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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
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Universidad de Cantabria Departamen
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A mis padres
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explicar las altas luminosidades de
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Además, una importante fracción (
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ealizar estudios de espectroscopía
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distribución diferencial que, al e
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materia sobre el agujero negro cent
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analizadas proviene de fuentes en t
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Haciendo uso del segundo catálogo
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With magic, you can turn a frog int
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Un capítulo aparte merecen mis com
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Summary Since its discovery more th
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xxxiv
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CONTENTS 1.6.1 The K-correction . .
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CONTENTS 5.3.2 Analytical model . .
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LIST OF FIGURES 4.6 Soft 1 − P µ
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Chapter 1 Introduction In the last
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CHAPTER 1: INTRODUCTION have confir
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CHAPTER 1: INTRODUCTION by this mis
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CHAPTER 1: INTRODUCTION Figure 1.2
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CHAPTER 1: INTRODUCTION [161], [242
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CHAPTER 1: INTRODUCTION tant contri
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CHAPTER 1: INTRODUCTION to-noise ra
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CHAPTER 1: INTRODUCTION Compton up-
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CHAPTER 1: INTRODUCTION ([142]). It
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CHAPTER 1: INTRODUCTION (NLR) and i
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CHAPTER 1: INTRODUCTION optically c
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CHAPTER 1: INTRODUCTION ber of AGN
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CHAPTER 1: INTRODUCTION Figure 1.5
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CHAPTER 1: INTRODUCTION 1.7.3 The X
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CHAPTER 1: INTRODUCTION AGN are ess
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CHAPTER 1: INTRODUCTION subjects ma
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CHAPTER 2: AGN SURVEYS WITH XMM-New
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R R OQP ONM 40 Table 2.1: Continued
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CHAPTER 6: SUMMARY OF THE RESULTS b
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CHAPTER 6: SUMMARY OF THE RESULTS F
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Appendix A Sensitivity maps The val
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APPENDIX A: SENSITIVITY MAPS clearl
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APPENDIX A: SENSITIVITY MAPS 160
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REFERENCES [16] Barger, A. J., Cowi
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REFERENCES [61] Ehle, M., Breitfell
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REFERENCES [107] Hawkins, M. R. S.
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REFERENCES [148] Matarrese, S., Col
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REFERENCES [190] Richstone, D., Ahj
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REFERENCES [236] Wisotzky, L., 1998
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