A redshift-independent efficiency model: star formation and stellar masses in dark matter halos at z>4
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We explore the connection between the UV luminosity functions (LFs) of high-$z$ galaxies and the distribution of stellar masses and star-formation histories (SFHs) in their host dark matter halos. We provide a baseline for a redshift-independent star-formation efficiency model to which observations and models can be compared. Our model assigns a star-formation rate (SFR) to each dark matter halo based on the growth rate of the halo and a redshift-independent star-formation efficiency. The dark matter halo accretion rate is obtained from a high-resolution $N$-body simulation in order to capture the stochasticity in accretion histories and to obtain spatial information for the distribution of galaxies. The halo mass dependence of the star-formation efficiency is calibrated at $z=4$ by requiring a match to the observed UV LF at this redshift. The model then correctly predicts the observed UV LF at $z=5-10$. We present predictions for the UV luminosity and stellar mass functions, \textit{JWST} number counts, and SFHs. In particular, we find a stellar-to-halo mass relation at $z=4-10$ that scales with halo mass at $M_{\rm h}<10^{11}~M_{\odot}$ as $M_{\star}\propto M_{\rm h}^2$, with a normalization that is higher than the relation inferred at $z=0$. The average SFRs increase as a function of time to $z=4$, although there is significant scatter around the average: about 6\% of the $z=4$ galaxies show no significant mass growth. Using these SFHs, we present redshift-dependent UV-to-SFR conversion factors, mass return fractions, and mass-to-light ratios for different intial mass functions and metallicities, finding that current estimates of the cosmic SFR density at $z\sim10$ may be overestimated by $\sim0.1-0.2~\mathrm{dex}$.
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