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Next: Spectral Capabilities Up: FEASIBILITY: XMA+PSPC Previous: Minimum detectable count rates

Expected Count Rates


The expected PSPC count rates depend sensitively on the assumed incident spectrum which is unknown for most sources. In general, the convolution of effective area and incident spectrum is non-trivial because of substantial changes in effective area as a function of energy. In order to facilitate count rate calculations, the count rate curves are provided for power law spectra, thermal line spectra and blackbody spectra as a function of interstellar absorption column density tex2html_wrap_inline2416 .

In Figures 10.2 gif - 10.7gif, the energy-to-counts conversion factor (ECF) is shown, i.e., the factor by which the unabsorbed source flux (in units of tex2html_wrap_inline2420  ergs cm tex2html_wrap_inline1930  s tex2html_wrap_inline1894 in the 0.1 - 2.4 keV band) has to be multiplied in order to obtain the expected PSPC on-axis count rate. Figure 10.2 gif shows the ECF for power law spectra with photon index tex2html_wrap_inline2288 for various N tex2html_wrap_inline2428 values between tex2html_wrap_inline2430  cm tex2html_wrap_inline1930 and tex2html_wrap_inline2434  cm tex2html_wrap_inline1930 . Whereas for small values of N tex2html_wrap_inline2428 a distinct variation of ECF vs. tex2html_wrap_inline2288 occurs, the ECF is basically constant (with respect to tex2html_wrap_inline2288 ) at values around tex2html_wrap_inline2444  counts cm tex2html_wrap_inline1870  erg tex2html_wrap_inline1894 for larger values of tex2html_wrap_inline2416 typically found for AGNs. Figure 10.3 gif shows the equivalent curve for thermal line spectra. For such spectra the ECF does depend sensitively on the assumed temperature (in addition to tex2html_wrap_inline2416 ) with the largest ECF values found at temperatures tex2html_wrap_inline2454  K. Lastly, Figure 10.4 gif shows the ECF for blackbody spectra; here the maximum ECF is found at tex2html_wrap_inline2456 .

 fig10-2 figure901

 fig10-3 figure909

 fig10-4 figure917

Figures 10.5 gif - 10.7gif show the ECF for the PSPC used with the boron filter for power law, thermal line and blackbody spectra for various values of tex2html_wrap_inline2416 . Although the general shapes of the curves remain unchanged, the absolute values change significantly due to the reduced transmission of the boron filter.

 fig10-5 figure928

Figures 10.8 gif - 10.13gif show the ECF for the PSPC if only the hard pulse height channels are used for power law, thermal line and blackbody spectra for various values of tex2html_wrap_inline2416 . Because the PSPC background is dominated by soft events (cf., Chapter 7 gif), sources with hard spectrum can be more easily detected in the higher energy band; the curves provided in Figures 10.8 gif - 10.13gif allow to assess (in conjunction with Figure 12.1 gif) whether a restriction to the higher energies increases sensitivity or not.

The curves shown in Figures 10.2 gif - 10.13gif should be used as follows:

  1. Calculate the expected source flux tex2html_wrap_inline2506 (in units of tex2html_wrap_inline2420  erg cm tex2html_wrap_inline1930  s tex2html_wrap_inline1894 ) 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 tex2html_wrap_inline2416 and power laws and/or temperatures read from Figures 10.2 gif - 10.7 gif the resulting energy-to-count conversion factor ECF.
  4. 4. Multiply tex2html_wrap_inline2506 by ECF to obtain the expected ROSAT PSPC count rate.

Example 1:

The expected count rate from a coronal source with tex2html_wrap_inline2520  ergs s tex2html_wrap_inline1894 at a distance of 50 pc and tex2html_wrap_inline2524  cm tex2html_wrap_inline1930 is to be estimated. The temperature of the source is assumed to be tex2html_wrap_inline2528  K. With these parameters an unabsorbed flux of tex2html_wrap_inline2530  ergs cm tex2html_wrap_inline1930  s tex2html_wrap_inline1894 is calculated. From Figure 10.3 gif a ECF of 1.25 is estimated, hence a count rate of 4.25 counts s tex2html_wrap_inline1894 is expected. Similarly, using the boron filter, a ECF of 0.6 is found from Figure 10.6 gif, and consequently the count rate is expected to be 2.0 counts s tex2html_wrap_inline1894 . Note that no corrections for dead time, vignetting or scattering out of the detect cell have been applied. Therefore the curves in Figures 10.2 gif - 10.7gif apply only to on-axis observations of point sources with sufficiently large detect cell sizes.

 fig10-6 figure974

 fig10-7 figure982

 fig10-8 figure990

 fig10-9 figure998

 fig10-10 figure1006

 fig10-11 figure1014

 fig10-12 figure1022

 fig10-13 figure1030

Example 2: A power law source with photon index 1.7 and an intensity (at 1 keV) of 0.01 keV cm tex2html_wrap_inline1930  s tex2html_wrap_inline1894  keV tex2html_wrap_inline1894 is to be observed through an absorbing column density of tex2html_wrap_inline2616  cm tex2html_wrap_inline1930 . With this spectrum one obtains an unabsorbed flux of tex2html_wrap_inline2620  ergs cm tex2html_wrap_inline1930  s tex2html_wrap_inline1894 in the pass band 0.1-2.4 keV. From Figure 10.2 gif, one finds a ECF of 0.55, hence a count rate of 2.4 counts s tex2html_wrap_inline1894 is expected. Similarly, for the boron filter one calculates an expected count rate of 1.2 counts s tex2html_wrap_inline1894 with a ECF of 0.28 taken from Figure 10.5 gif.

next up previous contents
Next: Spectral Capabilities Up: FEASIBILITY: XMA+PSPC Previous: Minimum detectable count rates

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