A Redshift-independent Efficiency Model: Star Formation and Stellar Masses in Dark Matter Halos at z ≳ 4

Abstract

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 redshiftindependent 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, 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 h < 10 11 M as M ∝ M 2 h , 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 ∼ 10 may be overestimated by ∼ 0.1 − 0.2 dex.

It is feasible to directly measure black hole masses in the first galaxies

“…1. The upper x−axis shows the absolute magnitudes (M UV ) corresponding to this mass range, computed from the relation of Ref. [27] at z = 6. Fig.…”

“…The halo is assumed to follow a Navarro-Frenk-White [25] profile with a concentration parameter [26] c = 3.5, and contains a central supermassive black hole, with mass M BH , and an exponential stellar disc with spin parameter λ = 0.03 (the inferred total stellar mass M * is also indicated, along with the corresponding UV magnitude, M UV obtained from the relation of Ref. [27]). The circular velocities v rot (in km/s) induced by the black hole (orange dashed lines), stellar disc (green solid lines) and dark matter halo (blue solid lines) are plotted along with the total circular velocity (red solid line).…”

Astrophysics from the 21 cm Background

“…This procedure reveals the mapping between mass and light, dL/dm h , upon repeated integration over a grid of L h values, solving for the M h value needed for abundances to match. Results of this simple procedure show that galaxy luminosity is a function of both halo mass and cosmic time [146,100,6,139,78,138,79]. While the HMF can be readily used to predict the abundances of halos out to arbitrary redshifts, one shortcoming of this approach is that any evolution in dL/dM must be modeled via extrapolation.…”

“…The end result of this exercise is a calibrated SFE curve, which can then be used to make predictions for galaxy properties too faint or too distant to have been detected by current surveys. A representative example [139] is shown in Figure 2.3 (which includes a common dust correction -see §2.2.3). The rise and fall in the SFE is a generic result of semi-empirical models [79,138,78,139,5], indicating a change in how galaxies form stars in halos above and below ∼ 10 12 M .…”

“…A representative example [139] is shown in Figure 2.3 (which includes a common dust correction -see §2.2.3). The rise and fall in the SFE is a generic result of semi-empirical models [79,138,78,139,5], indicating a change in how galaxies form stars in halos above and below ∼ 10 12 M . Such models generally agree that star formation is inefficient, with peak values f * 0.1, and f * 0.01 in the less massive (but numerous) population of galaxies residing in halos M h 10 11 M .…”