Space Telescope Science Institute   9.2 Determining Count Rates from Sensitivities  9.2.2 Spectroscopy

9.2.1 Imaging


Point Source

For a point source, the count rate, C, can be expressed as the integral over the bandpass of the filter:

Where:

The peak counts/second/pixel/ from the point source, is given by:

Where:

Again, the integral is over the bandpass.

If the flux from your source can be approximated by a flat continuum (F = constant) and f is roughly constant over the bandpass, then:

We can now define an equivalent bandpass of the filter (B) such that:

Where:

The count rate from the source can now be written as:

In Tables 9.1 to 9.3, we give the value of for each of the filters.

Alternatively, we can write the equation in terms of V magnitudes:

where V is the visual magnitude of the source, the quantity under the integral sign is the mean sensitivity of the detector+filter combination, and is tabulated in Tables 9.1 to 9.3, and n is the filter-dependent correction for the deviation of the source spectrum from a constant F spectrum. This latter quantity is tabulated for several different astronomical spectra in Tables 10.1 to 10.3 in Chapter 10.

Diffuse Source

For a diffuse source, the count rate, C, per pixel, due to the astronomical source can be expressed as

:

Where:

Emission Line Source

For a source where the flux is dominated by a single emission line, the count rate can be calculated from the equation

where C is the observed count rate in counts/second, (QT) is the system throughput at the wavelength of the emission line, F() is the emission line flux in units of erg/cm2/second, and is the wavelength of the emission line in Angstroms. (QT) can be determined by inspection of the plots in Chapter 10. See Section 9.6.4 for an example of emission-line imaging using ACS.


 9.2 Determining Count Rates from Sensitivities  9.2.2 Spectroscopy
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