Black-body luminance and magnitudes per square arcsecond in the Johnson-Cousins BVR photometric bands

A relevant number of light pollution studies deal with unwanted visual effects of artificial light at night, including the anthropogenic luminance of the sky that hinders the observation of celestial bodies which are the main target of ground-based astrophysical research, and a key asset of the intangible heritage of humankind. Most quantitative measurements and numerical models, however, evaluate the anthropogenic sky radiance in any of the standard Johnson-Cousins UBVRI photometric bands, generally in the V one. Since the Johnson-Cousins V band is not identical with the visual CIE V(λ) used to assess luminance, the conversion between these two photometric systems turns out to be spectrum-dependent. Given its interest for practical applications, in this Letter we provide the framework to perform this conversion and the transformation constants for black-body spectra of different absolute temperatures.