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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` 10^{20} cm^{-2} (log(N
_{H}) = 20.7).
The AGN luminosity in the ROSAT band is L_{x} = 10^{44} ergs s^{-1}.
We want to determine how long an observation is required for a
10
detection. The unabsorbed flux is
*F*_{S, 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` 10^{10},
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
level
is about 13,700 seconds.

*rsdc@cfa.harvard.edu *

1999-05-25