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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
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Summary Since its discovery more th
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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 4: CLUSTERING OF AXIS AND X
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Chapter 5 Luminosity function of XM
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CHAPTER 5: LUMINOSITY FUNCTION OF X
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CHAPTER 6: SUMMARY OF THE RESULTS s
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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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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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