3.3 Expected Count Rates

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With the 1997 May revision, this section has been rewritten in order to give ECF tables based on the current version of the IRAF/PROS software and effective area tables (PROS 2.4); and to provide conversion factors which refer to the total countrate of a source (not the "50% detection cell"). Therefore, it is up to the user to apply the appropriate vignetting, scattering, and other corrections to the countrate.

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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 corresponding figures 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:

1.

Power Law Spectrum, where $\alpha$ is the energy index.

2.

Thermal Bremsstrahlung (Exponential plus Gaunt Factor) Spectrum, where kT is in keV.

3.

Raymond-Smith Plasma Spectrum where kT is in keV.

4.

Blackbody Spectrum, where kT is in keV.

For each spectral model we calculate the factor by which the unabsorbed source flux in the 0.1 - 2.4 keV band measured in cgs units (erg cm^-2 s^-1) has to be multiplied in order to obtain the expected HRI on-axis count rate. The conversion factor is a function of the intrinsic source spectrum (characterized by $\alpha$ or kT), and the interstellar absorption column density N_H.

The ECF values were derived by multiple runs of the task 'hxflux' in IRAF/PROS vs 2.4. The effective area curve is that included in the PROS release, and differs in small ways from that used previously: although the same calibration points were used, the model fits were slightly different. Therefore, do not expect to find perfect agreement with the effective area shown in the figure and table of the section on effective area.

Except for the Raymond-Smith spectra (Table 10), most entries in the new tables agree with their previous counterparts to 10% or better. Significant differences occur for soft spectra with non-negligable column densities. We believe this results from the poorly known effective area at soft energies, not from software problems. In the extreme case of high absorption and extremely soft spectra, the model 'presented to' the mirror/detector mimics a delta function in energy, and it is clear that markedly different results can be obtained form small differences in the fit to the effective area.

The newly derived ECF factors for the Raymond-Smith spectra are within 10% of the previous values only for kT > 3 keV and for kT close to 0.3 keV. We suspect that the larger changes for other temperatures arise because of differences in the version of the RS tables. The Raymond-Smith tables resident in PROS 2.4 are those which were new in 1992 Oct (PROS release 2.1); the previous ECF values used an older version (circa 1990.5).

The tables should be used as follows:

1.

Estimate the unabsorbed source flux F_{S, 0} in cgs units (ergs cm^-2 s^-1) in the ROSAT pass band 0.1-2.4 keV. This is the flux which would have been incident on the Earth in the absence of any absorption.

2.

Estimate the interstellar absorption column density.

3.

With the assumed values of N_H and spectral parameter ($\alpha$ or kT) read the resulting energy-to-counts conversion factor ECF.

4.

Multiply F_{S, 0} and ECF to obtain the expected ROSAT HRI count rate.

counts/sec = ECF * F_{S, 0}

  

Table 8: ROSAT HRI Energy to Count Conversion Factors
log(N_H)
Power Law

$\alpha$	0.0	18.0	18.7	19.0	19.7	20.0	20.7	21.0	21.7	22.0	22.7	23.0
0.0	2.63e10	2.62e10	2.60e10	2.58e10	2.43e10	2.30e10	1.89e10	1.64e10	7.80e9	4.00e9	1.61e8	1.04e7
0.5	3.02e10	3.00e10	2.95e10	2.90e10	2.61e10	2.38e10	1.75e10	1.48e10	6.50e9	3.18e9	1.14e8	7.03e6
1.0	3.39e10	3.36e10	3.27e10	3.18e10	2.64e10	2.28e10	1.42e10	1.14e10	4.56e9	2.12e9	6.78e7	4.00e6
1.5	3.66e10	3.62e10	3.48e10	3.32e10	2.53e10	2.02e10	9.93e9	7.40e9	2.65e9	1.17e9	3.28e7	1.85e6
2.0	3.78e10	3.73e10	3.54e10	3.33e10	2.30e10	1.70e10	6.22e9	4.18e9	1.30e9	5.41e8	1.33e7
2.5	3.80e10	3.72e10	3.48e10	3.21e10	2.04e10	1.39e10	3.71e9	2.15e9	5.69e8	2.21e8	4.70e6
3.0	3.72e10	3.64e10	3.35e10	3.05e10	1.77e10	1.13e10	2.21e9	1.07e9	2.31e8	8.32e7	1.53e6

  

