A Semi-analytic Framework of Population III and Subsequent Galaxy Formation on Cosmological N-body Simulations

TL;DR

This work develops a semi-analytic framework for Pop III and subsequent galaxy formation that runs on dark matter halo merger trees and includes spatially inhomogeneous Lyman-Werner feedback and baryon streaming velocity. It is anchored by a high-resolution N-body simulation (Phi-4096, 16 h^{-1} Mpc box) and uses sub-stepping, a mass-formation criterion M_crit = min(M_K21,M_a), and a mass assignment model that yields a top-heavy Pop III IMF with two distinct peaks. The results demonstrate a substantial fraction of supermassive Pop III stars residing in atomic cooling halos, a double-peaked Pop III SFRD driven by H_2 and atomic cooling regimes, and a strong dependence on LW inhomogeneity and box size for capturing the second peak. These findings have implications for the seeds of supermassive black holes, the high-redshift galaxy population, and JWST-era observations, while highlighting the need to account for spatial LW fluctuations and sufficiently large simulation volumes in future studies.

Abstract

We develop a new semi-analytic framework of Population (Pop) III and subsequent galaxy formation designed to run on dark matter halo merger trees. In our framework, we consider the effect of the Lyman-Werner flux from Pop III and II stars and the dark matter baryon streaming velocity on the critical halo mass for the Pop III formation. Our model incorporates the Lyman-Werner feedback in a self-consistent way, therefore, the spatial variation of Lyman-Werner feedback naturally emerges. The Pop III mass depends on the properties of a halo as reproducing radiative hydrodynamical simulation results. We perform statistical studies of Pop III stars by applying this framework to high-resolution cosmological N-body simulations with a maximum box size of 16 Mpc/h and enough mass resolution to resolve Pop III-forming halos. A top-heavy initial mass function emerges and two peaks corresponding to the H$_2$ ($20 \lesssim z \lesssim 25$) and atomic cooling halos ($z \lesssim 15$) exist in the distribution. Supermassive stars can be formed in the atomic cooling halos, and the fractions of such supermassive stars increase with the value of streaming velocity. At least an 8 Mpc/h simulation box and the self-consistent model for the Lyman-Werner feedback are necessary to correctly model the Pop III formation in the atomic cooling halos. Our model predicts one supermassive star per halo with several $10^9$ Msun at z=7.5, which is enough to reproduce a high redshift quasar.

Figures (11)

• Figure 1: Difference of the self-consistent (first and third rows) and the uniform models (second and fourth rows) on the fiducial Phi-4096 simulation ($L=16$$\, h^{-1} \rm Mpc$) with zero streaming velocity. Supermassive Pop III stars (more massive than $10^{4.5}$$\, \rm M_\odot$) are displayed by crosses. From left to right, each panel shows the spatial distribution of the total mass density of Pop III, Pop II stars, and Lyman-Werner flux, respectively. See also Figure \ref{['fig:jlw']}.
• Figure 2: Critical halo mass $M_{\rm crit}$ of Pop III-forming halos as a function of redshift employed in our semi-analytic model [Eq \ref{['eq:mcrit']}]. Solid, dashed, and dot-dashed curves indicate examples for various combinations of $(J_{\rm LW}, v_{\rm bc})$. Upward thick- and downward thin-dotted curves represent the critical mass of atomic cooling halos [Eq \ref{['eq:atomic_cooling']}] and the critical mass of the HD cooling [Eq \ref{['eq:hd_cooling']}], respectively.
• Figure 3: (Left) Number density of Pop III stars formed at all redshift as a function of the Pop III mass in a halo. We divide a single-digit mass range into four logarithmic bins and calculate the number density in each bin. Four model results with the different values of streaming velocity, $v_{\rm bc}=0$, 1$\sigma_{\rm vbc}$, 2$\sigma_{\rm vbc}$, and 3$\sigma_{\rm vbc}$, are shown. (Right) Cumulative probability distribution of the number of Pop III stars as a function of the Pop III mass in a halo.
• Figure 4: Dependence of Pop III mass on virial mass (left), redshift (middle), and Lyman-Werner flux (right) of host halos. From top to bottom, model results with $v_{\rm bc}=0,1,2$, and 3$\sigma_{\rm vbc}$ are presented. Color bars show the number of Pop III stars at each pixel.
• Figure 5: (Left) Star formation rate density (SFRD) of Pop III (solid curves) and Pop II (dashed) stars. Four model results with the different values of streaming velocity, $v_{\rm bc}=0$, 1$\sigma_{\rm vbc}$, 2$\sigma_{\rm vbc}$, and 3$\sigma_{\rm vbc}$, are shown. Filled and open symbols show other semi-analytic results for Pop III and Pop II, respectively Hedge2023Feathers2024Trinca2024. (Right) Formation rate density of Pop III-forming halos per $\rm Mpc^3$ and year.