 c φ(D c)dD c
) 2
(4.3.11)
where φ(D c ) is the selection function (the probability that a source at a comoving
distance D c is detected in the survey). The comoving distance D c is related
to the redshift through ([110]):
D c (z) =
c H 0
∫ z
0
dz ′
E(z ′ )
(4.3.12)
with:
E(z) =
[
Ω m (1 + z) 3 + Ω Λ
] 1/2
(4.3.13)
in a spatially flat Universe (Ω k = 0), and H 0 being the Hubble constant ([175],
[110]).
The number of objects in a survey that subtend a solid angle Ω S in the sky
within a redshift shell dz is:
( )
dN
c
dz = Ω SDc 2 φ(D c ) E −1 (z). (4.3.14)
H 0
101

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Combining these equations, Limber’s equation becomes:
w(θ) = 2 H 0
c
∫ ∞
0
( 1
N
)
dN 2 ∫ ∞
E(z)dz ξ(r, z)du. (4.3.15)
dz
0
Considering that the physical separation between two sources that project an
angle θ in the sky can be written as:
r ≃ 1
1 + z (u2 + x 2 θ 2 ) 1/2 (4.3.16)
under the small angle approximation assumption, if we now combine equations
4.3.10 and 4.3.15 we obtain:
where
θ γ−1
0
= H γ
(
r
γ
0 H 0
c
) ∫ ∞
( 1
N
0
)
dN 2
E(z)(1 + z) −3−ɛ+γ
dz Dc
γ−1 (z)
dz (4.3.17)
with Γ being the gamma function.
H γ = Γ( 2 1 γ−1
)Γ(
2 )
Γ( γ 2 ) (4.3.18)
We can now invert this equation and obtain r 0 given an angular amplitude θ 0 ,
but we also need to determine the source redshift distribution dN/dz. Since
we have no redshift information of the AXIS sources we can approximately
measure dN/dz using an estimate of the AGN luminosity function. We can
do that via the equation 4.3.14 writing the selection function (degradation of
sampling as a function of the distance in flux-limited surveys) as:
φ(D c ) =
∫ ∞
L min (z)
Φ(L x , z)dL x (4.3.19)
which depends on the evolution of the source luminosity function Φ(L x , z) but
is independent of the cosmological model.
We have determined the selection function (see Figure 4.8) of the AXIS sources
using a luminosity function following a Luminosity-dependent Density evolution
model (see Chapter 5). The best-fit model used for both the Soft and Hard
bands is that obtained for the luminosity function of the XMS sources along
with other deeper and shallower surveys (see Chapter 5 for details). The computed
redshift distribution plotted in Figure 4.8 has been calculated using the
102

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Figure 4.8 The redshift selection function for the AXIS soft (solid line) and hard (dashed
line) sources.
103

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Table 4.2 Spatial correlation lengths r 0 for different clustering models (ɛ) obtained from
Limber’s equation. The slope γ is equivalent to that of Table 4.1
Band (Ω m , Ω Λ ) γ ɛ r 0 (Mpc)
Soft (0.3,0.7) 1.8 -1.2 17.6 +2.4
−2.9
Soft (0.3,0.7) 1.8 -3 8.9 +1.2
−1.5
Soft (0.3,0.7) 2.2 -0.8 11.1 +2.0
−2.9
Soft (0.3,0.7) 2.2 -3 6.8 +1.3
−1.7
Hard (0.3,0.7) 1.8 -1.2 5.5 +2.4
−5.5
Hard (0.3,0.7) 1.8 -3 4.8 +2.1
−4.8
Hard (0.3,0.7) 2.1 -0.9 2.6 +1.7
−2.6
Hard (0.3,0.7) 2.1 -3 2.5 +1.6
−2.5
effective area Ω of AXIS so that it is representative of this sample. Our results
on the inversion of Limber’s equation for different clustering evolution parameters
are listed in Table 4.2.
In the Soft band, our r 0 results using the canonical slope γ ≡ 1.8 and a comoving
clustering model ɛ = −1.2 are fully compatible with those of [18],
but significantly larger than those obtained for optically selected AGN surveys
r 0 ≃ 5.4 − 8.6h −1 Mpc ([3], [43], [89]) and for X-ray selected surveys ([161],
r 0 ≃ 7.4h −1 Mpc). Nonetheless, if we assume that the clustering remains constant
for physical coordinates ɛ = −3, our results and those of [18] are in excellent
agreement with the results of [161].
In the Hard band, our deprojected spatial amplitude is significantly lower than
the value from [17] who obtained r 0 ≃ 12 − 19h −1 Mpc using hard sources
from the XMM-Newton 2dF survey. However, they find that their correlation
length are much larger (over a factor 2) than the ones provided in the literature
for AGN ([45]) or 2dF ([105]) and SDSS ([29]) galaxy distributions. In fact, the
r 0 values obtained by [17] can be compared instead to that of Extremely Red
Objects (EROs) and luminous radio sources ([193], [168], [197]) which are in the
range r 0 ≃ 12 − 15h −1 Mpc. One of the latests works in deprojection of the
angular correlation function is [159], who use the sources in the XMM-Newton
COSMOS field. If we compare our results in the hard band to theirs it can be
seen that we are fully consistent (within the 1-σ level) with their results for the
104

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
2-4.5 keV band, although we are sistematically below their values (at ∼2σ) in
the 4.5-10 keV band. It must be taken into account that the values of θ 0 which
we have used to invert Limber’s equation in the hard band correspond to a
marginal detection (or no detection at all) of angular clustering in that band,
and hence we might be underestimating that value somehow. We would like to
stress that the absence of angular clustering measured in the hard band is likely
to be due to the low number of pairs of sources per field compared that of the
soft band (see section 4.3.3).
4.4 Spatial clustering of XMS sources
The angular correlation function discussed in section 4.3 is an useful tool as
a first approach to the clustering analysis of a sample which lacks reliable redshift
determinations or has low identification completeness. However, it is only
a rough measure of the real clustering problem since it deals with projected angular
distances in the sky between sources that might be at different redshifts
and therefore do not form part of the same physical structure and belong to different
populations. A three-dimensional deprojection of the angular clustering
can be done by inverting Limber’s equation as explained in section 4.3.5 assuming
a redshift distribution. Since the XMS sample (see section 2.2) is highly
identified in all energy bands, we will make use of it to check whether our AGN
present spatial clustering.
4.4.1 Method
As we explained in section 4.3.1, the most common method employed to quantify
clustering is the two-point correlation function ([174]), which measures the
excess probability of finding a pair of objects as a function of the physical separation
between them. The spatial equivalent to equation 4.3.1 is:
δP = n 2 0 δV 1δV 2 [1 + ξ(r)] (4.4.1)
where n 0 is the mean density of objects and r is the comoving distance between
two sources. ξ(r) is the two-point spatial correlation function. If the distribution
of objects is random and homogeneous the probabilities of finding objects
105

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
in the comoving volumes δV 1 and δV 2 are independent such that ξ(r) = 0. If
objects are more clustered than this homogeneous distribution, then ξ(r) > 0.
Analogously to the angular correlation function, the spatial one is well described
by a power law model:
ξ(r) =
( r
r 0
) −γ
(4.4.2)
To compute the correlation function we have chosen the estimator proposed by
[131], which has been demonstrated to minimise the variance:
ξ(r) = N r(N r − 1) DD(r)
N d (N d − 1) RR(r) − N r − 1 DR(r)
N d RR(r) + 1 (4.4.3)
where DD(r) is the number of actual data pairs with a separation r in redshift
space. Similarly, RR(r) is the number of random pairs and DR(r) is the number
of pairs having one real and one randomly simulated source at the same separation
r. N d and N r are the total number of objects in the sample and the number
of objects in the random sample, respectively. The uncertainties are calculated
assuming that the error of the DR and RR pairs are zero, and the uncertainty of
the DD pairs is Poissonian ([242]):
∆ξ(r) = 1 + ξ(r) √
DD(r)
. (4.4.4)
To calculate the comoving distances r between pairs of sources we use the standard
relations described in [175] or [110]. The transverse comoving distance
between the observer and an object at redshift z is:
⎧
⎪⎨
D M =
⎪⎩
1
D H √ sinh[ √ D
Ω C
Ωk
k D H
] ; i f Ω k > 0
D C ; i f Ω k = 0
1
D H √ sin[√ |Ω |Ωk | k | D C
D H
] ; i f Ω k < 0
⎫
⎪⎬
⎪⎭
(4.4.5)
where D C is:
D C = D H
∫ z
0
dz ′
√
ΩM (1 + z ′ ) 3 + Ω k (1 + z ′ ) 2 + Ω Λ
(4.4.6)
106

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
and D H is the Hubble distance:
D H = c H 0
. (4.4.7)
If we consider two sources separated in the sky an angle θ and with transverse
comoving distances to the observer D M1 and D M2 , respectively, the comoving
separation of the second object measured from the first object is ([161]):
r =
√
d 2 D 2 M1 + D2 M2 − 2dD M1D M2 cosθ (4.4.8)
where ([167], [148])
d =
√
1 + Ω k
(
H0 D M1
c
⎡ √
) 2
+ D M1cosθ
⎣1 −
D M2
1 + Ω k
(
H0 D M2
c
) 2
⎤
⎦ . (4.4.9)
In a spatially flat Universe (Ω k = 0), d = 1 and equation 4.4.8 reduces to the
cosine rule for Euclidean space:
r =
√
D 2 M1 + D2 M2 − 2D M1D M2 cosθ. (4.4.10)
The procedure to generate the random sample is very similar to that we followed
for the angular clustering. We formed a pool with real sources with detection
likelihood higher than 15 in the band under study and a secure redshift
identification. For each field, we drew a source from the pool and generated
its new position at random but keeping its distance to the optical axis of the
telescope (see section 4.3.1) and checked whether its count rate was above the
field sensitivity map. In this case, the source is kept, along with its redshift,
and a new source is drawn from the pool until the number of extracted random
sources is equal to the number of real sources in the field. If the source count
rate is below the sensitivity map in the new position, the source is discarded
and the procedure is repeated. Following this method, the average redshift distribution
of the simulated samples resembles the real distributions with great
accuracy (see Fig. 4.9).
107