Table 9: ROSAT HRI Energy to Count Conversion Factors
log(N_H)
Thermal Bremsstrahlung

kT	0.0	18.0	18.7	19.0	19.7	20.0	20.7	21.0	21.7	22.0	22.7	23.0
0.03	3.13e10	3.02e10	2.64e10	2.26e10	8.98e9	4.00e9	1.49e8	1.33e7
0.05	3.65e10	3.57e10	3.25e10	2.93e10	1.52e10	8.51e9	6.58e8	8.91e7
0.10	4.14e10	4.08e10	3.84e10	3.58e10	2.27e10	1.49e10	2.14e9	5.77e8	2.14e7	2.46e6
0.30	3.85e10	3.81e10	3.67e10	3.51e10	2.67e10	2.09e10	8.08e9	5.17e9	1.19e9	3.84e8	3.97e6
0.50	3.67e10	3.65e10	3.55e10	3.43e10	2.79e10	2.34e10	1.24e10	9.20e9	2.85e9	1.11e9	1.98e7
1.00	3.44e10	3.42e10	3.35e10	3.28e10	2.84e10	2.51e10	1.65e10	1.33e10	5.03e9	2.22e9	5.80e7	3.12e6
3.00	3.09e10	3.08e10	3.03e10	2.99e10	2.71e10	2.49e10	1.85e10	1.55e10	6.66e9	3.20e9	1.07e8	6.36e6
5.00	2.99e10	2.98e10	2.95e10	2.90e10	2.65e10	2.45e10	1.87e10	1.58e10	6.99e9	3.40e9	1.20e8	7.25e6

  

Table 10: ROSAT HRI Energy to Count Conversion Factors
log(N_H)
Raymond-Smith

kT	0.0	18.0	18.7	19.0	19.7	20.0	20.7	21.0	21.7	22.0	22.7	23.0
0.01	4.21e10	3.86e10	2.77e10	1.89e10	2.09e9	3.50e8
0.03	2.79e10	2.66e10	2.21e10	1.80e10	5.57e9	2.06e9	4.53e7	3.93e6
0.05	3.65e10	3.55e10	3.19e10	2.84e10	1.39e10	7.21e9	3.57e8	4.68e7
0.10	4.54e10	4.47e10	4.22e10	3.96e10	2.75e10	1.92e10	3.30e9	1.03e9	3.78e7	4.03e6
0.30	3.59e10	3.58e10	3.54e10	3.49e10	3.19e10	2.94e10	2.12e10	1.66e10	3.78e9	8.64e8	4.66e6
0.50	4.18e10	4.16e10	4.13e10	4.08e10	3.86e10	3.70e10	3.03e10	2.51e10	6.90e9	1.81e9	1.52e7
1.00	3.71e10	3.70e10	3.64e10	3.57e10	3.26e10	3.09e10	2.57e10	2.22e10	8.84e9	3.47e9	6.08e7	3.43e6
3.00	3.12e10	3.11e10	3.07e10	3.03e10	2.78e10	2.59e10	2.01e10	1.72e10	7.70e9	3.69e9	1.14e8	6.78e6
5.00	3.00e10	2.99e10	2.95e10	2.92e10	2.68e10	2.50e10	1.94e10	1.65e10	7.40e9	3.60e9	1.22e8	7.44e6

  

Table 11: ROSAT HRI Energy to Count Conversion Factors
log(N_H)
Blackbody

kT	0.0	18.0	18.7	19.0	19.7	20.0	20.7	21.0	21.7	22.0	22.7	23.0
0.03	4.07e10	4.00e10	3.72e10	3.42e10	1.96e10	1.16e10	9.43e8	1.17e8
0.05	4.62e10	4.56e10	4.37e10	4.14e10	2.90e10	2.03e10	3.14e9	7.70e8	1.33e7
0.10	3.43e10	3.41e10	3.33e10	3.24e10	2.68e10	2.21e10	9.35e9	5.63e9	8.08e8	1.71e8
0.30	3.25e10	3.24e10	3.23e10	3.22e10	3.14e10	3.06e10	2.64e10	2.30e10	1.00e10	4.62e9	1.20e8	6.08e6
0.50	2.55e10	2.55e10	2.54e10	2.54e10	2.50e10	2.46e10	2.22e10	1.99e10	1.01e10	5.29e9	2.06e8	1.26e7
1.00	1.89e10	1.89e10	1.89e10	1.89e10	1.87e10	1.84e10	1.70e10	1.55e10	8.64e9	4.84e9	2.42e8	1.66e7
3.00	1.54e10	1.54e10	1.54e10	1.54e10	1.53e10	1.51e10	1.40e10	1.29e10	7.54e9	4.40e9	2.48e8	1.81e7
5.00	1.49e10	1.49e10	1.49e10	1.48e10	1.47e10	1.46e10	1.36e10	1.25e10	7.35e9	4.32e9	2.49e8	1.83e7