Population III star formation in an X-ray background: V. Environmental dependence and halo occupation probability

Abstract

An X-ray background in the early Universe enhances molecular hydrogen formation, the main coolant of primordial gas, thereby lowering the threshold for Pop III star formation. Continuing our series on X-ray impacts on Pop III star formation, we investigate how a soft X-ray background promotes Pop III star formation using cosmological zoom-in simulations of ten cosmic volumes spanning a range of halo number densities. Each volume is irradiated by the Lyman-Warner (LW) H$_{2}$ dissociating background and a weak (J$_{21} \sim 10^{-5}$), soft ($E \sim 0.2-2.0$ keV) X-ray background produced by pair-instability SNe (PISNe) from Pop III stars and calculated self-consistently as described in a companion paper. We also compare the same simulations with and without X-rays to isolate the X-ray effect. The background promotes Pop III star formation in two ways: (1) by reducing the mean host halo mass by a factor of $\sim 2-3$, and (2) by enabling Pop III star formation in haloes that would otherwise remain sterile, thereby increasing the halo occupation fraction. The resulting gain in Pop III number density is largest in underdense regions (a factor of $\approx 3$ on average, reaching up to 7). In the most extreme case, Pop II stars form only in the presence of X-rays and the gas-phase metallicity rises by an order of magnitude, suggesting that dwarf galaxies in underdense regions may be significantly influenced by an early X-ray background. We also provide fitting functions for the halo occupation probability of Pop III stars as a function of redshift for both X-ray and LW-only simulations, which can serve as inputs for semi-analytic models.

Figures (15)

• Figure 1: Top: Overdensity as a function of redshift for the 10 simulations used in this study. Volume 1 corresponds to an overdense region, and Volume 2 is a mean-density region. The remaining volumes correspond to underdense regions. Bottom: Number density of haloes more massive than $10^6~{\rm M}\sb{\mathrm{\odot}}$ ($n_6 = n(M > 10^6~{\rm M}\sb{\mathrm{\odot}})$) as a function of redshift.
• Figure 2: Global radiation backgrounds calculated on-the-fly from the simulations of Volume 2. Solid lines show the intensities (in units of ${\rm J}_{21}$) of the X-ray ($E = 0.36$ keV; red) and LW (blue) backgrounds as a function of redshift in the V2X simulation (Volume 2 with X-rays+LW). Note that $J_{X} \equiv \nu J_\nu$ often reported in the literature is related to $J_{\nu, 21}$ by the relationship $J_{X} = 0.87\times 10^{-4} (E/0.36~{\rm keV})J_{\nu,21}$. The LW background from V2LW (Volume 2 with LW-only) is shown in grey. Dashed lines denote the corresponding local backgrounds for comparison. The vertical dashed line show the redshift where the calculation of the backgrounds switches from the analytic approximation to on-the-fly calculation (see PR26a).
• Figure 3: Redshifts of Pop III star formation and the corresponding masses of their host haloes. Results are shown for Volume 1 (overdense region), Volume 2 (mean-density region), and the remaining volumes (underdense regions), from top to bottom. The left and middle columns show the results of the LW + X-ray (left) and LW-only (middle) simulations, respectively. The right panels present the average halo masses over several redshift intervals for the two simulations. At a given redshift, Pop III-hosting haloes span a wide mass range with no significant difference of the minimum and maximum masses between the X-ray and LW-only cases. However, as indicated by the differing number of points, Pop III-hosting halo counts increase in the presence of the X-ray background.
• Figure 4: Panel a: Halo mass functions at $z=9$. Dashed lines show the mass functions of all haloes in Volume 2; solid lines indicate Pop III-hosting haloes. The Press-Schechter (PS) mass function computed with colossusdiemer_colossus_2018 is shown as a dot-dashed line. The mass functions of V2X and V2LW agree well with the PS fit at $z = 9$. Colours indicate the presence of an X-ray background (see legend in Panel b). Note that Fig. \ref{['fig:mhz']} shows halo masses at the epoch of Pop III star formation, whereas this figure shows masses at $z = 9$ regardless of when stars formed. Panel b: Same as Panel a on a linear scale to compare more clearly the mass functions of Pop III-forming haloes. Panel c: Occupation fraction, defined as the ratio of Pop III-forming haloes to all haloes in each mass bin.
• Figure 5: Left: Cumulative number of Pop III stars in the X-ray (red lines) and LW-only (blue lines) simulations. The final total count of Pop III stars is indicated in the legend of each panel. Right: Pop III star formation rates (SFRs) in number per year. Since $M_{pop3} = 100~{\rm M}\sb{\mathrm{\odot}}$, multiplying by the Pop III mass yields the SFR in ${\rm M}\sb{\mathrm{\odot}}/$yr. From top to bottom, we show the results of Volume 1 and Volume 2, and low-density regions in total (Volumes 3-10), respectively.