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
Number of sources
Number of sources
0 10 20 30
0 10 20 30
0 1 2 3 4
Redshift
0 1 2 3 4
Redshift
Figure 4.9 Redshift distributions of the real XMS (solid) and the average simulated
sources (dashed) in the Soft (top panel) and Hard band (bottom panel).
108

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
4.4.2 Results
Unlike the angular correlation function of AXIS sources (see section 4.3.2) and
the predictions obtained via the inversion of Limber’s equation (see section 4.3.5)
based in that results, we do not find evidence of spatial clustering in the XMS
sample.
Our results for the spatial correlation function are shown in Fig. 4.10. Red triangles
are the estimate of the spatial correlation in the absence of clustering,
calculated via simulations of a random homogeneous distribution similarly as
we did when we evaluated the integral constraint in section 4.3.2. It can be
seen that in both Soft and Hard bands that such a bias is almost negligible in
this case and that our method obtains the expected value ξ(r) = 0 for a truly
random distribution of sources. Black solid dots in Fig. 4.10 represent the ξ(r)
of XMS sources at different spatial scales. It is clear that our results are fully
compatible with no clustering in both bands.
These results are in contradiction with a group of recent spatial clustering works
([45], [161], [84], [242]). They all find strong clustering evidence fitting a power
law in the form of equation 4.4.2. [45] uses more than 10000 sources from the
2dF QSO Redshift (2QZ) survey, obtaining spatial correlation lengths about
r 0 ≃ 5.7 ± 0.5h −1 Mpc and slopes γ ≃ 1.6 ± 0.1, quite similar to the known
clustering values of local normal galaxies ([221], [188]). In [161] they use over
200 AGN from the ROSAT NEP survey ([233]) to calculate the spatial correlation
function. They claim to have found significative clustering (>4-σ) in the
0.5-2 keV band with r 0 = 7.5 +2.7
−4.2 h−1 Mpc and γ = 1.85 +1.90
−0.8
, also consistent
the values found for normal galaxies and optically selected AGN. [84] have
made use of the CDF North and South surveys (see section 2.3) gathering 240
and 124 sources, respectively, finding r 0 = 8.6 ± 1.2h −1 Mpc in the CDF-S and
r 0 = 4.2 ± 0.4h −1 Mpc in the CDF-N, respectively, with slopes mutally compatible:
γ = 1.33 ± 0.11 and γ = 1.42 ± 0.07. [242] have also used Chandra sources
from the CLASXS survey in the 2-8 keV band, which sum up to 233 sources.
They found strong clustering (>6.7σ) for pairs at scales

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
ξ(r)
ξ(r)
−2 −1 0 1 2
−2 −1 0 1 2
100 1000
r (Mpc)
100 1000
r (Mpc)
Figure 4.10 ξ(r) versus r of XMS sources in the Soft (top panel) and Hard band (bottom
panel). Solid dots are the observed values. Red triangles are the values obtained for a
random homogenous simulated sample.
110

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
131 in the Hard band) have found such strong evidences of clustering while we
have not. This can be explained in terms of the dillution of the signal across
the sky. The XMS survey consists of 25 fields widely spread over the sky (see
section 2.2), which means that, given the amount of sources stated above, the
source density is scarce (about 7 sources per field in the Soft band, only about 5
in the Hard band). If all our sources were concentrated in a single deep pencilbeam
field or in a few contiguous fields, we would probably have reported an
spatial clustering signal similar to that found in the literature.
4.5 Summary
In this chapter we have studied the large scale structure of the extragalactic
sources (mainly AGN) comprised in the AXIS and XMS surveys. After excluding
two fields in which the presence of stellar clusters would have distorted our
results, we used the AXIS sources to study the presence of cosmological structure
in the X-ray sky through the cosmic variance in the number of sources per
field and the distribution of the angular separations between pairs of sources.
The former method is in principle more sentitive to the presence of significant
overdensities in a few fields, while the latter detects any overall angular clustering
of sources. No cosmic variance is detected at all in the Hard (2-10 keV) and
Ultrahard (4.5-7.5 keV) bands while some signal at the ∼90% level is present in
the Soft (0.5-2 keV) and XID (0.5-4.5 keV) bands, probably due to their larger
number of sources.
Angular clustering studies the excess probability of finding a pair of sources at
a given angular distance projected in the sky. We have studied it in two ways.
The first is the standard two-point angular correlation function w(θ). Using
this method we have detected evidence of clustering at about the 99% level in
the Soft and XID bands but not in the Hard and Ultrahard bands (see Table 4.1
and Figures 4.1 and 4.2). The strength of the clustering signal we have found is
intermediate between those of previous results ([72], [18], [17], [229]). A more
appropiate method using Poisson statistics detects clustering at the 99-99.9%
level in the Soft and XID bands, but again not in the Hard and Ultrahard bands
(see Figures 4.3 and 4.4). We have checked that if we remove at random two out
every three sources in the soft sample, the clustering signal disappears which
implies that angular clustering may also exist in the hard band but we have
111

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
failed to detect it due to the smaller number of sources in that band. Dividing
the soft sample into several subsamples reveals that the signal is widespread
over the sky and it is not limited to a few deep fields. This means that if this
structure has a cosmic origin it must come from z ≤ 1.5, the peak of the redshift
distribution of medium flux surveys ([12]). Additionally, we cannot confirm the
detection of clustering signal among hard-spectrum sources reported by [72].
We have used the angular amplitudes θ 0 obtained in the angular correlation
function and some assumptions in the luminosity function of these sources to
deproject these values by inverting Limber’s equation in order to find an estimate
of their spatial clustering. The deprojected spatial amplitudes r 0 that we
have found for the AXIS sources are in agreement with those calculated by [18]
and [161] in the Soft band for different clustering models. In spite of the lack of
signal in the hard band, the values of r 0 obtained in this band are also in excellent
agreement with those of [159] using sources from the COSMOS survey, but
not with the ones of [17] which are sistematically larger than any other spatial
correlation lengths reported for AGN.
The XMS sample has very high completenesses of secure espectroscopic redshifts
in all bands. Since we can compute the real physical distances between
these sources, we have studied the possible spatial clustering among them. For
that, we have calculated the two-point spatial correlation function in the Soft
and Hard bands, without finding evidences of large scale structure in the redshift
space (see Figure 4.10). Previous works with number of sources comparable
to ours ([161], [84] or [242]) have reported strong spatial clustering for
AGN. This discrepancy can be explained in terms of the dillution of the clustering
signal since the XMS fields are widespread over the sky leading to a low
source density (about 7 and 5 sources per field in the Soft and Hard bands,
respectively).
112

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
114

Chapter 5
Luminosity function of XMS sources
5.1 Motivation
One of the main goals of X-ray surveys is to study the comological properties
of Active Galactic Nuclei (AGN) as they are strongly linked to the accretion history
of the Universe and the formation and growth of the supermassive black
holes that are believed to reside in the centre of all galaxies, active or not ([126],
[141], [190]). The first studies in this field were constrained to the soft X-ray
band (≤2 keV) which could be biased against absorbed AGN ([140], [23], [172],
[157]). Therefore, hard X-ray surveys (>2 keV) are essential to describe the
luminosity function of the entire AGN population, including obscured AGN
which are the main contributors to the cosmic X-ray background (see [64] for
a review). Moreover, the large majority of energy density generated by accretion
power seems to take place in obscured AGN ([65]), as demonstrated by
the integrated energy density of the cosmic X-ray background (see e.g. [42],
[83]). Not taking into account the obscured AGN population could therefore
bias our understanding of the cosmic evolution of the structures in the X-ray
Universe. Furthermore, it has been confirmed that the fraction of absorbed
AGN decreases with increasing X-ray luminosity in X-ray selected samples of
AGN ([224], [215]) as well as in optically selected AGN (i.e. [212]). On the contrary,
some authors claim to have found a positive evolution of the fraction of
absorbed AGN with redshift ([130], [220] and, more recently, [100]) while others
([224], [57], [83]) have not.
Hard X-ray photons with energies

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
sources with intrinsic column densities up to N H < 10 24 cm −2 , although they
are not energetic enough to escape from Compton-thick objects (N H > 1.5 ×
10 24 cm −2 , for which the Compton-scattering optical depth σ T equals unity).
Previous hard X-ray surveys in the 2-10 keV band ([32], [69], [79], [4]) have provided
unbiased and highly complete samples of sources, many of them being
obscured AGN. Notwithstanding this, an important fraction of the AGN detected
in deep fields fail to provide good quality X-ray information, and their
optical counterparts are far too faint to make reliable spectroscopic identifications
of the totality of the samples.
Previous works have studied the X-ray luminosity function (XLF, hereafter) of
AGN, mainly in the 0.5-2 keV and 2-10 keV bands. For instance, [157] and [104]
studied the the 0.5-2 keV XLF of AGN testing a variety of models. Their results
seem to rule out both Pure Luminosity and Pure Density Evolution models in
favour of a Luminosity Dependent Density Evolution model. This paper aims
to confirm this results and to improve the accuracy of the determination of the
model parameters by using a sample that contains ∼30% more AGN than the
[157] sample and is comparable to that of [104].
[211] studied the XLF of high redshift AGN in the 2-8 keV band but they did
not consider the intrinsic absorption of the sources due to the limited count
statistics. Other works in the 2-10 keV band such as [224] and [130] have taken
into account the N H distribution of the sources when calculating the XLF, but
an important fraction of the N H values were derived from the hardness ratios
of the sources rather than from a spectral analysis. This may introduce a certain
degree of uncertainty since a template spectrum has to be assumed to compute
the N H . The XLF of very hard sources (>5 keV) is almost unexplored so far with
the exception of the work by [48], who studied the de-evolved (z = 0) luminosity
function of absorbed and unabsorbed AGN in the 4.5-7.5 keV band but was
unable to perform detailed evolutionary studies due to the low statistics.
In this chapter we use the XMM-Newton Medium Survey (XMS, [12], see section
2.2), along with other highly complete deeper and shallower surveys, to
compute the X-ray luminosity function (XLF, hereafter) in several energy bands.
Furthermore, given the availability of high-quality X-ray spectral information
in the XMS, we are able to model the intrinsic absorption of the hard sources
(those detected in the 2-10 and 4.5-7.5 keV bands) as a function of the X-ray
luminosity up to column densities of ∼ 10 24 cm −2 . These issues are key tools
116

