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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. 132
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
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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 2: AGN SURVEYS WITH XMM-New
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Chapter 3 Source counts of the AXIS
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CHAPTER 3: SOURCE COUNTS OF THE AXI
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61 Table 3.1 Maximum likelihood fit
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Page 206 and 207: REFERENCES [16] Barger, A. J., Cowi
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Page 216: REFERENCES [236] Wisotzky, L., 1998
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