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where t is the exposure time in seconds, the QT integral is given in Table 6.16.3.1 Count Rates for Stellar Sources
To estimate the number of electrons collected from a point source of apparent visual magnitude V, one can use the equation:
where Fn is the flux in erg cm-2 s-1 Hz-1.
Equation 6.1 may be trivially rewritten to give the count rate Robject in units of e- s-1 pixel-1 for a target with a stellar spectrum as:
where S_nu is the flux in ergs cm^-2 s^-1 Hz^-1 as in Oke and Gunn, Ap. J., 266, 713 (1983) at the effective mean wavelength of the filter
if the integrands are weighted by a source with spectral index a in the definition of lambda. See also Koornneef, J., et al. "Synthetic Photometry and the Calibration of the Hubble Space Telescope" in Highlights of Astronomy (7, 833, J.-P. Swings Ed (1983). Combining the above equations gives
where F is the emission line flux in units of ergs cm^-2 s^-1, and l is the wavelength of the line in Angstroms. The quantity QT is the (system + filter) quantum efficiency at the wavelength of the line, which can be determined from inspection of the figures in section A.2, "Passbands including the System Response", on page 211. For lines near the maxima of the filter transmission curves, it should be sufficient to use QTmax from Table 6.1
In cases where the width of the line approaches that of the filter, it will be necessary to convolve the line shape and filter bandpass using either the SYNPHOT or XCAL programs.
For example, H_a emission at 6563Å, with total source flux F=10^-16 erg s^-1 cm^-2, observed through the F656N filter (total system throughput T=0.104 from "F656N, F658N, F673N, F675W, F702W, F785LP" on page 217), will produce a target count rate R_object=0.155 e- s-1 integrated over the entire source.
6.3.2 Count Rates for Power Law Sources
If one knows the spectral index a (which is zero for a source with a flat continuum), V+AB_nu can also be calculated as the monochromatic Oke system magnitude at the corrected mean wavelength of the filter:
. It can be shown that
6.3.3 Count Rates for Emission Line Sources
The count rate in units of e- s-1 for a monochromatic emission line is given by