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
to probe the accretion history of the Universe across cosmic time. Thanks to
the extremely high identification completeness of the XMS sample and the accompanying
surveys we have assembled an overall sample of ∼1000 identified
AGN in the 0.5-2 keV, ∼450 identified AGN in the 2-10 keV band, and ∼120
identified AGN in the 4.5-7.5 keV bands, leading to one of the largest and most
complete sample up to date in all three energy bands.
This chapter is organized as follows: in section 5.2 we study the absorbing column
density distribution of the spectroscopically identified AGN detected in
hard X-rays (>2 keV) and we model the intrinsic fraction of absorbed AGN as
a function of both luminosity and redshift in the 2-10 and 4.5-7.5 keV bands.
In section 5.3 we discuss the method used to compute the X-ray luminosity
function of AGN in several energy bands using two methods: a modified version
of the classic 1/V a method to construct binned luminosity functions, and a
Maximum Likelihood fit technique to an analytical model using all the sources
available without binning. In section 5.4 we discuss the results obtained and we
compare them with those obtained in previous works. Finally, the conclusions
extracted from this work are reported in section 5.5.
Throughout this chapter we have assumed a cosmological framework with
H 0 = 70 km s −1 Mpc −1 , Ω M = 0.3 and Ω Λ = 0.7 ([213]).
5.2 The N H function
In this chapter we are pursuing to calculate the cosmological evolution of the
X-ray luminosity function of all AGN (both Type-1 and Type-2) within our sample
in three energy bands. This should be done by calculating the intrinsic (before
absorption) luminosity and absorption (N H ) function in order to obtain
purely observation-based results. Since hard X-ray photons are less affected
by absorption, absorbed AGN are more likely to be detected at energies above
2 keV and hence we have applied such method to the hard (2-10 keV) and ultrahard
(4.5-7.5 keV) sources, for which we have detailed spectral information
(photon index Γ and instrinsic absorbing column densities N H ). The ultrahard
sources are particularly interesting since we would expect to detect absorbed
sources more easily in this band than in the softer ones. Around 25% of the
XMS sources in the Hard and Ultrahard bands have been classified as Type-2
AGN, having most of them an intrinsic log N H > 22, which is the N H value
117

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
log N h
20 22 24
AGN1
AGN2
42 42.5 43 43.5 44 44.5
log L x (4.5−7.5 keV)
Figure 5.1 Intrinsic N H versus X-ray luminosity of XMS sources detected in the Ultrahard
band. Dots represent those sources identified as Type-1 AGN while the Triangles
are those classified as Type-2 AGN. The dashed line at log N H = 22 marks the standard
separation between absorbed and unabsorbed AGN.
commonly used to separate absorbed AGN from the unabsorbed ones (see Figure
5.1). An appropiate calculation of the XLF of these sources would therefore
require a previous modelling of the intrinsic absorption in order to avoid possible
selection effects. On the contrary, sources detected in the soft band (0.5-
2 keV) are so strongly affected by absorption that we can assume that we are
mainly sampling unabsorbed AGN in this band.
The N H function f (L X , z; N H ) is a probability distribution function for the absorption
column density as a function of the X-ray luminosity and redshift. It is
measured in units of (log N H ) −1 and is normalized to unity over a defined N H
region:
∫ log NH max
f (L X , z; N H )d log N H = 1 (5.2.1)
log N Hmin
We have chosen the N H limits to be log N Hmin = 20 and log N Hmax = 24 given
118

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
the intrinsic N H range spanned by our joint samples (see Figure 5.2).
The observed fraction of obscured AGN (those with log N H > 22) is measured
by the parameter ψ, which is generally function of the both luminosity and
redshift. If we compare the value of ψ at different luminosity ranges we observe
that the fraction of absorbed AGN is not constant, decreasing as the luminosity
increases in both the hard and ultrahard bands (see Figures 5.3 and 5.4). On the
other hand, there is not significant variation in the value of ψ with redshift at
a given luminosity in the ultrahard band (see Figure 5.4), which can be partly
explained by the poor redshift coverage of this sample. The fraction, however,
clearly increases with redshift in the case of the hard band (see Figures 5.3).
We will therefore assume that the formal expression of ψ is dependent on both
the X-ray luminosity and redshift and hence we have formalized it as a linear
function of both log L X and z, similarly as in [130]:
ψ(L X , z) = ψ 44 [(log L X − 44)β L + 1] [(z − 0.5)β z + 1] (5.2.2)
where ψ 44 is the fraction of absorbed AGN at log L X = 44 and z = 0.5, and
β L and β z are the slopes of the linear dependencies on luminosity and redshift,
respectively.
Given equation 5.2.1, the normalized N H function can be written as:
f (L X , z; N H ) =
{ 1−ψ(LX ,z)
2
; 20 ≤ log N H < 22
ψ(L X ,z)
2
; 22 ≤ log N H ≤ 24
}
(5.2.3)
In order to obtain the best-fit values of the free parameters ψ 44 , β L and β z we
have performed a χ 2 fit on the sources of the hard and ultrahard samples, although
in the latter case we have fixed β z = 0 to account for the absence of
dependence on redshift observed in this band. The values thus obtained are
ψ 44 = 0.41 +0.03
−0.04 , β L = −0.22 +0.04
−0.05 and β z = 0.57 +0.12
−0.10
for the hard band, and
ψ 44 = 0.22 ± 0.04 and β L = −0.45 +0.20
−0.25
for the ultrahard band (see Table 5.2).
The 1σ errors correspond to ∆χ 2 = 1. The expected fraction of absorbed AGN
in the hard band at z = 0 is ψ 44 = 0.29 ± 0.05, while the expected fraction in
the ultrahard band coverted to the 2-10 keV band is ψ 44 = 0.27 ± 0.08, mutually
consistent with each other.
If we compare these results with those of [224] and [130], we find that our bestfit
value at log L 2−10 = 44 (ψ 44 = 0.41 +0.03
−0.04
) is in excellent agreement with the
119

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
log L < 43.5
43.5 < log L < 44.5
log L > 44.5
All Sample
0 10 20 30 40 10 20 30 40 50 10 20 30 40
50 100
20 20.5 21 21.5 22 22.5 23 23.5 24
log N h
(cm −2 )
log L > 43.75
43 < log L < 43.75
0 10 20
log L < 43
All Sample
5 10
0 2 4 6 8
0 10 20 30 40
20 20.5 21 21.5 22 22.5 23 23.5 24
log N h
(cm −2 )
Figure 5.2 Observed N H distributions of the joint XMS/AMSS/CDF-S sample in the
Hard band (Top panel) and XMS/HBSS sample in the Ultrahard band (Bottom panel),
respectively. The distribution is shown for the full sample and in different luminosity
ranges. The first bin accounts for both the sources only observed in that bin (lower
step) and these sources plus the sources with log N H < 20 or uncomputed absorptions
(higher step). 120

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Fraction of Absorbed AGNs
0.2 0.4 0.6
41 42 43 44 45 46 47
log L X (2−10 keV)
Fraction of Absorbed AGNs
0.2 0.4 0.6 0.8
43.5 < log L 2−10
< 44.5
0.5 1 1.5 2 2.5 3
Redshift
Figure 5.3 Top panel: Fraction of absorbed AGN as a function of the 2-10 keV luminosity.
Bottom panel: Fraction of absorbed AGN as a function of redshift in the luminosity range
log L X = 43.5 − 44.5. Dashed lines represent the best-fit model of the N H function using
N H = 10 22 cm −2 as the dividing value between obscured and unobscured AGN.
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CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Fraction of Absorbed AGNs
0.1 0.2 0.3 0.4 0.5
Fraction of Absorbed AGNs
0 0.2 0.4 0.6
42 43 44 45 46
log L X (4.5−7.5 keV)
43 < log L < 43.75
0.2 0.4 0.6 0.8
Redshift
Figure 5.4 Top panel: Fraction of absorbed AGN as a function of the 4.5-7.5 keV luminosity.
Bottom panel: Fraction of absorbed AGN as a function of redshift in the luminosity
range log L X = 43 − 43.75. Dashed lines represent the best-fit model of the N H function
using N H = 10 22 cm −2 as the dividing value between obscured and unobscured AGN.
122

