Spectroscopy: Sensitivity Tables

These sensitivities are based on data taken with the 4 pixel slit in seeing conditions of 0.5-0.7 arcseconds (i.e. average). They depend closely on the slit width chosen and the delivered image quality. Under similar conditions, a 2-pixel slit would yield 1/sqrt(2) times the signal-to-noise ratio (due to halving the slit width [the increased resolution won't affect the S/N because the flux per pixel doesn't decrease, i.e. narrower slits don't give smaller wavelength coverage...]). The sensitivities also assume nodding the source up and down the slit; for extended objects which require nodding to blank sky, sensitivities will be 0.4 mag (or a factor of 1.5) poorer, i.e. subtract 0.4mag from the numbers below.

Those preparing telescope proposals should also consider the overheads associated with spectroscopic observations. These can be considerable for short exposure times (see the section on read speed and efficiency for details). For brighter science targets, two minutes per source, e.g. one "quad" (one object-sky-sky-object group) comprising four 30sec exposures, is probably a sensible "minimum time" to spend on each target (provided they don't saturate, of course).

The sensitivity figures are measured near the center of the wavelength range covered by the grism, or at a wavelength where the transmission is good. Sensitivity may decrease towards the edges of the wavelength range, or between atmospheric windows. Click on the grism name to get a rough idea of how the transmission changes across the wavelength range. See also the discussion on obtaining background limited performance.

Which values should I use...?

• For Point, continuum sources - Use Table 1
• For Point, line-emission sources - Use Table 1 (see notes)
• For Extended, continuum sources - Use Table 2, column 3
• For Extended, line-emission sources; line spectrally RESOLVED - Use Table 2, column 5
• For Extended, line-emission sources; line spectrally UNRESOLVED - Use Table 2, column 6

• The above values were derived from the signal-to-noise measured on an optimally-extracted spectrum of a faint standard star.
• Values apply to the wavelength specified in column 2. The S/N will of course degrade towards the edges of the atmospheric window associated with each grism (as noted above).
• Values are per spectral pixel, so this is what you'd get with unsmoothed, though coadded continuum source data. The spectral resolution is ~4 pixels, so sensitivities per resolution element (e.g. for comparison with CGS4 figures) will be 0.8mag better (add 0.8mag to the above numbers). To get the "per resn element" sensitivity, observers would have to bin their spectra over 4 pixels.
• For spectrally unresolved emission-line point sources, remember that the line flux will be spread over 4 spectral pixels (with the 4-pix slit), so for your source you must use a line magnitude per spectral pixel (add 1.5mag with the 4-pixel slit) before comparing your line flux with the above table: e.g. for a 15.6mag line spread over 4 pixels, will effectively get 17.1mag per spectral pixel and so would expect 3sigma in 30mins with the HK grism. (Smoothing spectra will again improve sensitivity for fainter lines of course.)
• In the non-thermal, the tabulated performance was achieved with long (240sec) exposure times; in the J-band (IJ grism), 600 second exposures were used. Shorter exposure times will probably give poorer performance (discussed here).
• At thermal wavelengths extracted spectra were divided by a standard star to remove telluric absorption features. Sensitivities at these wavelengths (particularly at short_L and M) will be dependent on stable atmospheric conditions and good sky-subtraction.

• The surface brightness sensitivities in columns 4-6 were derived from per resolution element point source values (i.e. the values in column 3, plus 0.8mags for the 4-pixel slit/resolution). They are therefore appropriate for spectrally unresolved emission-line sources (i.e. where the quoted flux is spread over 4-pixel resolution element).
• To get the mag/arcsec sensitivities in column 3 and 4, we have assumed flux from point source calibrator spread over 10 rows, or 40 pixels with the 4-pixel slit (so first ADDED 2.5 log(sqrt[40])); the pixel scale is 0.12 arcsec (so then SUBTRACTED 2.5 log(1/0.12")).
• For weak emission lines superimposed onto bright continuum sources the S/N will be worse than the 3sigma prediction (because of the additional poisson noise). Here's one possible way of doing it.
• IMPORTANT: All extended source sensitivities assume nodding the source up and down the slit; for extended objects which require nodding to blank sky, sensitivities will be 0.4 mag (or a factor of 1.5) poorer, i.e. subtract 0.4mag from the numbers below.