Wavelength and Magnitude Conversions

This page gives information about how to convert between the wavelength and magnitude conventions used by the SDSS and other systems.

Conversion between vacuum and air wavelengths

The SDSS data describing spectral line wavelengths use vacuum wavelengths. However, the wavelengths of atomic transitions are usually quoted at standard temperature and pressure (S.T.P.); this is how the CRC Handbook of Chemistry and Physics lists them for any transitions redward of 2000 Ångströms.

Thus, recognizing spectral lines associated with atomic transitions may require converting the SDSS data to the equivalent values at S.T.P.

Since Data Release 9 (DR9) in 2012, the SDSS has used the following equation, based on the formulas given in Ciddor (1996), to convert from vacuum (VAC) wavelengths in Ångströms to air (AIR) wavelengths:

AIR = VAC / ( 1.0 +  5.792105E-2/(238.0185 - (1E4/VAC)^2) + 1.67917E-3/( 57.362 - (1E4/VAC)^2))

Air and Vacuum Wavelength of some Common Transitions

[O III]4958.9114960.295
[O III]5006.8435008.239
[N II]6548.056549.86
[N II]6583.456585.27
[S II]6716.446718.29
[S II]6730.826732.68

Note also that the wavelengths are shifted such that measured velocities will be relative to the solar system barycentric at the mid-point of each exposure (using TAI-BEG + 0.5 * EXPTIME from the header).

Conversion from SDSS ugriz magnitudes to AB ugriz magnitudes

The SDSS photometry is intended to be on the AB system (Oke & Gunn 1983), by which a magnitude 0 object should have the same counts as a source of Fν = 3631 Jy. However, this is known not to be exactly true, such that the photometric zeropoints are slightly off the AB standard. We continue to work to pin down these shifts. Our present estimate, based on comparison to the STIS standards of Bohlin, Dickinson, & Calzetti (2001) and confirmed by SDSS photometry and spectroscopy of fainter hot white dwarfs, is that the u band zeropoint is in error by 0.04 mag, uAB = uSDSS – 0.04 mag, and that g, r, and i are close to AB. The z band zeropoint is not as certain at this time, but there is mild evidence that it may be shifted by about 0.02 mag in the sense zAB = zSDSS + 0.02 mag.

The large shift in the u band was expected because the adopted magnitude of the SDSS standard BD+17 in Fukugita et al. (1996) was computed at zero airmass, thereby making the assumed u response bluer than that of the USNO system response.

These statements are certainly not precise to better than 0.01 mag; in addition, they depend on the system response of the SDSS 2.5-meter, which was measured by Doi et al. (2010) and found to differ somewhat from the curves used to estimate the offsets just mentioned, and to probably be a function of time. They estimate the u-g change due to these differences to be at the 0.01 to 0.02 mag level.

Note that our relative photometry across the sky is quite a bit better than these numbers would imply; repeat observations and simulations of the ubercal pipeline show that our calibrations are about 1% in gri and about 2% in u and z.

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