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
ones calculated by [224] (ψ 44 = 0.41 ± 0.03) and [130] (ψ 44 = 0.42 +0.03
−0.04
). [100]
found a strong linear decrease from ∼80% to ∼20% in the range log L X = 42 −
46. A linear fit to the data in Table 5 of [100] yields a best-fit value at log L 2−10 =
44 of 0.38 ± 0.04, and a slope of −0.226 ± 0.014, also in agreement with our
results in the 2-10 keV band within the error bars.
The decrease in the absorbed AGN fraction at high luminosities have been reported
by many authors ([224], [130], [2]). In [130] is also reported that the
absorbed fraction is also dependent on redshift. Redshift dependency is also
found by [220] while [57] did not find dependence on either the luminosity and
redshift. In a recent paper, [100] has found a strong decrease in the fraction of
absorbed AGN with X-ray luminosity and a significant increase of that fraction
with redshift. The result of [100] suggests that the evolution of this fraction at a
fixed luminosity of log L 2−10 = 43.75 is faster than the result obtained by [220]
(probably due to the fact that the latter used the Broad Line AGN classification
only, which tends to overestimate the fraction of absorbed AGN at low redshifts)
and is consistent with our best fit model at a typical redshift of z = 0.5
(ψ(z = 0.5) = 0.37 ± 0.07 against our prediction of ψ(z = 0.5) = 0.39 ± 0.08).
The lack of dependence on redshift in our ultrahard sample, however, must be
handled with caution since it comes from two similar XMM-Newton surveys
only and spans a limited redshift range. As stated in [178], who found no luminosity
dependence in a sample of 117 sources in the 2-10 keV band, deeper
X-ray surveys are needed to take into account those sources at higher redshifts
and lower luminosities in order to fully investigate the true incidence of absorption.
Only combining several surveys at different depths, as we have done
in the hard band, and therefore covering wider regions in the L X − z plane is
possible to unveil the real dependencies.
In a recent work ([48]) the dependency on luminosity of the fraction of absorbed
AGN detected in the 4.5-7.5 keV band is calculated using N H = 4 × 10 21 cm −2 as
the dividing value between obscured and unobscured AGN. This corresponds
to A V ∼ 2 magnitudes for a given Galactic A V /N H ratio of 5.27 × 10 22 mag
cm −2 which is the best dividing value between optical Type-1 AGN and optical
Type-2 AGN in the HBSS sample (see section 2.3) as shown in [31].
In we repeat the calculations in the ultrahard band using this N H value as a
dividing line we obtain ψ 44 = 0.30 +0.04
−0.05 and β L = −0.42 +0.15
−0.18
as the best fit parameters
for the N H function. They are slightly different but consistent within
123

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
the 1σ error bars to those calculated with a dividing value of N H = 10 22 cm −2 .
[48] also found a fraction of absorbed AGN with L 2−10 ≥ 3 × 10 42 erg s −1 of
0.57 ± 0.11 which was in excellent agreement with the results obtained by a variety
of SWIFT and INTEGRAL surveys (see Table 3 in [48]). The value predicted
by our ultrahard N H function, converting 2-10 keV luminosities to 4.5-7.5 keV
using Γ = 1.7, is 0.55 ± 0.18 using a dividing value of N H = 4 × 10 21 cm −2 ,
which fully agrees with that of [48]. Considering a dividing value of N H =
10 22 cm −2 , our predicted fraction decreases to 0.42 ± 0.18 which coincides with
the INTEGRAL result of [201] (0.42 ± 0.09) who also used the latter dividing N H
value between absorbed and unabsorbed AGN. The predicted fraction in the
hard band at L 2−10 ≥ 3 × 10 42 erg s −1 is 0.39 ± 0.09, still consistent with the
value of [201].
5.3 Method
In this section we will calculate the X-ray luminosity function of our sources
in the soft, hard and ultrahard bands. Although the backbone of this study
is the XMS sample, it is imperative to combine it with other complementary
shallower and deeper surveys in order to cover a wider L x − z range. Shallower,
wider area surveys will provide significant numbers of bright sources at low
redshifts while deep pencil-beam surveys will probe fainter sources at greater
distances. The accompanying surveys used in this chapter are summarized in
Table 5.1 and they have been described in section 2.3.
In order to have an optimal L X − z plane coverage (see Figure 5.5) we will constrain
our analysis to those sources identified as AGN with redshifts in the
range 0.01 < z < 3 in the soft and hard bands (spanning up to seven and
six orders of magnitude in luminosity, respectively) and 0.01 < z < 2 in the
ultrahard band (spanning up to four orders of magnitude in luminosity). The
total sky area covered by these surveys is shown in Figure 5.6. For the purposes
of this work and to avoid errors and biases caused by further classification, we
have used the entire AGN population available (within the redshift limits stated
above) irrespective of whether they were identified as Type-1 AGN or Type-2
AGN.
The differential XLF measures the number of AGN per unit of comoving vol-
124

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Table 5.1 Summary of surveys used in this work, along with their flux limits, sky coverage,
identification completeness and the number of identified AGN for each energy
band.
Soft (0.5-2 keV)
Survey Flux limit (erg cm −2 s −1 ) Area (deg 2 ) Completeness (%) N AGN
RBS 2.5×10 −12 20300 100 310
RIXOS8 8.4×10 −14 4.44 100 40
RIXOS3 3.0×10 −14 15.77 94 182
XMS 1.5×10 −14 3.33 96 178
RDS 5.5×10 −15 0.30 92 39
CDF-S 5.5×10 −17 0.12 100 a 226
Hard (2-10 keV)
Survey Flux limit (erg cm −2 s −1 ) Area (deg 2 ) Completeness (%) N AGN
AMSS 3.0×10 −13 68 99 79
XMS 3.3×10 −14 3.33 84 120
CDF-S 4.5×10 −16 0.11 100 a 236
Ultrahard (4.5-7.5 keV)
Survey Flux limit (erg cm −2 s −1 ) Area (deg 2 ) Completeness (%) N AGN
HBSS 7.0×10 −14 25.17 97 62
XMS 6.8×10 −15 3.33 86 57
a Including photometric redshifts (see section 2.3).
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CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
log L x (0.5−2 keV)
40 42 44 46
XMS
CDFS
RIXOS
RDS
RBS
0 1 2 3 4
z
log L x (2−10 keV)
40 42 44 46
XMS
CDF−S
AMSS
0 1 2 3 4
z
log L x (4.5−7.5 keV)
42 43 44 45
XMS
HBSS
0 0.5 1 1.5
z
Figure 5.5 Luminosity-redshift plane of different X-ray surveys in the Soft (top panel),
Hard (Center panel) and Ultrahard (Bottom panel) bands.
126

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Sky Area (deg 2 )
10 −6 10 −5 10 −4 10 −3 0.01 0.1 1 10 100 1000 10 4
Overall
CDF−S
XMS
RIXOS
RDS
RBS
10 −17 10 −16 10 −15 10 −14 10 −13 10 −12 10 −11
Flux (cgs) (0.5−2 keV)
Sky Area (deg 2 )
10 −6 10 −5 10 −4 10 −3 0.01 0.1 1 10 100
Overall
CDF−S
XMS
AMSS
10 −17 10 −16 10 −15 10 −14 10 −13 10 −12 10 −11
Flux (cgs) (2−10 keV)
Sky Area (deg 2 )
0.01 0.1 1 10
Overall
HBS
XMS
10 −14 10 −13 10 −12
Flux (cgs) (4.5−7.5 keV)
Figure 5.6 Sky area of the survey as a function of flux in the Soft (top panel), Hard (Center
panel) and Ultrahard (Bottom panel) bands.
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CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
ume V and log L X , and is function of both luminosity and redshift:
dΦ(L X , z)
d log L X
= d2 N(L X , z)
dVd log L X
(5.3.1)
and it is assumed that is a continous function over the luminosity and redshift
ranges over which it is defined.
As a first approach we will estimate the XLF in fixed luminosity and redshift
bins (section 5.3.1) which will allow us to have a general overview of the overall
XLF behavior. In section 5.3.2 we will express the XLF in terms of an analytical
model over which we will perform a Maximum Likelihood (ML) fit, using
the full information available from each single source and thus avoiding biases
coming from finite bin widths and the imperfect sampling of the L X − z plane.
5.3.1 Binned luminosity function
There are a variety of methods to estimate the binned XLF. The classical approach
is the 1/V a method ([203]), which was later generalized by [9] for samples
with multiple flux limits. This method has been widely used to compute
the binned XLF in evolution studies of flux-limited samples (i.e. [140], [62])
but it can lead to systematic errors, especially when dealing with sources very
close to the flux limit. A number of techniques have been proposed to solve
this problem ([129], [170], [158]). In this work, we have used the alternative
method proposed by [170] to calculate the differential binned luminosity function,
which avoids most of the biases that accompany the classic 1/V a method.
The differential XLF can be approximated by:
dΦ(L X , z)
d log L X
≈
∫ Lmax
L min
∫ zmax (L)
z min
N
dV
dz dzd log L X
(5.3.2)
where N is the number of objects found in a given luminosity-redshift bin ∆L∆z
which is surveyed by the double integral in the denominator. The differential
comoving volume has been calculated using the expression from [110]:
dV
dz =
c ( ) 2 DL ( ) −1/2
Ω M (1 + z) 3 + Ω Λ Ω(LX , z) (5.3.3)
H 0 1 + z
where D L is the luminosity distance and Ω(L X , z) is the solid angle subtended
by the survey. Note that some portion of the ∆L∆z bin may represent objects
128

