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We present new measurements of the very low-mass end of the galaxy stellarmass function (GSMF) at $z\sim6-7$ computed from a rest-frame ultravioletselected sample of dropout galaxies. These galaxies lie behind the six HubbleFrontier Fields clusters and are all gravitationally magnified. Using deepSpitzer/IRAC and Hubble Space Telescope imaging, we derive stellar masses byfitting galaxy spectral energy distributions and explore the impact ofdifferent 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 Schechterfunction which allows for a turnover at very low masses. Using a Monte-CarloMarkov Chain analysis of the GSMF, including accurate treatment of lensinguncertainties, 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 withconstant 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, issignificantly affected by the assumed functional form of the star formationhistory and the degeneracy between stellar mass and dust attenuation. Forexample, the low-mass end slope ranges from $\alpha\simeq-1.82_{-0.07}^{+0.08}$for an exponentially rising SFH to $\alpha\simeq-2.34_{-0.10}^{+0.11}$ whenallowing $A_V$ of up to 3.25. Future observations at longer wavelengths andhigher angular resolution with the James Webb Space Telescope are required tobreak these degeneracies and to robustly constrain the stellar mass of galaxieson the extreme low-mass end of the GSMF.

monthly notices of the royal astronomical society

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