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# Expected Count Rates

The expected HRI count rates depend sensitively on the assumed incident spectrum, which is not well known for many sources. In general the convolution of the effective area and incident spectrum needs to be calculated to predict the HRI counting rate. Since the effective area is not a simple analytic function, the convolution is not straight-forward. In order to facilitate count rate calculations we provide a series of tables and graphs which give the energy-to-counts conversion factor (ECF) for several spectral models and various spectral parameters.

Tables for computing the expected count rates in the ROSAT HRI were generated for four spectral models. These are:

• Thermal Bremsstrahlung (Exponential plus Gaunt Factor) Spectrum (Table 11.2 , Figure 11.4 , where kT is in keV.
• Power Law Spectrum (Table 11.3 , Figure 11.5 ), where is the energy index.
• Raymond-Smith Plasma Spectrum (Table 11.4 , Figure 11.6 ), where kT is in keV.
• Blackbody Spectrum (Table 11.5 , Figure 11.7 ), where kT is in keV

For each spectral model we calculate the factor by which the unabsorbed source flux (in units of  ergs cm  s ) has to be multiplied in order to obtain the expected HRI on-axis count rate within the 5'' detect cell as a function of the spectral parameter ( or kT), and the interstellar absorption column density .

The curves shown in Figures 11.4  - 11.7 (or Tables 11.2 - 11.5) should be used as follows:

1. Calculate the expected source flux (in units of  ergs cm  s ) in the ROSAT pass band 0.1 - 2.4 keV assuming no interstellar absorption.
2. Determine the expected interstellar absorption column density.
3. With the assumed values of and spectral parameter ( or kT) read from the figures or tables the resulting energy-to-counts conversion factor ECF.
4. Multiply and ECF to obtain the expected ROSAT HRI count rate.

ROSAT HRI Energy to Count Conversion Factors
log( )
 kT 0 18 18.7 19 19.7 20 20.7 21 21.7 22 0.01 0.0391 0.0376 0.0321 0.0264 0.00594 0.00113 2.53e-05 1e-09 1.0 0e-9 1e-09 0.03 0.118 0.115 0.104 0.0921 0.0394 0.0177 0.000683 6.07e-05 1.0 0e-9 1e-09 0.05 0.169 0.166 0.153 0.14 0.0757 0.0428 0.00342 0.000467 2.1 0e-6 1e-08 0.10 0.212 0.209 0.198 0.186 0.121 0.0805 0.0122 0.0035 1.5 0e-4 1.82e-05 0.30 0.205 0.203 0.196 0.188 0.142 0.11 0.0416 0.0262 6.0 2e-3 0.00193 0.50 0.198 0.196 0.191 0.185 0.15 0.124 0.0651 0.0478 1.4 8e-2 0.00573 1.00 0.186 0.185 0.182 0.178 0.153 0.135 0.0881 0.0706 2.6 7e-2 0.0117 3.00 0.168 0.168 0.165 0.163 0.147 0.135 0.0995 0.0836 3.5 9e-2 0.0172 5.00 0.163 0.163 0.16 0.158 0.144 0.133 0.101 0.0855 3.7 7e-2 0.0183

ROSAT HRI Energy to Count Conversion Factors
log( )
 0 18 18.7 19 19.7 20 20.7 21 21.7 22 0.0 0.144 0.143 0.142 0.141 0.132 0.125 0.103 0.0893 4.25 e-2 0.0217 0.5 0.164 0.163 0.161 0.158 0.141 0.129 0.0945 0.0796 3.50 e-2 0.0171 1.0 0.181 0.18 0.175 0.17 0.141 0.121 0.0752 0.0602 2.42 e-2 0.0112 1.5 0.19 0.19 0.181 0.173 0.132 0.105 0.0509 0.0379 1.36 e-2 0.00597 2.0 0.188 0.186 0.177 0.167 0.116 0.085 0.0306 0.0205 6.41 e-3 0.00265 2.5 0.178 0.176 0.166 0.154 0.0985 0.0668 0.0175 0.0101 2.67 e-3 0.00104 3.0 0.164 0.161 0.151 0.139 0.082 0.0519 0.00992 0.00476 1.04 e-3 0.000374

ROSAT HRI Energy to Count Conversion Factors
log( )
 kT 0 18 18.7 19 19.7 20 20.7 21 21.7 22 0.01 0.517 0.498 0.429 0.356 0.0875 0.0186 1.59e-05 2e-07 1.0 0e-9 1e-09 0.03 0.339 0.328 0.29 0.25 0.0841 0.028 0.000409 3.2e-05 1.0 0e-9 1e-09 0.05 0.297 0.292 0.273 0.251 0.143 0.0816 0.0055 0.000624 2.7 0e-6 1e-07 0.10 0.274 0.272 0.263 0.252 0.188 0.138 0.0254 0.00727 2.6 9e-4 2.91e-05 0.30 0.192 0.192 0.189 0.186 0.168 0.152 0.102 0.0782 1.7 5e-2 0.00395 0.50 0.241 0.24 0.238 0.235 0.222 0.212 0.175 0.147 4.2 9e-2 0.0114 1.00 0.227 0.226 0.222 0.217 0.195 0.183 0.151 0.131 5.3 3e-2 0.0208 3.00 0.175 0.174 0.172 0.169 0.154 0.144 0.111 0.095 4.2 7e-2 0.0205 5.00 0.166 0.166 0.164 0.161 0.148 0.138 0.106 0.0907 4.0 8e-2 0.0199

ROSAT HRI Energy to Count Conversion Factors
log( )
 kT 0 18 18.7 19 19.7 20 20.7 21 21.7 22 0.01 0.0559 0.0538 0.0465 0.0388 0.00998 0.00235 4.8e-06 1e-07 1.0 0e-9 1e-09 0.03 0.202 0.198 0.185 0.171 0.0985 0.0579 0.00462 0.000561 9.0 0e-7 1e-09 0.05 0.248 0.245 0.235 0.223 0.155 0.108 0.0166 0.004 7.0 7e-5 3.5e-06 0.10 0.189 0.187 0.183 0.178 0.147 0.121 0.0507 0.0305 4.4 0e-3 0.000929 0.30 0.177 0.177 0.176 0.176 0.171 0.166 0.144 0.125 5.4 5e-2 0.0252 0.50 0.139 0.139 0.139 0.138 0.136 0.134 0.121 0.109 5.5 2e-2 0.0288 1.00 0.104 0.104 0.103 0.103 0.102 0.101 0.0929 0.0849 4.7 2e-2 0.0265 3.00 0.0848 0.0848 0.0847 0.0846 0.0838 0.0829 0.0771 0.0711 4.1 3e-2 0.0241 5.00 0.0818 0.0817 0.0817 0.0816 0.0809 0.08 0.0745 0.0688 4.0 3e-2 0.0237

Next: Examples Up: FEASIBILITY: XMA + HRI Previous: Point Source Sensitivity

Michael Arida
Tue Jun 11 16:18:41 EDT 1996