Bayesian hierarchical modelling of the $\mathrm{M_{\star}}$-SFR relation from 1<z<6 in ASTRODEEP

Abstract

The Hubble Frontier Fields represent the opportunity to probe the high-redshift evolution of the main sequence of star-forming galaxies to lower masses than possible in blank fields thanks to foreground lensing of massive galaxy clusters. We use the BEAGLE SED-fitting code to derive stellar masses, $\mathrm{M_{\star}}=\log(M/\mathrm{M_{\odot}})$, SFRs, $\Psi=\log(\psi/\mathrm{M_{\odot}}\,\mathrm{yr}^{-1})$ and redshifts from galaxies within the ASTRODEEP catalogue. We fit a fully Bayesian hierarchical model of the main sequence over $1.25<z<6$ of the form $\Psi = \alpha_\mathrm{9.7}(z) + \beta(\mathrm{M_{\star}}-9.7) + \mathcal{N}(0,\sigma^2)$ while explicitly modelling the outlier distribution. The redshift-dependent intercept at $\mathrm{M_{\star}}=9.7$ is parametrized as $\alpha_\mathrm{9.7}(z) = \log[N (1+z)^{\gamma}] + 0.7$. Our results agree with an increase in normalization of the main sequence to high redshifts that follows the redshift-dependent rate of accretion of gas onto dark matter halos with $\gamma=2.40^{+0.18}_{-0.18}$. We measure a slope and intrinsic scatter of $\beta=0.79^{+0.03}_{-0.04}$ and $\sigma=0.26^{+0.02}_{-0.02}$. We find that the sampling of the SED provided by the combination of filters (Hubble + ground-based Ks-band + Spitzer 3.6 and 4.5 $\mathrm{\mu m}$) is insufficient to constrain $\mathrm{M_{\star}}$ and $\Psi$ over the full dynamic range of the observed main sequence, even at the lowest redshifts studied. While this filter set represents the best current sampling of high-redshift galaxy SEDs out to $z>3$, measurements of the main sequence to low masses and high redshifts still strongly depend on priors employed in SED fitting (as well as other fitting assumptions). Future data-sets with JWST should improve this.