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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
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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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ealizar estudios de espectroscopía
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distribución diferencial que, al e
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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 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 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 [236] Wisotzky, L., 1998
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