Magnitude to luminance conversions and visual brightness of the night sky

The visual brightness of the night sky is not a single-valued function of its brightness in other photometric bands, because the transformations between photometric systems depend on the spectral power distribution of the skyglow. We analyse the transformation between the night sky brightness in the Johnson-Cousins V band (m_V, measured in magnitudes per square arcsecond, mpsas) and its visual luminance (L, in SI units cd m^-2) for observers with photopic and scotopic adaptation, in terms of the spectral power distribution of the incident light. We calculate the zero-point luminances for a set of skyglow spectra recorded at different places in the world, including strongly light-polluted locations and sites with nearly pristine natural dark skies. The photopic skyglow luminance corresponding to m_V=0.00 mpsas is found to vary in the range 1.11-1.34 × 10⁵ cd m^-2 if m_V is reported in the absolute (AB) magnitude scale, and in the range 1.18-1.43 × 10⁵ cd m^-2 if a Vega scale for m_V is used instead. The photopic luminance for m_V=22.0 mpsas is correspondingly comprised between 176 and 213 μcd m^-2 (AB), or 187 and 227 μcd m^-2 (Vega). These constants tend to decrease for increasing correlated colour temperature (CCT). The photopic zero-point luminances are generally higher than the ones expected for blackbody radiation of comparable CCT. The scotopic-to-photopic luminance (S/P) ratio for our spectral data set varies from 0.8 to 2.5. Under scotopic adaptation the dependence of the zero-point luminances with the CCT, and their values relative to blackbody radiation, is reversed with respect to photopic ones.