Attenuation proxy hidden in surface brightness-colour diagrams. A new strategy for the LSST era
Large future sky surveys, such as the LSST, will provide optical photometry for billions of objects. This paper aims to construct a proxy for the far ultraviolet attenuation (AFUVp) from the optical data alone, enabling the rapid estimation of the star formation rate (SFR) for galaxies that lack UV or IR data. To mimic LSST observations, we use the deep panchromatic optical coverage of the SDSS Photometric Catalogue DR~12, complemented by the estimated physical properties for the SDSS galaxies from the GALEX-SDSS-WISE Legacy Catalog (GSWLC) and inclination information obtained from the SDSS DR7. We restricted our sample to the 0.025-0.1 z-spec range and investigated relations among surface brightness, colours, and dust attenuation in the far UV range for star-forming galaxies obtained from the spectral energy distribution (SED). {Dust attenuation is best correlated with (u-r) colour and the surface brightness in the u band ($\rm μ_{u}$). We provide a dust attenuation proxy for galaxies on the star-forming main sequence, which can be used for the LSST or any other type of broadband optical survey. The mean ratio between the catalogue values of SFR and those estimated using optical-only SDSS data with the AFUVp prior calculated as $Δ$SFR=log(SFR$_{\tiny{\mbox{this work}}}$/SFR$_{\tiny{}\texttt{GSWLC}}$) is found to be less than 0.1~dex, while runs without priors result in an SFR overestimation larger than 0.3~dex. The presence or absence of theAFUVp has a negligible influence on the stellar mass estimation (with $Δ$M$_{star}$ in the range from 0 to $-0.15$ dex). Forthcoming deep optical observations of the LSST Deep Drilling Fields, which also have multi-wavelength data, will enable one to calibrate the obtained relation for higher redshift galaxies and, possibly, extend the study towards other types of galaxies, such as early-type galaxies off the main sequence.