# 6.3 Target Count Rates

We now consider estimation of count rates for objects with stellar, power law, and emission line spectra.

### 6.3.1 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 t is the exposure time in seconds, the QT integral is given in Table 6.1, and AB is given in Table 6.2 as a function of spectral type and wavelength for some example spectral energy distributions. The quantity AB is a color-dependent correction from V magnitude to AB magnitude at frequency . The AB magnitude system is defined as (Oke and Gunn 1983)

where F is the flux in erg cm-2 s-1 Hz-1.

Table 6.2: AB as a Function of Wavelength. AB is defined as a color-dependent correction from V magnitude to AB magnitude at frequency . Wavelength (Å) runs along the top; spectral classes run down the left most column. The second column contains B-V. See Target Count Rates.
 B-V 1500 2000 2500 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000 sky 1.10 2.45 5.46 5.46 3.12 2 1.03 0.55 0.18 -0.11 -0.33 -0.55 -0.65 -0.75 B0 -0.31 -1.6 -1.5 -1.2 -0.78 -0.62 -0.46 -0.36 -0.22 0.16 0.46 0.76 0.96 1.17 A0 0.00 2.22 1.35 1.11 1.21 1 -0.23 -0.16 -0.09 0.11 0.22 0.33 0.36 0.4 F0 0.27 7.22 4.1 3.11 1.99 1.38 0.29 0.06 0.03 0.03 0.05 0.08 0.09 0.1 G0 0.58 8.9 6.35 4.61 2.46 1.63 0.67 0.26 0.08 -0.04 -0.12 -0.21 -0.23 -0.25 K0III 1.07 13 10.3 8.11 5.46 2.13 1.16 0.46 0.2 -0.24 -0.42 -0.61 -0.66 -0.72 M0III 1.60 15 12.3 9.36 6.21 4.63 2.26 0.96 0.51 -0.46 -0.76 -1.06 -1.12 -1.19 gE 1.00 6.82 6.41 5.43 3.63 2.49 1.4 0.55 0.21 -0.19 -0.52 -0.81 -1.07 -1.29 Sa 0.80 5.4 4.8 4.1 3 2.01 1.12 0.44 0.19 -0.17 -0.44 -0.7 -0.95 -1.16 Sbc 0.60 4.03 3.18 2.86 2.46 1.54 0.84 0.34 0.17 -0.14 -0.37 -0.6 -0.84 -1.04 Scd 0.45 2.67 2.29 2.15 1.76 1.35 0.65 0.28 0.13 -0.11 -0.26 -0.39 -0.47 -0.58 Ir I 0.30 1.77 1.4 1.36 1.24 0.94 0.43 0.34 0.17 0.13 -0.04 -0.21 -0.33 -0.45

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:

### 6.3.2 Count Rates for Power Law Sources

If one knows the spectral index (which is zero for a source with a flat continuum), V+AB can also be calculated as the monochromatic Oke system magnitude at the corrected mean wavelength of the filter:

where S 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 . It can be shown that

if the integrands are weighted by a source with spectral index in the definition of . 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

### 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

where F is the emission line flux in units of ergs cm-2 s-1, and 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 F622W, F631N, F656N. For lines near the maxima of the filter transmission curves, it should be sufficient to use QTmax from Table 6.1. Note that the integrated filter efficiency is not relevant for the signal calculation.

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 emission at 6563Å, with total source flux F=10-16 erg s-1 cm-2, observed through the F656N filter (total system throughput T=0.11 from the plots F622W, F631N, F656N), will produce a target count rate Robject=0.17 e- s-1 integrated over the entire source.

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