Formation of first star clusters under the supersonic gas flow -- III. Environmental trends and halo-to-halo scatter in the Pop III IMF

Abstract

The first generations of stars ionised and enriched their host galaxies and seeded the growth of massive black holes. Models often assume that Pop III stellar masses in different minihaloes are stochastic realisations of a single universal initial mass function (IMF). We use 138 cosmological zoom-in hydrodynamics simulations to test this assumption and to map the first-star IMF across redshift, halo mass, and baryon-dark matter streaming velocity (SV). We construct a dense-cloud merger tree and assign first-star masses by mapping the radial gas accretion-rate profile to stellar mass, yielding per-halo stellar mass functions without imposing any a priori IMF. The high-mass tail and multiplicity increase systematically with redshift, halo mass, and SV. Low-mass, low-SV haloes form only one or a few first stars, whereas massive, high-SV haloes host rich first star clusters and commonly produce very massive ($\gtrsim10^3$-$10^4\,{\rm M}_\odot$) first stars. Even in a fixed environment, halo-to-halo scatter remains substantial. Nevertheless, group-averaged IMFs converge to well-defined forms, ruling out a single universal IMF at the halo level across the range of environments probed here. Mapping our seeds onto the redshift-mass plane, we show that high-SV and massive haloes preferentially populate the heavy-seed regime relevant to luminous high-redshift sources. At the same time, low-SV environments are consistent with single/few-event enrichment signatures in metal-poor stars. Our results deliver a practical, physically motivated prescription for per-halo IMF.

Figures (11)

• Figure 1: Formation redshift and virial mass of all first-star-forming haloes in our simulation suite. The horizontal axis shows the redshift $z$ at which the gas first reaches the density threshold for cloud identification, and the vertical axis shows the corresponding virial mass $M_{\rm v}$. Marker shapes indicate the formation-redshift class: upward triangles for Class High, diamonds for Class Middle, and downward triangles for Class Low. Filled circles labelled Add denote 18 additional runs with enhanced $\sigma_8$ that extend the sample to higher redshifts and virial masses. Colours encode the streaming-velocity amplitude in units of the root-mean-square value, $v_{\rm SV}/\sigma_{\rm SV} = 0$, 1, 1.5, 2, 2.5, and 3. Dashed curves show the virial masses for three different virial temperatures, $T_{\rm v} = 1000$, $3000$, and $8000$ K.
• Figure 2: Histogram of first-star masses, $M_{\rm s}$, in the model I08S08V20. Hatched regions indicate the mass ranges $10 < M_{\rm s}/{\rm M}_\odot < 40$ (CCSN progenitors), $120 < M_{\rm s}/{\rm M}_\odot < 260$ (PISN progenitors), and $M_{\rm s}/{\rm M}_\odot > 10^{3}$ (IMBH-seed regime).
• Figure 3: Gas-density structure of the representative model I08S08V20 at $t_{\rm th}=2$ Myr after the first cloud in the halo reaches the threshold density $n_{\rm th}=10^6\,{\rm cm^{-3}}$. The left panel shows the projected gas density in a cube of side length 1 kpc centred on the halo, encompassing the virial radius $R_{\rm v} \simeq 300$ pc. Large-scale filaments feed the central region while the initial baryon-DM streaming velocity with $v_{\rm SV}/\sigma_{\rm SV}=2$ is directed from left to right in this projection. The right panel zooms in on the central 30 pc, where a dense filament has fragmented into multiple clumps with peak densities exceeding $n_{\rm th}$. These clumps correspond to the Jeans-unstable clouds identified as nodes in the merger-tree analysis and host the formation of $N_{\rm s}=44$ first stars in this halo over the subsequent 2 Myr.
• Figure 4: Radial gas profiles around four representative first stars in the model I08S08V20 at their formation epochs (defined by the first crossing of $n_{\rm th}=10^6\,{\rm cm^{-3}}$ in the collapsing core). Panel (a) shows the spherically averaged number-density profiles as a function of radius from each protostar. Panel (b) shows the corresponding gas temperature profiles. Different coloured lines correspond to stars with masses spanning $M_{\rm s} \simeq 10$--$10^4\,{\rm M}_\odot$, as indicated in the legend.
• Figure 5: Panels (a)-(c) show the mean numbers of clouds and first stars per halo as a function of the streaming velocity, $v_{\rm SV}/\sigma_{\rm SV}$. Lines indicate the three formation-redshift classes: High (orange), Middle (red), and Low (purple). We plot the mean number of Jeans-unstable clouds $\langle N_{\rm c} \rangle$ in panel (a), the mean number of first stars $\langle N_{\rm s} \rangle$ in panel (b), and the mean multiplicity per cloud $\langle N_{\rm s}/N_{\rm c} \rangle$ in panel (c). Panels (d)-(f) show the corresponding fractions of haloes hosting different numbers of first stars. We plot the fraction of single-star haloes $f_{\rm single}$ in panel (d), the fraction of haloes with at least five first stars $f_{\rm cl,5}$ in panel (e), and the fraction with at least ten first stars $f_{\rm cl,10}$ in panel (f).