Population III star formation in an X-ray background: IV. On-the-fly calculation of radiation backgrounds and their impact on the intergalactic medium

Abstract

In this paper, part of a series on the effects of X-ray sources in promoting Population III (Pop III) star formation, we investigate the ionisation and heating of the intergalactic medium (IGM) and the consequent enhancement of molecular hydrogen (H$_{2}$) and Pop III formation using cosmological zoom-in simulations. We adopt a minimal X-ray feedback model in which X-rays originate solely from Pop III supernovae, and compute the global X-ray and Lyman-Werner (LW) radiation backgrounds on-the-fly during the simulation of a mean-density region of the Universe. This approach self-consistently captures the feedback loop between Pop III stars and the radiation backgrounds they produce. Pop III supernovae generate a weak X-ray background (J$_{\mathrm{X,21}} \sim 10^{-5}$) and a moderate LW background (J$_{\mathrm{LW,21}} \sim 10^{-1}$); the latter intensifies below $z \approx 12$ (J$_{\mathrm{LW,21}} \sim 10^{1}-10^{2}$) with the onset of Pop II star formation. Applying these backgrounds to regions of varying mean density produces a net positive X-ray feedback that increases the Pop III number density, with stronger enhancement in underdense regions. The positive feedback is more pronounced when the X-ray background is computed on-the-fly rather than by post-processing, demonstrating the importance of the feedback loop. The X-ray background also raises the Thomson scattering optical depth at high redshift, while the total optical depth remains consistent with Planck 2018 constraints. Because our model includes only Pop III supernovae as X-ray sources, it represents the most conservative scenario; stronger X-ray feedback is expected when additional sources are included, as will be explored in future work.

Figures (14)

• Figure 1: Schematic diagram illustrating the relationship between Pop III stars and radiation background. The scope of this paper is highlighted with a bright red box. Since the formation of the first Pop III stars at $z \sim 30$tegmark_how_1997, Pop III stars and the radiation background interact to form a feedback loop. We briefly comment on the potential influence of the background on the formation of the first galaxies in PR26b but this will be handled in detail in future work.
• Figure 2: Schematic diagram of the work process. (a) We performed two dark matter-only simulations. (b) DM haloes were identified using rockstar halo finder behroozi_rockstar_2013. (c) Based on the halo properties (masses and positions), we selected sub-volumes. (d) Volume 2 was designated as the representative volume, for which we carried out zoom-in simulations to calculate the radiation backgrounds on-the-fly. LW-only simulation (V2LW) and LW + X-ray simulation (V2X) were performed for this purpose. (e) Each resulting radiation background (spectrum) was tabulated as a function of redshift. (f) These LW-only and LW + X-ray backgrounds were applied to the other sub-volumes. For instance, we ran two simulations for Volume 1 (V1LW and V1X).
• Figure 3: Panels a and b: The projected DM density maps of the DM-only simulations of $L = 8$ and $4~{\rm Mpc}/h$, respectively. Coloured boxes indicate the 10 sub-volumes chosen for zoom-in simulations. Panel c: Halo mass functions of the zoom-in simulations of these sub-volumes. The mass functions at $z = 9$ are shown except for V1 (red, $z = 13.94$). Colours correspond to the sub-volumes marked in Panel a and b. For reference, the PS mass function at $z = 9$, calculated using colossusdiemer_colossus_2018, is shown as a dashed line. The mass function of Volume 2 (orange) is similar to the PS prediction; we therefore regard its Pop III star formation history as representative of the cosmic average.
• Figure 4: Snapshot of the zoom-in simulation V2X (see Table \ref{['tab:simulation']}) at $z=9$. In the top panel, the gas density map of the full $8~{\rm Mpc}/h$ box is depicted. Only gas cells within the central $1.2~{\rm Mpc}/h$ zoom-in region, outlined by the solid white square, are eligible for refinement and star formation. The bottom panel provides an enlarged view of the zoom-in region. The dashed line marks the boundary between the target region (inner area) and the padding (outer area). All analyses in this work are based on the stars and gas located within the target region.
• Figure 5: Schematic diagram of the on-the-fly background calculation. The $x$-axis represents both the distance and lookback time (redshift). We compute the specific intensity at the observed frequency $\nu_{o}$ in the zoom-in region at $z_{o}$ denoted by ${\rm J}_{\nu_{o}}(z_{o})$, by numerically integrating equation (\ref{['eq:background']}). The left-hand panel shows a snapshot including the target region (white dashed square) and the surrounding padding. We assume that sources existing between $z_{box}$ and $z_{start}$ contribute to the global radiation background. Photons emitted at frequency $\nu = \nu_{o} (1+z)/(1+z_{o})$ are redshifted and contribute to the intensity at the observed frequency $\nu_{o}$ at the current redshift $z_{o}$.