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Examples

1. The expected count rate from a source with a blackbody spectrum (perhaps a neutron star) needs to be estimated. The source has L  ergs s in the ROSAT energy band (0.1 to 2.4 keV), and is at a distance of 2 kpc with  cm (log( ). The assumed temperature is equivalent to 0.1 keV. The unabsorbed flux for this source is  ergs cm  s , or in units of the flux is . From the Table 11.5  or Figure 11.7  the appropriate ECF is , and the expected count rate is  counts s . We estimate that a detection of this source at the level will require an observation time of about 4,000 s.
2. 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  cm (log( ). The AGN luminosity in the ROSAT band is L  ergs s . We want to determine how long an observation is required for a detection. The unabsorbed flux is  ergs cm  s . The ECF for this spectral model is taken from Table 11.3  or Figure 11.5 , it is , which gives a count rate  counts s . Using the sensitivity formula from § 11.2 , we calculate that the observation time needed to detect this source at the level is about 12,600 s.
3. What is the conversion factor from counts per second to energy flux for a particular spectrum? For example, a Raymond-Smith Plasma with a temperature corresponding to 1 keV and a column of  cm (log( ). The ECF for this spectral model is taken from Table 11.4  or Figure 11.6 , it is . That is, a flux of  ergs cm  s in the ROSAT energy band (0.1 to 2.4 keV) will give a count rate of  counts s in the HRI. Inverting this relationship gives the result that 1 count s  ergs cm  s . In general the conversion factor from counts per second to energy flux is given by: 1 count s /ECF ergs cm  s .