The Evolution of the Galaxy Stellar Mass Function at z= 4-8: A Steepening Low-mass-end Slope with Increasing Redshift

Mimi Song, Steven L. Finkelstein, Matthew L. N. Ashby, A. Grazian, Yu Lu, Casey Papovich, Brett Salmon, Rachel S. Somerville, Mark Dickinson, K. Duncan, Sandy M. Faber, Giovanni G. Fazio, Henry C. Ferguson, Adriano Fontana, Yicheng Guo, Nimish Hathi, Seong-Kook Lee, Emiliano Merlin, S. P. Willner

Published 2015-07-20Version 1

We present galaxy stellar mass functions (GSMFs) at $z=$ 4-8 from a rest-frame ultraviolet (UV) selected sample of $\sim$4,500 galaxies, found via photometric redshifts over an area of $\sim$280 arcmin$^2$ in the CANDELS/GOODS fields and the Hubble Ultra Deep Field. The deepest Spitzer/IRAC data yet-to-date from the Spitzer-CANDELS (26.5 mag, 3$\sigma$) and the IRAC Ultra Deep Field 2010 (26.4-27.1 mag, 3$\sigma$) surveys allow us to place robust constraints on the low-mass-end slope of the GSMFs, while the relatively large volume provides a better constraint at higher masses compared to previous space-based studies. Supplemented by a stacking analysis, we find a linear correlation between the rest-frame UV absolute magnitude at 1500\AA\ ($M_{\rm UV}$) and logarithmic stellar mass ($\log M_*$). We use simulations to validate our method of measuring the slope of the $\log M_*$-$M_{\rm UV}$ relation, finding that the bias is minimized with a hybrid technique combining photometry of individual bright galaxies with stacked photometry for faint galaxies. The resultant measured slopes do not significantly evolve over $z=$ 4-8, while the normalization of the trend exhibits a weak evolution towards lower masses at higher redshift for galaxies at fixed $M_{\rm UV}$. We combine the $\log M_*$-$M_{\rm UV}$ distribution with observed rest-frame UV luminosity functions at each redshift to derive the GSMFs. While we see no evidence of an evolution in the characteristic mass $M^*$, we find that the low-mass-end slope becomes steeper with increasing redshift from $\alpha=-1.53^{+0.07}_{-0.06}$ at $z=4$ to $\alpha=-2.45^{+0.34}_{-0.29}$ at $z=8$. The inferred stellar mass density, when integrated over $M_*=10^8$-$10^{13} M_{\odot}$, increases by a factor of $13^{+35}_{-9}$ between $z=7$ and $z=4$ and is in good agreement with the time integral of the cosmic star-formation rate density.