The First Billion Years project: constraining the dust attenuation law of star-forming galaxies at z $\simeq$ 5

We present the results of a study investigating the dust attenuation law at $z\simeq 5$, based on synthetic spectral energy distributions (SEDs) calculated for a sample of N=498 galaxies drawn from the First Billion Years (FiBY) simulation project. The simulated galaxies at $z\simeq 5$, which have M$_{1500} \leq -18.0$ and $7.5 \leq \rm{log(M/M}_{\odot}\rm{)} \leq 10.2$, display a mass-dependent $\alpha$-enhancement, with a median value of $[\alpha/\rm{Fe}]_{z=5}~\simeq~4~\times~[\alpha/\rm{Fe}]_{Z_{\odot}}$. The median Fe/H ratio of the simulated galaxies is $0.14\pm0.05$ which, even including the effects of nebular continuum, produces steep intrinsic UV continuum slopes; $\langle \beta_{i} \rangle = -2.4 \pm 0.05$. Using a set of simple dust attenuation models, in which the wavelength-dependent attenuation is assumed to be of the form $A(\lambda) \propto \lambda^{n}$, we explore the parameter values which best reproduce the observed $z=5$ luminosity function (LF) and colour-magnitude relation (CMR). We find that a simple model in which the absolute UV attenuation is a linearly increasing function of log stellar mass, and the dust attenuation slope ($n$) is within the range $-0.7 \leq n \leq-0.3$, can successfully reproduce the LF and CMR over a wide range of stellar population synthesis model (SPS) assumptions. This range of attenuation curves is consistent with a power-law fit to the Calzetti attenuation law in the UV ($n=-0.55$), and other similarly `grey' star-forming galaxy attenuation curves recently derived at $z\simeq2$. In contrast, attenuation curves as steep as the Small Magellanic Cloud (SMC) extinction curve ($n=-1.24$) are formally ruled out. Finally, we show that our models are consistent with recent 1.3mm ALMA observations of the Hubble Ultra Deep Field (HUDF), and predict the form of the $z\simeq5$ IRX$-\beta$ relation.