How Do Star-Forming Galaxies at Z\u3e3 Assemble Their Masses?

We investigate how star-forming galaxies typically assemble their masses at high redshift. Using the deep multi-wavelength coverage of the GOODS dataset, we measure stellar mass of a large sample of star-forming galaxies at z~4 and 5, and make a robust determination of stellar mass function (SMF). We report a broad correlation between stellar mass and UV luminosity, such that more UV-luminous galaxies are, on average, more massive. However, the correlation has a substantial intrinsic scatter evidenced by a non-negligible number of UV-faint but massive galaxies. Furthermore, the low-mass end of the SMF does not rise as steeply as the UV luminosity function (alpha_UVLF} -(1.7-1.8), alpha_SMF -(1.3-1.4)) of the same galaxies. In a smooth formation scenario where star formation (SF) is sustained at the observed rates for a long time, these galaxies would have accumulated more mass (by a factor of ~3) than observed and therefore the SMF would mirror more closely that of the UVLF. The relatively shallow slope of the SMF is due to the fact that many of the UV-selected galaxies are not massive enough, and therefore are too faint in their rest-frame optical bands, to be detected in the current observations. Our results favor a episodic formation history in which SF in low-mass galaxies vary significantly over time, a scenario favored by galaxy clustering. Our findings for the UV-faint galaxies are in contrast with those found for more UV-luminous galaxies, which exhibit tighter SFR-M_star correlations. The discrepancy may suggest that galaxies at different luminosities may have different evolutionary paths