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
that are fainter than the survey flux limit. The upper limit of the integral in
redshift z max (L) is hence either the top of the redshift shell ∆z or the redshift at
the survey flux limit for a given luminosity: z max (L) = z lim (L X , S lim ).
If the sample is composed of multiple flux-limited surveys (as it happens in
this work), they are added ’coherently’ as explained in [9]. This means we will
assume that each object could be found in any of the survey areas for which is
brighter than the corresponding flux limit.
The binned XLF thus obtained for our sample presents an overall double powerlaw
shape (see Figures 5.7, 5.8 and 5.9), with a steeper slope at brighter luminosities
beyond a given break luminosity that takes place somewhere in the
range log L X = 43 − 44. The position of this break seems to change with redshift,
moving to higher values of log L X as we go deeper, thus showing clear
evidences of evolution in the AGN that compose our sample. The shape at
higher redshifts is less constrained due to the limited statistics. An analytical
model is therefore needed to account for these changes in shape as it evolves
with z, and whose parameters could be compared with previous works.
5.3.2 Analytical model
In the light of the results obtained in section 5.3.1, we will express the XLF as
an analytic function with an smooth behavior over the range of L X and z under
study in this work. The parameters of this function will describe its overall
shape and how it changes with luminosity and redshift, which will express
physical properties of the population under study.
As shown in many works in the soft and hard bands (i.e. [157], [224], [104],
[211]), the XLF seems to be best described as a double power law modified by a
factor for evolution. Here we implement two different models: the simpler Pure
Luminosity Evolution (PLE) model in which the X-ray luminosity evolves with
redshift, and the more complicated Luminosity-dependent Density Evolution
(LDDE) model in which the evolution factor not only depends on the redshift
but also on the luminosity. Both models can be expressed respectively as:
dΦ(L X , z)
d log L X
= dΦ(L X/e(z), 0)
d log L X
(5.3.4)
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CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
for the PLE model, and:
dΦ(L X , z)
d log L X
= dΦ(L X, 0)
d log L X
e(z, L X ) (5.3.5)
for the LDDE model. The first factor of the second term in equation 5.3.5
describes the shape of the present-day XLF for which we adopt a smoothlyconnected
double power law:
dΦ(L X , 0)
d log L X
[( ) γ1
( ) γ2
] −1 LX LX
= A +
(5.3.6)
L 0 L 0
where γ 1 and γ 2 are the slopes, L 0 is the value of the luminosity where the
change of slope occurs, and A is the normalization.
The evolution factor of the PLE model is expressed as:
⎧
⎫
⎨ (1 + z) p 1 ; z < z c ⎬
e(z) =
( )
⎩ (1 + z c ) p p2
1 1+z
1+z c
; z ≥ z c
⎭
(5.3.7)
where the parameters p 1 and p 2 account for the evolution below and above, respectively,
the cut-off redshift z c . However, in the LDDE model we will assume
that the cut-off redshift depends on the X-ray luminosity:
⎧
⎫
⎨ (1 + z) p 1 ; z < z c (L X ) ⎬
e(z, L X ) =
(
⎩ (1 + z c (L X )) p p2
1 1+z
1+z c (L X ))
; z ≥ z c (L X ) ⎭
⎧
⎨
z c (L X ) =
⎩
z ∗ c
z ∗ c
(
LX
La
) α
; L X ≥ L a
; L X < L a
⎫
⎬
⎭
(5.3.8)
(5.3.9)
where α measures the strength of the dependence of z c with luminosity.
5.3.3 Model fitting to soft sources
We have fitted our sample in the soft band to the PLE and LDDE models described
above using a Maximum Likelihood (ML) method, which optimally
exploits the information from each source without binning and is therefore free
from all the biases commented in section 5.3.1.
The ML technique we have implemented here is that of [145], in which the
likelihood function is defined as the probability of observing exactly one object
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CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
in the differential element dzd log L X at each (z i , L Xi ) for the N objects in the
sample, multiplied by the product of the probability of observing zero objects
in all other differential elements in the accessible regions of the z − L X plane.
The expression to be minimized is hence:
S = −2 ∑ N i=1 ln dΦ(Li X ,zi )
+2 ∑ N sur
j=1
∫ z2
z 1
∫ L2
L 1
d log L X
dΦ(L X ,z)
d log L X
C j (L X , z) dVj (L X ,z)
dz
dzd log L X
(5.3.10)
Here, the index i runs over all the sources present in the sample whereas the index
j runs over all the surveys that compose the sample. The factor C j (L X , z) is a
correction for spectroscopic incompleteness in the j-th survey, and is function of
the X-ray flux. The integrals are calculated over the full redshift (0.01 < z < 3)
and luminosity (40 log L X < 46) ranges spanned by our sample in the soft
band taking into account the flux limits of the different surveys that compose
the sample.
The expression for S is minimized using the MINUIT software package ([116])
from the CERN Program Library. 1σ errors for each parameter are calculated
by fixing the parameter of interest at different values and leaving the other parameters
to float freely until ∆S=1. Since the model is rather complex and some
of the parameters are unconstrained when performing the fit using the 9 free
parameters, we have fixed some of them. In particular we have fixed p 2 , z c and
L a to the values obtained by [104] in the 0.5-2 keV band. This left us with 6 free
parameters to fix: A, γ 1 , γ 2 , L 0 , p 1 and α (see Table 5.2).
5.3.4 Model fitting to hard and ultrahard sources
For the sources in the hard and ultrahard bands we will make use of the information
obtained in section 5.2 when performing the ML fit. Given the coverage
of the three-dimensional space L X − z − N H spanned by our Hard and Ultrahard
samples, we were not able to fit simultaneously the N H function and the
XLF (which would lead us to a functional form with 11 free parameters). Instead,
we will add the N H function to the analytic expression to be minimized
but fixing their parameters, ψ 44 , β L and β z , to those obtained in section 5.2.
131

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Table 5.2 Parameters of the X-ray luminosity function.
Soft (0.5-2 keV) Hard (2-10 keV) Ultrahard (4.5-7.5 keV)
PLE LDDE PLE LDDE PLE LDDE
Present day XLF parameters
A a 49.27±0.58 9.83±2.94 17.96 +9.97
−6.09 4.78 +0.20
−0.23 10.41 +1.87
−1.46 1.32±0.20
log L b 0 42.90 +0.04
−0.03 43.36±0.11 43.60±0.13 43.91 +0.01
−0.02 43.00 +0.18
−0.21 43.43 +0.23
−0.32
γ 1 0.36±0.01 0.51±0.02 0.81±0.06 0.96±0.02 1.14±0.01 1.28 +0.08
−0.16
γ 2 2.01±0.04 2.13±0.10 2.37 +0.19
−0.18 2.35±0.07 2.72 +0.29
−0.28 2.53±0.32
Evolution parameters
p 1 1.80±0.06 3.65±0.21 2.04 +0.13
−0.12 4.07 +0.06
−0.07 3.03 +0.17
−0.22 6.46 +0.69
−0.29
p 2 0.00 ( f ixed) -1.5 ( f ixed) 0.00 ( f ixed) -1.5 ( f ixed) 0.00 ( f ixed) -1.5 ( f ixed)
z c 1.7 ( f ixed) 1.42 ( f ixed) 1.9 ( f ixed) 1.9 ( f ixed) 1.9 ( f ixed) 1.9 ( f ixed)
log L a
b ... 44.6 ( f ixed) ... 44.6 ( f ixed) ... 44.6 ( f ixed)
α ... 0.108±0.005 ... 0.245±0.003 ... 0.245 ( f ixed)
N H function parameters
ψ 44 ... ... 0.41 +0.03
−0.04 0.41 +0.03
−0.04 0.22±0.04 0.22±0.04
β L ... ... -0.22 +0.04
−0.05 -0.22 +0.04
−0.05 -0.45 +0.20
−0.25 -0.45 +0.20
−0.25
β z ... ... 0.57 +0.12
−0.10 0.57 +0.12
−0.10 0.00 ( f ixed) 0.00 ( f ixed)
P 2DKS (L X , z) c 2×10 −4 0.21 3×10 −4 0.18 0.28 0.84
a In units of 10 −6 h 3 70 Mpc−3 .
b In units of h −2
70 erg s−1 .
c 2D K-S test probability.
Taking this into account, the expression for S is:
S = −2 ∑i=1 N ln dΦ(Li X ,zi )
d log L
f (L i X X , zi ; NH i )
+2 ∑ N sur
j=1
∫ z2
z 1
∫ L2
L 1
∫ NH2
N H1
×C j (L X , z, N H ) dVj (L X ,z,N H )
f (L X , z; N H ) dΦ(L X,z)
d log L X
(5.3.11)
dz
dzd log L X d log N H
Again, the integrals are calculated over the full L X − z − N H space in the ranges
0.01 < z < 2, 20 < log N H < 24, 40 log L X(2−10) 46 (in the hard band)
and 42 log L X(4.5−7.5) < 45 (in the ultrahard band). As we did in the previous
section, we fixed the XLF parameters p 2 , z c and L a to those obtained by [224]
for sources detected in the hard band and, in addition, given the poor coverage
of the L x − z plane achieved by the ultrahard sample, we have also fixed the
strength of the dependence of z c on luminosity α to the value we obtained when
fitting the hard sample.
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CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
5.4 Results
5.4.1 Discussion
The best-fit parameters of the XLF calculated by the ML method explained
above are summarized in Table 5.2. Best fit results to the PLE and LDDE models
along with data points from the binned XLF are shown in Figures 5.7, 5.8 and
5.9.
It has been shown in different works that the LDDE model for the XLF provides
the best framework that describes the evolutionary properties of AGN,
both in soft ([157], [104]) and hard X-rays ([224], [130], [211]), as well as in
the optical range ([22]). We show in this paper that this analytical model also
works for AGN detected at harder X-rays such as the ones comprised in the
joint XMS/HBSS sample.
At first sight our best-fit models in the soft band (0.5-2 keV) reveal strong differences
between the PLE and LDDE models. Although the PLE best-fit seems
to be a fair description of the XLF at low redshifts (z < 1) it clearly fails to reproduce
the behaviour at high redshifts, where the LDDE model matches better
with our binned XLF data points.
The best-fit parameters obtained by our ML technique slightly differ from the
soft XLF models reported in [157] and [104] using a variety of ROSAT, XMM-
Newton and Chandra surveys. For instance, our best-fit PLE model requires less
evolution (p 1 parameter) than that of [104] PLE model and the present-day luminosity
break L 0 is displaced at fainter luminosities in our model (but consistent
within 2σ with that of [104]).
The LDDE model provides a better overall description of the XLF. However, our
present day XLF power law shape has flatter slopes and the luminosity break L 0
is also displaced at fainter luminosities than in [104] by more than 2σ, although
it is consistent with the LDDE models of [157] within the error bars. Our best-fit
evolution parameter p 1 reveals less evolution below the cut-off redshift (fixed
to the value obtained by [104]: z c = 1.42) and a much weaker dependence of z c
on luminosity α than in these works.
Similarly, in the hard band (2-10 keV) the LDDE model outperforms the PLE
model at z > 0.5, failing the latter to describe the evolution of the binned data
points at the faint end of the XLF underestimating the data at log L X > 44 by
133

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
d φ / d log L x
10 −11 10 −10 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 0.01
0.01

