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Next: 3.3.3 Raymond-thermal spectrum example Up: 3.3 Expected Count Rates Previous: 3.3.1 Blackbody spectrum example

3.3.2 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 5 x 1020 cm-2 (log(N H) = 20.7). The AGN luminosity in the ROSAT band is Lx = 1044 ergs s-1. We want to determine how long an observation is required for a 10$ \sigma$ detection. The unabsorbed flux is FS, 0 = 8.37 x 10-13 ergs cm-2 s-1. The ECF for this spectral model is taken from Table 8 or Figure 30, it is 1.75 x 1010, which gives a count rate 0.0146 ct s-1. Using the sensitivity formula from Section 3.2.1 with R=0.0073 ct s-1 (50% of the total so as to refer to the 5  '' x 5'' detect cell), we calculate that the observation time needed to detect this source at the 10$ \sigma$ level is about 13,700 seconds.