How robustly can we constrain the low-mass end of the $z\sim6-7$ stellar mass function? -- The limits of lensing models and stellar population assumptions in the Hubble Frontier Fields

TL;DR

This study measures the low-mass end of the galaxy stellar mass function at redshifts 6-7 using gravitational lensing and deep imaging, revealing a steep slope and a potential turnover, but with uncertainties due to model assumptions.

Contribution

It provides new constraints on the low-mass end of the high-redshift GSMF, accounting for lensing uncertainties and exploring the impact of different stellar population models.

Findings

Steep low-mass end slope of about -1.96

Detection of a possible turnover at low masses around 10^7 M_sun

Significant dependence of results on star formation history assumptions

Abstract

We present new measurements of the very low-mass end of the galaxy stellar mass function (GSMF) at $z\sim6-7$ computed from a rest-frame ultraviolet selected sample of dropout galaxies. These galaxies lie behind the six Hubble Frontier Fields clusters and are all gravitationally magnified. Using deep Spitzer/IRAC and Hubble Space Telescope imaging, we derive stellar masses by fitting galaxy spectral energy distributions and explore the impact of different model assumptions and parameter degeneracies on the resulting GSMF. Our sample probes stellar masses down to $M_{\star}>10^{6}\,\text{M}_{\odot}$ and we find the $z\sim6-7$ GSMF to be best parametrized by a modified Schechter function which allows for a turnover at very low masses. Using a Monte-Carlo Markov Chain analysis of the GSMF, including accurate treatment of lensing uncertainties, we obtain a relatively steep low-mass end slope $\alpha\simeq-1.96_{-0.08}^{+0.09}$ and a turnover at $\log(M_T/\text{M}_{\odot})\simeq7.10_{-0.56}^{+0.17}$ with a curvature of $\beta\simeq1.00_{-0.73}^{+0.87}$ for our minimum assumption model with constant star-formation history (SFH) and low dust attenuation, $A_V\leq0.2$. We find that the $z\sim6-7$ GSMF, in particular its very low-mass end, is significantly affected by the assumed functional form of the star formation history and the degeneracy between stellar mass and dust attenuation. For example, the low-mass end slope ranges from $\alpha\simeq-1.82_{-0.07}^{+0.08}$ for an exponentially rising SFH to $\alpha\simeq-2.34_{-0.10}^{+0.11}$ when allowing $A_V$ of up to 3.25. Future observations at longer wavelengths and higher angular resolution with the James Webb Space Telescope are required to break these degeneracies and to robustly constrain the stellar mass of galaxies on the extreme low-mass end of the GSMF.