Dust attenuation in 2<z<3 star-forming galaxies from deep ALMA observations of the Hubble Ultra Deep Field

We present the results of a new study of the relationship between infrared excess (IRX ≡ L IR/L UV), ultraviolet (UV) spectral slope (β) and stellar mass at redshifts 2 < z < 3, based on a deep Atacama Large Millimeter Array (ALMA) 1.3-mm continuum mosaic of the Hubble Ultra Deep Field. Excluding the most heavily obscured sources, we use a stacking analysis to show that z ≃ 2.5 star-forming galaxies in the mass range 9.25 ≤ log(M*/M ⊙) ≤ 10.75 are fully consistent with the IRX-β relation expected for a relatively grey attenuation curve, similar to the commonly adopted Calzetti law. Based on a large, mass-complete sample of 2 ≤ z ≤ 3 star-forming galaxies drawn frommultiple surveys, we proceed to derive a new empirical relationship between β and stellar mass, making it possible to predict UV attenuation (A1600) and IRX as a function of stellar mass, for any assumed attenuation law. Once again, we find that z ≃ 2.5 star-forming galaxies follow A1600-M* and IRX-M* relations consistent with a relatively grey attenuation law, and find no compelling evidence that star-forming galaxies at this epoch follow a reddening law as steep as the Small Magellanic Cloud (SMC) extinction curve. In fact, we use a simple simulation to demonstrate that previous determinations of the IRX-β relation may have been biased towards low values of IRX at red values of β, mimicking the signature expected for an SMC-like dust law. We show that this provides a plausible mechanism for reconciling apparently contradictory results in the literature and that, based on typical measurement uncertainties, stellar mass provides a cleaner prediction of UV attenuation than β. Although the situation at lower stellar masses remains uncertain, we conclude that for 2 < z < 3 star-forming galaxies with log(M*/M ⊙) ≥ 9.75, both the IRX-β and IRX-M* relations are well described by a Calzetti-like attenuation law.