Evolution of dust attenuation in star-forming galaxies with UV slope, stellar mass, and redshift out to $z \sim 5$

Aims. We derive a dependence of the IRX on UV slope $β$, stellar mass $M_\ast$, and redshift out to $z \simeq 5$, and establish consistent functional relations that can be used for correcting the UV/optical-selected galaxy samples for the effects of dust absorption. Methods. This work is based on a $K$-band selected sample of $\sim 10^5$ star-forming galaxies detected in the UDS and COSMOS fields. Quiescent sources and known starbursts are removed, and the IR luminosities are established through stacking in FIR {\it Herschel} and JCMT maps. UV slopes are found from SED fits and stacked IRX values are derived by taking the median of individual IRX measurements in bins of $β$, $M_\ast$ and redshift. Results. While our best-fit IRX-$β$ relation is consistent with a Calzetti-like attenuation curve at $β\gtrsim -1$, at bluer values the IRX seems to increase with redshift due to different mass-completeness limits imposed. When deriving the IRX-$β$ relation in stellar-mass bins, a systematic trend is found, where the effective slope of the attenuation law becomes progressively shallower with increasing mass. We incorporate this into the IRX-$β$ relation through the slope of the underlying reddening law, $dA_{1600}/dβ$, being a quadratic function of $\log(M_\ast/{\rm M_\odot})$. Expressing IRX as a function of the stellar mass we find a tight correlation, with IRX rising monotonically with mass but exhibiting a clear high-mass turnover at $z\lesssim 2-3$, consistent with suppressed cold-gas accretion and dust growth in massive systems.