Bayesian hierarchical modelling of the M*–SFR relation from 1 ≲ z ≲ 6 in ASTRODEEP

Abstract

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, $\rm{{M_{\star }}}=\log ({\it M}/{\rm{M_{\odot }}})$, SFRs, $\rm{{\Psi }}=\log (\rm{{\psi }}/{\rm{M_{\odot }}}\, {\rm{yr}}^{-1})$, 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 $\rm{{\Psi }}= \rm{\alpha _\mathrm{9.7}}(z) + \rm{\beta }({\rm{M_{\star }}}-9.7) + \mathcal {N}(0,\rm{\sigma }^2)$ while explicitly modelling the outlier distribution. The redshift-dependent intercept at $\rm{{M_{\star }}}=9.7$ is parametrized as $\rm{\alpha _\mathrm{9.7}}(z) = \log [{\it N}(1+{\it z})^{\rm{\gamma }}] + 0.7$. 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 on to dark matter haloes with $\rm{\gamma }=2.40^{+0.18}_{-0.18}$. We measure a slope and intrinsic scatter of $\rm{\beta }=0.79^{+0.03}_{-0.04}$ and $\rm{\sigma }=0.26^{+0.02}_{-0.02}$. 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 μm) is insufficient to constrain M⋆ and Ψ 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.