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
a factor of several. Comparing our results in the hard band (2-10 keV) with
previous major works in this band ([224], [130], [211]) we find an overall good
agreement between our work and theirs, although with some differences in
detail. The general shape of the present day XLF, described by the smooth double
power law, is similar to that reported in other works within the error bars.
The evolution below the redshift cut-off p 1 is also consistent with the results
of [224] and [130] (both using samples corrected by the intrinsic absorption of
their sources), and [211] well within the 1σ confidence level. The stronger difference
between these models arises with the strength of the dependence of the
cut-off redshift z c on luminosity, measured by the parameter α. The values of
α obtained by [224] and [211] are consistent with each other while the ones calculated
by [130] (α ∼ 0.2) and in this work (α ∼ 0.25) are sistematically lower.
Overall, our best-fit LDDE parameters are more constrained than in the other
works attending to the computed 1σ error bars. We have left the evolution parameter
above the cut-off redshift p 2 fixed to that of [224] (the value obtained
in [130] reveals less evolution beyond z c but consistent with [224] within 1σ).
The model in [211] requires a much stronger evolution p 2 = −3.27 +0.31
−0.34 than
the others. It must be noted, nevertheless, that it is extremely difficult to properly
constrain the faint end of the luminosity function given the necessity of
highly complete deep pencil-beam surveys that account for the population of
high-redshift low-luminosity AGN.
In a recent work, [48] have computed the intrinsic present day XLF of the HBSS
sample in the 4.5-7.5 keV (ultrahard) band for absorbed and unabsorbed AGN.
In this work we have added the HBSS sample to ours, and performed the same
analysis as in the soft and hard bands using both absorbed and unabsorbed
sources. This way we have doubled the number of available AGN and improved
the L X − z coverage, which is directly reflected in that the best-fit parameters
are more constrained.
Moreover, given the availability of detailed
spectral information for the vast majority of the sources in both samples, we
have carried out the XLF analysis by convolving the N H function with the XLF
analytical model when performing the fit (see section 5.3.4). Like in the other
energy bands, the PLE best-fit clearly underestimates the data at faint luminosities
and high redshifts. From the binned data points it can be inferred that
a very strong evolution p 1 is required to describe properly the behaviour of
the ultrahard sources, which is achieved by the LDDE model. Our results are
fully consistent with those reported in [48] albeit with smaller error bars. The
135

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
d φ / d log L x
10 −11 10 −10 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 0.01
0.01

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
shape of our best-fit present day XLF would correspond to the average of the
absorbed and unabsorbed present day XLF calculated in [48] thus lying inside
the 1σ confidendence levels spanned by their parameters. Our best-fit value for
the evolution parameter p 1 = 6.46 +0.69
−0.29
is in excellent agreement with that of
[48] (p 1 = 6.5) and also with that of [22] obtained from a selected AGN sample
in the optical range from the VIMOS-VLT survey (p 1 = 6.54) and that of the
bolometric quasar luminosity function of [112] (p 1 = 5.95 ± 0.23). This value
represents a much stronger evolution below the cut-off redshift than that obtained
by [224] (p 1 = 4.23 ± 0.39) and [130] (p 1 = 4.62 ± 0.26) in the 2-10 keV
band. Some works (i.e. [157], [104], [22]) suggest that the evolution parameter
p 1 might depend linearly on the X-ray luminosity, increasing as the luminosity
increases. Given the lack of deep surveys, which mainly account for intrincally
faint objects, in the ultrahard band, this result could be biased towards highluminosity
sources and hence provides higher evolution rates below the cut-off
redshift.
5.4.2 Accretion history of the Universe
The X-ray luminosity function of AGN, whose bolometric emission is directly
linked to accretion power, constrains the history of the formation of the supermassive
black holes that reside in the galactic centers along cosmic times.
The comoving density of AGN as a function of redshift can be calculated straightforward
from our best-fit XLF LDDE model:
Φ(z) =
∫ L2
L 1
dΦ(L X , z)
d log L X
d log L X (5.4.1)
As we can see in Figure 5.10, the most luminous AGN are formed before the
less luminous ones in all bands, although this is difficult to say in the ultrahard
band due to the limited statistics. AGN with log L X > 44 reach a maximum in
density at redshift ∼1.5 while fainter AGN (log L X < 44) peak at z ∼ 0.7.
Similarly to the comoving density, we can derive the luminosity density as a
function of redshift in all bands and, from that, calculate the accretion rate density.
Here we will assume that the accretion rate onto a supermassive black
hole is related to the bolometric luminosity by a constant factor ɛ which is the
137

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
d φ / d log L x
d φ / d log L x
d φ / d log L x
10 −11 10 −10 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 0.01
10 −11 10 −10 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 0.01
10 −11 10 −10 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 0.01
0.01

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Number Density (Mpc −3 )
Number Density (Mpc −3 )
10 −7 10 −6 10 −5 10 −4 10 −3 0.01
10 −7 10 −6 10 −5 10 −4 10 −3 0.01
41.5 < log L 0.5−2 keV
< 44.0
44.0 < log L 0.5−2 keV
< 46.5
0 0.5 1 1.5 2 2.5 3
z
42.5 < log L 2−10 keV
< 44.0
44.0 < log L 2−10 keV
< 46.0
0 0.5 1 1.5 2 2.5 3
z
Number Density (Mpc −3 )
10 −7 10 −6 10 −5 10 −4 10 −3 0.01
43.0 < log L 4.5−7.5 keV
< 44.0
44.0 < log L 4.5−7.5 keV
< 45.0
0 0.5 1 1.5 2
z
Figure 5.10 Comoving density of AGN in different luminosity bins as a function of
redshift in the soft (top panel), hard (Center panel) and ultrahard (Bottom panel) bands.
Overplotted are the predictions from our best-fit LDDE model in the low luminosity
(solid line) and high luminosity (dashed line) ranges
139
.

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
radiative efficiency of the accretion flow ([144], [130]):
L bol =
ɛ
1 − ɛ Ṁaccc 2 (5.4.2)
We can derive the bolometric luminosities by means of a bolometric correction
factor K simply using L bol = KL X . The accretion rate density is hence:
˙ρ acc (z) = 1 − ɛ
ɛc 2
∫ L2
L 1
KL X
dΦ(L X , z)
d log L X
d log L X (5.4.3)
We will assume a nominal radiative efficiency of ɛ = 0.1 ([244], [144], [16]). The
values of the bolometric correction K are derived from the polynomic expressions
of [144], that accounts for changes in the overall spectral energy distribution
of AGN as a function of the optical luminosity. Hence, the total accreted
mass onto supermassive black holes is:
ρ(z) =
∫ z0
z
˙ρ acc (z) dt dz (5.4.4)
dz
where we assume that the initial mass of seed black holes at z 0 is negligible with
respect to the total accreted mass ([130]).
In Figures 5.11 and 5.12 is clearly seen that the vast majority of the accretion
rate density and the total mass density are produced by low-luminosity AGN
(log L X < 44). The total accreted mass density at z = 0 obtained from our XLF
model (∼ 3 × 10 5 M ⊙ Mpc −3 ) in the hard band is in good agreement with that
of [144] (2.25 +0.94
−0.68 × 105 M ⊙ Mpc −3 ) determined using the local black hole mass
function.
From these results it can be inferred that high-luminosity AGN grow and feed
very efficiently in the early Universe and are fully formed at redshifts 1.5-2,
whereas the low-luminosity AGN keep forming down to z ∼ 1, in agreement
with an anti-hierarchical black hole growth scenario as shown by the LDDE
model of the XLF.
5.5 Summary
We have discussed here the cosmic evolution of a sample of AGN in three X-
ray bands: soft (0.5-2 keV), hard (2-10 keV) and ultrahard (4.5-7.5 keV). The
140

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Figure 5.11 Accretion rate density of matter onto supermassive black holes as a function
of redshift in the soft (top panel), hard (Center panel) and ultrahard (Bottom panel)
bands. Dashed lines correspond to the redshift range in which the model has been
extrapolated.
141

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
Figure 5.12 Total accreted mass onto supermasive black holes as a function of redshift
in the soft (top panel), hard (Center panel) and ultrahard (Bottom panel) bands. Dashed
lines correspond to the redshift range in which the model has been extrapolated.
142

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
backbone of our sample is the XMS survey ([12]) which is a flux-limited highlycomplete
sample at medium redshifts. We have combined the XMS with other
shallower and wider highly complete X-ray surveys in all three bands to end up
with a total sample of ∼1000, 435 and 119 AGN in the soft, hard and ultrahard
bands, respectively.
We have used the detailed spectral information on the sources that compose
the ultrahard sample, XMS and HBSS ([48]) to model their instrinsic absorption
(N H function). We find that the fraction of absorbed of AGN in the 4.5-7.5 keV
band, assuming a dividing value of N H = 10 22 cm −2 , is dependent on the X-
ray luminosity but not on the redshift. This could be motivated by the narrow
redshift range spanned by the sample, with the bulk of the sources located at
low redshifts (z < 1). The same analysis applied to the hard (2-10 keV) sources
reveals dependency on both the X-ray luminosity and redshift. Our predictions
on the behaviour of the fraction of absorbed AGN in this band is in excellent
agreement with the results of [224] and [130] and with the more recent work
of [100], who studied the evolution of the absorption properties of AGN in a
compiled sample of 1290 AGN in the 2-10 keV band.
We have calculated the X-ray luminosity function of AGN using two methods.
First, a modified version of the 1/V a method ([203]) discussed in [170]
to compute the binned XLF. Secondly, a fit to an analytic model using a Maximum
Likelihood technique ([145]) that fully exploits the available information
on each individual source without binning. The adopted model consists of a
smoothly connected double power law that accounts for the present day (z = 0)
XLF modified by an evolution factor that depends either on the redshift (PLE
model) or on both redshift and luminosity (LDDE model). We have found that
the LDDE model outperforms the PLE model at faint luminosities and high
redshifts. The latter is ruled out as a possible description of the observations by
a two-dimensional Kolmogorov-Smirnov test performed over the whole luminosity
and redshift ranges spanned by our sample, whereas the LDDE model
fit achieves better acceptance probabilities, especially in the ultrahard band (see
Table 5.2).
The best-fit XLF parameters in the soft sample show slight discrepancies in both
the overall shape and evolution with respect previous works in that band ([157],
[104]). In the hard band, where we have computed the intrinsic XLF taking into
account the intrinsic absorption N H of each source, we are in good agreement
143

