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3.2 Summary

The following allows us to compute the exposure time we need as a function of signal-to-noise:

SNR=signal-to-noise ratio per spectral resolution element that you require.

t=integration time in seconds needed to achieve this SNR.

is the number of e per second per spectral resolution element from your object; i.e., take something like the dashed lines in Fig. 8 and scale by the magnitude of your object ( and multiply by your spectral resolution in Å.

is the number of e per second per spectral resolution element contributed by the sky. Use Fig. 9 and/or the table above to find the sky brightness in magnitudes per square arcsecond. Correct this by the number of square arcseconds by multiplying your slit width by the number of arcseconds in your extraction aperture. Determine your count rate from the solid lines in Fig. 8.

p is the number of pixels in a spectral resolution element integrated over the spatial profile.

R is the read-noise (in electrons, RMS), obtained from the table in Sec. 2.

Use when the sky contribution is negligible:

Use when the sky contribution is significant but read-noise is negligible:

Use when the sky contribution and the read-noise are all significant.

In practice, plan on splitting your exposures into separate integrations of 3600s or less to keep the cosmic-ray incidence finite.