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

TL;DR

This paper employs Bayesian hierarchical modeling to analyze the evolution of the star-forming main sequence from redshift 1.25 to 6, revealing how galaxy star formation correlates with stellar mass and redshift, and highlighting current limitations in SED fitting.

Contribution

It introduces a Bayesian hierarchical approach to model the M_star-SFR relation across high redshifts, explicitly accounting for outliers and redshift evolution, with implications for future JWST data.

Findings

Main sequence normalization increases with redshift following gas accretion rates.

Slope of the M_star-SFR relation is approximately 0.79.

Current SED data are insufficient to fully constrain galaxy properties at high redshift.

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.