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

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.

💡 Research Summary

This paper, the fourth installment in a series investigating Population III (Pop III) star formation under the influence of an X-ray background, presents cosmological zoom-in simulations that self-consistently calculate the global radiation backgrounds produced by Pop III supernovae and study their impact on the intergalactic medium (IGM) and subsequent star formation. The authors adopt a minimal feedback model where X-rays originate solely from Pop III supernovae, representing the most conservative scenario for early X-ray production.

The methodological core of this work is the “on-the-fly” calculation of radiation backgrounds. During the simulation of a mean-density region of the universe, the code computes the evolving global X-ray and Lyman-Werner (LW) radiation backgrounds in real-time, considering the light travel time and cosmological attenuation from all Pop III supernovae. This approach self-consistently captures the non-linear feedback loop: Pop III stars form, explode as supernovae, produce a radiation background, which then ionizes and heats the IGM, affecting the formation of molecular hydrogen (H2)—the primary coolant for primordial gas—and thereby influencing the formation of the next generation of Pop III stars.

The simulations reveal that Pop III supernovae generate a very weak X-ray background (with intensity J_X,21 ~ 10^-5) and a moderate LW background (J_LW,21 ~ 10^-1). The LW background intensifies significantly below redshift z ≈ 12 (J_LW,21 ~ 10^1-10^2) due to the onset of Pop II star formation in more massive halos. When these calculated backgrounds are applied as external conditions to simulations of regions with varying mean density (overdense and underdense), a net positive feedback effect is observed. The X-ray background increases the Pop III star number density. This enhancement is stronger in underdense regions, where X-rays help ionize the gas slightly, promoting the formation of H- ions which are crucial catalysts for H2 formation, thereby rescuing star formation in otherwise unfavorable environments.

A key finding is that the positive feedback is more pronounced when the radiation background is computed on-the-fly compared to a post-processing approach where a pre-computed background is applied. This demonstrates the critical importance of self-consistently modeling the feedback loop between star formation and the radiation environment. Furthermore, even this weak X-ray background raises the free electron fraction in the high-redshift IGM, leading to an increase in the Thomson scattering optical depth (τ_e) at z > 10. The total τ_e predicted by this conservative model remains consistent with the constraints from the Planck 2018 data.

The study concludes that Pop III supernovae alone can provide a non-negligible, positive X-ray feedback on Pop III star formation, particularly in underdense regions, and contribute to the high-z optical depth. Because the model includes only Pop III supernovae as X-ray sources, it establishes a lower limit for such effects; stronger X-ray feedback and a higher τ_e are expected when additional sources like high-mass X-ray binaries, accreting black holes, or quasars are included. This work sets an important benchmark and provides a sophisticated methodology for future simulations aiming to understand the complex radiative feedback in the epoch of the first stars and galaxies, especially in the context of upcoming observations from the James Webb Space Telescope.