The VANDELS survey: Dust attenuation in star-forming galaxies at z=3-4

We present the results of a new study of dust attenuation at redshifts $3 < z < 4$ based on a sample of $236$ star-forming galaxies from the VANDELS spectroscopic survey. Motivated by results from the First Billion Years (FiBY) simulation project, we argue that the intrinsic spectral energy distributions (SEDs) of star-forming galaxies at these redshifts have a self-similar shape across the mass range $8.2 \leq$ log$(M_{\star}/M_{\odot}) \leq 10.6$ probed by our sample. Using FiBY data, we construct a set of intrinsic SED templates which incorporate both detailed star formation and chemical abundance histories, and a variety of stellar population synthesis (SPS) model assumptions. With this set of intrinsic SEDs, we present a novel approach for directly recovering the shape and normalization of the dust attenuation curve. We find, across all of the intrinsic templates considered, that the average attenuation curve for star-forming galaxies at $z\simeq3.5$ is similar in shape to the commonly-adopted Calzetti starburst law, with an average total-to-selective attenuation ratio of $R_{V}=4.18\pm0.29$. We show that the optical attenuation ($A_V$) versus stellar mass ($M_{\star}$) relation predicted using our method is consistent with recent ALMA observations of galaxies at $2<z<3$ in the \emph{Hubble} \emph{Ultra} \emph{Deep} \emph{Field} (HUDF), as well as empirical $A_V - M_{\star}$ relations predicted by a Calzetti-like law. Our results, combined with other literature data, suggest that the $A_V - M_{\star}$ relation does not evolve over the redshift range $0<z<5$, at least for galaxies with log$(M_{\star}/M_{\odot}) \gtrsim 9.5$. Finally, we present tentative evidence which suggests that the attenuation curve may become steeper at log$(M_{\star}/M_{\odot}) \lesssim 9.0$.