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Power-law Spectrum Example

Consider a distant AGN with a power law spectrum of energy slope 0.5 which is at a luminosity distance of 1000 Mpc and is viewed through an absorption column of tex2html_wrap_inline17769  cm tex2html_wrap_inline17771 (log(N tex2html_wrap_inline17773 ). The AGN luminosity in the ROSAT band is L tex2html_wrap_inline17775  ergs s tex2html_wrap_inline17777 . We want to determine how long an observation is required for a tex2html_wrap_inline17779 detection. The unabsorbed flux is tex2html_wrap_inline17781  ergs cm tex2html_wrap_inline17783  s tex2html_wrap_inline17785 . The ECF for this spectral model is taken from Table 11.3 or Figure 11.5, it is tex2html_wrap_inline17787 , which gives a count rate tex2html_wrap_inline17789  counts s tex2html_wrap_inline17791 . Using the sensitivity formula from section 11.2, we calculate that the observation time needed to detect this source at the tex2html_wrap_inline17793 level (50% in detect cell) is about 12,600 seconds.

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