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
with the results of [224], [130] or [211]. Our best-fit model shows weaker evolution
of the AGN below the cut-off redshift than in these works albeit with
smaller error bars. In the ultrahard band, we have also calculated the intrinsic
XLF finding similar results as in [48] but with our best-fit parameters much
more constrained. The results in this band show that ultrahard AGN present a
significantly stronger evolution below the cut-off redshift than those detected at
softer energies. This could be due to the lack of complementary deep surveys
(which probe intrinsically faint sources) in the ultrahard band. If there exists
a dependency of the evolution rate on the X-ray luminosity ([157], [104]) we
could be biased towards high-luminosity objects thus measuring higher evolution
rates. In all three bands, the high-luminosity AGN (log L X > 44) are
formed before than the low-luminosity ones (log L X < 44), reaching the former
a maximum in density at redshift z ∼ 1.5 whereas the comoving density of the
latter peak at z ∼ 0.7.
Finally, we have used our best-fit XLF to compute the accretion rate density
and total accreted mass onto supermassive black holes as a function of redshift.
The total black hole mass density at z = 0 predicted by our best-fit model is in
agreement with the local supermassive black hole density of [144]. As shown by
the XLF model, the high-luminosity AGN have a more efficient growth in the
early stages of the Universe and are fully formed at z ∼ 1.5 − 2 while the less
luminous AGN keep forming down to redshifts below 1. This behaviour is also
found in the ultrahard sample thus confirming that the evolution of the XLF
along cosmic time is not caused by changes in the environment absorption but
by intrinsic variations in the accretion rate at different epochs of the Universe.
144

CHAPTER 5: LUMINOSITY FUNCTION OF XMS SOURCES
146

Chapter 6
Summary of the results
Throughout this thesis we have studied the large-scale, cosmological and evolutionary
properties of Active Galactic Nuclei (AGN), detected in X-rays by
the XMM-Newton observatory. The main source of energy of these sources is
acrettion of matter onto a supermassive black hole (∼10 6 -10 9 M ⊙ ), which has
allowed us to constrain the parameters that describe the accretion history of the
Universe through cosmic time.
This chapter is structured as follows: in section 6.1 we summarize the main
conclusions obtained from this thesis, while in section 6.2 we discuss possible
future lines of work that can be derived from the results presented here.
6.1 Summary
In order to carry out the investigations presented in this thesis, we have made
use of two X-ray surveys at medium fluxes which were led by the X-ray Astronomy
Group at the Instituto de Física de Cantabria, and in which the author of
this thesis has decisively participated by reducing optical and X-ray data and
identifying optical spectra:
• AXIS (An XMM-Newton International Survey, [13], [38]): the backbone of
the XMM-Newton Survey Science Center medium XID programme. It
has a wide sky coverage (∼4.3 deg 2 ) with fluxes ranging from ∼10 −15 -
10 −12 erg cm −2 s −1 in the 0.5-10 keV broadband. A total of 36 XMM-
Newton pointings were selected for optical follow-up of sources at high
Galactic latitudes (|b| > 20 ◦ ) with total exposure times above 15 ks. This
147

CHAPTER 6: SUMMARY OF THE RESULTS
survey was divided in four subsamples in the following energy ranges:
soft (0.5-2 keV), hard (2-10 keV), XID (0.5-4.5 keV) and ultrahard (4.5-
7.5 keV), in which we ended up with 1267, 397, 1359 and 91 X-ray sources,
respectively.
• XMS (XMM-Newton Medium Sensitivity Survey, [12]): a serendipitous X-
ray source survey at medium fluxes built from the AXIS survey. It covers
a geometric area of ∼3 deg 2 and also consists of four overlapping subsamples
in the soft, hard, XID and ultrahard energy bands. The soft, hard
and XID subsamples are flux limites while the ultrahard subsample is not
artificially limited due to the scarcity of its sources. An extensive identification
programme was carried out on the XMS survey, ending up with
272 out of distinct 318 sources spectroscopically identified (86% overall,
over 90% in the soft and XID bands). Most of the identified sources turned
out to be Type-1 AGN (∼70% in the soft and XID bands, ∼55% in the
hard and ultrahard bands) while the rest were identified as Type-2 AGN
(∼20%), galaxies (∼5%) and stars (∼4%).
These surveys contribute the main samples used in the investigations carried
out in this thesis but, in order to gather broader statistics, we have combined
them with other complementary XMM-Newton surveys as well as with surveys
from other present and past X-ray observatories such as ROSAT, ASCA
or Chandra. Shallower, wide area surveys provide brigh sources, while deep
pencil-beam surveys probe sources at fainter fluxes.
The main aims enumerated in Chapter 1 that we have addressed throughout
this thesis are:
1. The Cosmic X-ray Background (CXB) is a record of the accretion power
history of the Universe and it is now accepted that it comes from the integrated
emission of discrete extragalactic sources. Both absorbed (Type-
2) and unabsorbed (Type-1) AGN are the main contributors to the CXB,
with galaxy populations only contributing significantly at fainter X-ray
fluxes. We have calculated the sky density or source counts of the AXIS
sources, since these distributions are dependent on the cosmological properties
that configure the CXB emission. The more accurate the shape of
the source counts is constrained, the more precise will be the contribution
from discrete sources to the CXB.
148

CHAPTER 6: SUMMARY OF THE RESULTS
We have therefore used our best fit logN − logS to calculate both the total
resolved fraction of the Cosmic X-ray Background (including the contribution
from bright sources) and the relative contribution in different flux
bins to the total CXB). We have used the estimates of the average CXB intensity
in the Soft and Hard bands from [160] and converted them to the
XID and Ultrahard bands using a power law spectrum with Γ = 1.4. The
total resolved fraction down to the lowest fluxes of our combined sample
reaches 88% in the Soft band and 86% in the Hard band (where we have
been able to reach deep fluxes usin pencil beam surveys [19]), but it is only
60% in the XID band and 25% in the Ultrahard band. The total intensity
produced extrapolating our logN − logS to zero flux does not saturate the
CXB intensity. Assuming that another flux break occurs just below our detected
minimum fluxes, we have estimated the minimum slope needed to
reproduce the CXB with only discrete sources obtaining values of 1.85 in
the Soft band and 1.84 in the Hard band. If we compare these values with
those of the galaxy and AGN source counts from the Chandra Deep Field
(CDF, [19]), we find that galaxies could easily provide this steepening and,
among the AGN population, only the absorbed ones could do so as well.
The maximum fractional contribution to the CXB in the Soft, Hard and
XID bands comes from sources within a decade around ∼ 10 −14 cgs (where
the break in the source counts power law approximately occurs). This is
almost 50% of the total contribution in the Soft and Hard bands, which
means that medium deep surveys such as AXIS are essential to understand
the evolution of the X-ray emission in the Universe up to 10 keV.
2. The dominant population at medium and low X-ray fluxes are AGN, which
are known to cluster strongly (i.e. [242], [84], [161], [37]). Since to detect
source clustering it is needed a survey that it is both deep (to achieve high
angular density) and wide (to prevent a single structure to bias the overall
average), the AXIS and XMS surveys are ideal to investigate the large scale
structure of AGN.
Angular clustering studies the excess probability of finding a pair of sources
at a given angular distance projected in the sky. We have studied it in
two ways. The first is the standard two-point angular correlation function
w(θ). Using this method we have detected evidence of clustering at about
the 99% level in the Soft and XID bands but not in the Hard and Ultrahard
149

CHAPTER 6: SUMMARY OF THE RESULTS
bands. The strength of the clustering signal we have found is intermediate
between those of previous results ([72], [18], [17], [229]). A more appropiate
method using Poisson statistics detects clustering at the 99-99.9% level
in the Soft and XID bands, but again not in the Hard and Ultrahard bands.
We have checked out that if we remove at random two out every three
sources in the soft sample, the clustering signal disappears which implies
that angular clustering may also exist in the hard band but we have failed
to detect it due to the smaller number of sources in that band. Dividing the
soft sample into several subsamples reveals that the signal is widespread
over the sky and it is not limited to a few deep fields. This means that if
this structure has a cosmic origin it must come from z ≤ 1.5, the peak of
the redshift distribution of medium flux surveys ([12]). Additionally, we
cannot confirm the detection of clustering signal among hard-spectrum
sources reported by [72].
We have used the angular amplitudes θ 0 obtained in the angular correlation
function and some assumptions in the redshift distribution via the
luminosity function of these sources to deproject these values by inverting
Limber’s equation in order to find an estimate of their spatial clustering.
The deprojected spatial amplitudes r 0 that we have found for the AXIS
sources are in agreement with those calculated by [18] and [161] in the
Soft band for different clustering models. In spite of the lack of signal in
the hard band, the values of r 0 obtained in this band are also in excellent
agreement with those of [159] using sources from the COSMOS survey,
but not with the ones of [17] which are sistematically larger than any other
spatial correlation lengths reported for AGN.
The XMS sample has very high completeness of secure spectroscopic redshifts
in all bands. Since we can compute the real physical distances between
these sources, we have studied the possible spatial clustering among
them. For that, we have calculated the two-point spatial correlation function
in the Soft and Hard bands, without finding evidences of large scale
structure in the redshift space. Previous works with number of sources
comparable to ours ([161], [84] or [242]) have reported strong spatial clustering
for AGN. This discrepancy can be explained in terms of the dillution
of the clustering signal since the XMS fields are widespread over the sky
leading to a very low source density (about 7 and 5 sources per field in the
Soft and Hard bands, respectively).
150

