Attenuation proxy hidden in surface brightness - colour diagrams: A new strategy for the LSST era

Aims. Large future sky surveys, such as the Legacy Survey of Space and Time (LSST), will provide optical photometry for billions of objects. Reliable estimation of the physical properties of galaxies requires information about dust attenuation, which is usually derived from ultraviolet (UV) and infrared (IR) data. This paper aims to construct a proxy for the far-UV (FUV) attenuation (A_FUVp) from the optical data alone, enabling the rapid estimation of the star formation rate (SFR) for galaxies that lack UV or IR data. This will accelerate and improve the estimation of key physical properties of billions of LSST-like observed galaxies (observed in the optical bands only). Methods. To mimic LSST observations, we used the deep panchromatic optical coverage of the Sloan Digital Sky Survey (SDSS) Photometric Catalogue, Data Release 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 Data Release 7. We restricted our sample to the 0.025-0.1 spectroscopic redshift range and investigated relations among surface brightness, colours, and dust attenuation in the FUV range for star-forming galaxies obtained from the spectral energy distribution (SED). Results. Dust attenuation is best correlated with colour measured between u and r bands (u-r) and the surface brightness in the u band (μ_u). We provide a dust attenuation proxy for galaxies on the star-forming main sequence. This relation can be used for the LSST or any other type of broadband optical survey. The mean ratio between the catalogue values of SFRs and those estimated using optical-only SDSS data with the A_FUVp prior calculated as ΔSFR = log(SFR_thiswork/SFR_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 the A_FUVp has a negligible influence on the stellar mass (M_star) estimation (with ΔM_star in the range from 0 to -0.15 dex). Conclusions. We note that A_FUVp is reliable for low-redshift main sequence galaxies. 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.