XMM-Newton Science Simulator

## Count rate calculation

The count rate is calculated by dividing the flux density, at wavelength , by the photon energy , to give the photon flux. This is then integrated over the range of wavelengths to and multiplied by the telescope entrance area to give the total count rate:

 (7)

 where is the entrance area of the telescope is the wavelength is the stellar Flux per unit wavelength is the transmission of the optical system is the photocathode quantum efficiency is Planck's constant and is the speed of light

The transmission is made up of the following components:

 (8)

 where is the primary mirror reflectance is the secondary mirror reflectance is the dichroic reflectance is the filter transmission is the detector window transmission is the open area ratio of the MCP and is the ratio between measured and expected count rates

Each source in the input file specifies a spectral type and a magnitude . OSIM has a set of tables, giving the flux of standard spectral types for magnitude V=0.

The source flux density is calculated as follows:

 (9)

OSIM does not implement CCD readout frames or Poisson noise. Therefore, the total count is simply the count rate multiplied by the exposure time :

 (10)

Since the sources are regarded as point sources, this represents the number of counts at a single point in the focal plane. The application of the Point Spread Function subsequently distributes this total number of counts amongst a number of neighbouring pixels.

The symbols used above, correspond to the following keywords in the configuration file:

 area spectral files primary secondary dichroic window oa_ratio cr_ratio cathode filter files exposureTime lambdaMin lambdaMax

The source spectra are specified by tables giving the flux density, for various spectral types, as a function of wavelength. Similarly, the transmission and reflection coefficients of the optical components and the photocathode quantum efficiency are tabulated as a function of wavelength. The configuration file specifies the name of the files containing each of these tables.

Cubic-spline interpolation coefficients are calculated for each of the tables. The integration is then carried out numerically, by the trapezoidal method, using interpolated values for a sequence of closely-spaced wavelengths. The integration step size is controlled by the following additional parameter in the configuration file:

   lambdaStep


The tables should cover at least the range lambdaMin to lambdaMax, otherwise extrapolation will take place, leading to unreliable results (OSIM warns if this happens).

The wavelengths in the tables need not be equally spaced. More accurate interpolation will be achieved if the wavelengths are closely spaced in regions where the response is varying sharply.

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