CHAPTER 6: SUMMARY OF THE RESULTS
3. Other of the aims of this thesis is to study the evolutionary properties of
AGN, as they are strongly linked to the accretion history of the Universe
and the growth and formation of the supermassive black holes that are believed
to reside in the centre of all galaxies, active or not (i.e. [126], [141],
[190]). This can be achieved by computing the X-ray luminosity function
(XLF) of these sources. Hard (>2 keV) X-ray surveys are indeed essential
to describe the luminosity function of the whole AGN population, including
obscured AGN which are the main contributors to the CXB.
Hence, we have used the detailed spectral information on the sources that
compose the ultrahard sample, XMS and HBSS ([48]) to model their instrinsic
absorption (N H function). We find that the fraction of absorbed
of AGN in the 4.5-7.5 keV band, assuming a dividing value of N H =
10 22 cm −2 , is dependent on the X-ray luminosity but not on the redshift.
This could be motivated by the narrow redshift range spanned by the sample,
with the bulk of the sources located at low redshifts (z < 1). The same
analysis applied to the hard (2-10 keV) sources reveals dependency on
both the X-ray luminosity and redshift. Our predictions on the behaviour
of the fraction of absorbed AGN in this band is in excellent agreement with
the results of [224] and [130] and with the more recent work of [100], who
studied the evolution of the absorption properties of AGN in a compiled
sample of 1290 AGN in the 2-10 keV band.
4. We have calculated the X-ray luminosity function of AGN using two methods.
First, a modified version of the 1/V a method ([203]) discussed in [170]
to compute the binned XLF. Secondly, a fit to an analytic model using a
Maximum Likelihood technique ([145]) that fully exploits the available information
on each individual source without binning. The adopted model
consists of a smoothly connected double power law that accounts for the
present day (z = 0) XLF modified by an evolution factor that depends
on the redshift (PLE model) or on both redshift and luminosity (LDDE
model). We have found that the LDDE model outperforms the PLE model
at faint luminosities and high redshifts. In all three bands (soft, hard and
ultrahard), the high-luminosity AGN (log L X > 44) are formed before than
the low-luminosity ones (log L X < 44), reaching the former a maximum
in density at redshift z ∼ 1.5 whereas the comoving density of the latter
peak at z ∼ 0.7.
151

CHAPTER 6: SUMMARY OF THE RESULTS
Finally, we have used our best-fit XLF to compute the accretion rate density
and total accreted mass onto supermassive black holes as a function of
redshift. The total black hole mass density at z = 0 predicted by our bestfit
model is in agreement with the local supermassive black hole density of
[144]. As shown by the XLF model, the high-luminosity AGN have a more
efficient growth in the early stages of the Universe and are fully formed at
z ∼ 1.5 − 2 while the less luminous AGN keep forming down to redshifts
below 1. This behaviour is also found in the ultrahard sample thus confirming
that the evolution of the XLF along cosmic time is not caused by
changes in the environment absorption but by intrinsic variations in the
accretion rate at different epochs of the Universe.
We can conclude that we have achieved to show the importance of mediumdeep
serendipitous X-ray surveys for clustering and evolutionary studies. We
have shown that these sources are essential to trace the large-scale structure of
the cosmic web and to resolve the discrete origin of the Cosmic X-ray Background
in the 0.5-10 kev energy broadband. With them, we have been able to
accurately constrain the evolutionary history of AGN thus showing that obscured
accretion power plays a key role in the understanding of the cosmic
emission and evolution of the X-ray Universe.
6.2 Future prospects
Although the results presented in this thesis have contributed substantially to
the undestanding of evolutionary and clustering properties of AGN, there are
some aspects in which would be desirable to go deeper into.
• Although we have obtained evidence that extragalactic sources at medium
fluxes detected in soft X-rays cluster strongly forming cosmological largescale
structures, we were not able to confirm this for sources detected in
hard X-rays. We can find in the literature discrepant results on this subject,
being the main reason the low density of sources per field. In an ongoing
work using a large sample of serendipitous X-ray sources described in
[151], we intend to compute the most precise angular correlation function
of extragalactic sources detected in both soft and hard X-rays to date. Additionally,
we pursue to study the possible dependence on the flux limit of
152

CHAPTER 6: SUMMARY OF THE RESULTS
the correlation length of these sources, which could point to the fact that
different populations of sources have different clustering properties.
• The second catalogue of XMM-Newton sources, 2XMM 1 , the largest catalogue
of X-ray sources to date (2XMM is five times larger than the previous
available catalogue, 1XMM 2 ), which contains more than 250,000 sources
(150,000 unique detections) over a sky area of ∼600 sq. degrees, has been
recently released. Cross-correlating 2XMM with already existing catalogues
in other wavelengths such as the Sloan Digital Sky survey (SDSS)
will make possible to isolate potentially interesting sources for posterior
studies (i.e. high-redshift AGN, heavily obscured AGN, etc...)
• Cosmological properties of sources detected in very hard X-rays (4.5-7.5 keV
band), which are very efficient to select samples with small biases due to
absorption, are subject to high uncertainties. Specifically, the dependence
on redshift of the fraction of absorbed AGN in this band is not well constrained,
and some evolution parameters in their luminosity function need
a more detailed study. It is required, in order to address these issues, to
improve the sample statistics. Given that absorbed AGN have very low
angular density, it is required to survey larger sky areas so as to obtain a
significant amount of them to study their evolution at moderate redshifts
( ∼ < 1).
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153

Appendix A
Sensitivity maps
The value of the sensitivity map at a given point is defined as the minimum
count rate that must have a source to be detected with the desired likelihood at
that point. As explained in section 2.1.2, the detection likelihood provided by
;D=2?§;2@B;BAD@
takes into account the number of counts within the detection box, the
fit to the PSF shape, and the variation of the exposure map over the detection
box.
While, in principle, the likelihood is not trivially related to the Poisson probability
of having an excess in the number of detected counts over the expected
background rate in the detection box, we have found that the count rate assigned
by the software to a source (observed count rate) is proportional to the
count rate expected from a Poisson distribution for the same likelihood. This
way, for a given likelihood (_0/.B`7a§b L in the SAS source lists), radius of the detection
region (^7c§.,§-_
cutrad in the SAS source lists, in units of 4” pixels), total
value of the background map bgdim and average value of the exposure map in
that region expim, the expected Poisson count rate crpoisim can be calculated
at each point of the detector using the proportionality constants for the corresponding
observed count rates (,0-./ cr in the SAS source lists).
The values of cutrad are different for each source in each field since ;D=7?B;2@B;BAC@
chooses them to maximize the signal-to-noise ratio for source detection. We
have adopted a value of cutrad in each band by averaging the values from all
sources having L between 8 and 20. We have checked that assuming this average
value instead of the individual ones does not significatively affect the
subsequent calculations.
expim is the average of the exposure map within a circle of radius cutrad around
155

APPENDIX A: SENSITIVITY MAPS
Table A.1 Summary of the results of the linear fits of crpoisim dDe7f7g to : Band is the band
used for the fit, cutrad is the source extraction radius (in units of 4 ′′ pixels), LI is the
best fit multiplying constant, N is the number of sources in the fit, χ 2 LI is the χ2 value
of the best linear fit, χ 2 0 is the χ2 of the fit to LI ≡ 1 and P(F) the F-test probability of
allowing LI ̸= 1 and not being a significant improvement to the fit.
Band cutrad LI N χ 2 LI
χ 2 0
P(F)
(pixels)
1 5.12 1.14 284 104.5 185.5 < 10 −6
2 (soft) 5.08 1.10 653 140.1 226.0 < 10 −6
3 5.15 1.14 414 105.7 208.4 < 10 −6
4 (ultrahard) 5.49 1.14 127 25.7 56.2 < 10 −6
5 5.86 1.15 16 1.7 5.5 < 10 −4
9 (XID) 5.04 1.02 722 141.0 145.2 < 10 −5
3-5 (hard) 5.18 0.89 243 176.2 237.8 < 10 −6
the X-ray source positions. The exposure maps for the single bands are PPS
products, whereas for the composite bands were created using the SAS task
;;LF N) is expressed in 4.3.9.
P λ (≥ N) =
∞
∞
λ
∑ P λ (l) = ∑
l e −λ
l!
l=N
l=N
(A.0.2)
If we plot the values ,0-./ of versus crpoisim for the single and composites
bands, it can be seen that there is a linear ,0-.0/
proportionality = LI × crpoisim
for sources with L between 8 and 20 in each band (see Figure A.1). The best fit
values of LI along with the adopted cutrad values are listed in Table A.1. It is
156

APPENDIX A: SENSITIVITY MAPS
clearly seen from the values of χ 2 that this model is fairly good and therefore
more sophisticated models are not needed. The values of LI are within ∼10%
of 1 (equivalent ,0-./ to = crpoisim) but the difference is highly significant in
terms of χ 2 . The empirical estimate of the typical count rate of a source at the
position (X, Y) in image coordinates, detected with likelihood L, is therefore
sens(X, Y) = crpoisim × LI. The areas around the chip edges and around the
bright targets and the OOT regions have also been excluded in the sensitivity
maps.
To summarize, the recipe for creating a sensitivity map is then:
1. Create background and exposure maps
2. Chose a likelihood value L for the significance of the detections. This
recipe has been only tested in the likelihood range 8 ≤ L ≤ 20
3. Choose a source extraction radius cutrad appropriate for the band you are
interested in (Table A.1)
4. For each pixel (X, Y) in your input image:
(a) Calculate the sum of the values of the pixels in the background map
whose centres are within cutrad of (X, Y): bgdim
(b) Calculate the average of the values of the pixels in the exposure map
whose centres are within cutrad of (X, Y): expim
(c) Find ctspoisim such that log(P bgdim (> (ctspoisim + bgdim))) = L
(d) Calculate sens(X, Y) = ctspois/expim×LI.
5. sens(X, Y) is our empirical estimate of the typical count rate of a source at
(X, Y) detected with likelihood L
157

APPENDIX A: SENSITIVITY MAPS
Figure A.1 dDe7f7g
vs. crpoisim for all bands. Also shown are the best linear fits.
158

APPENDIX A: SENSITIVITY MAPS
160

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