The impact of the IGM thermal state on the Ly$α$ flux 3D power spectrum from linear to highly non-linear scales

Tomáš Šoltinský, Gabriele Autieri, Vid Iršič, Matteo Viel

First listed 2026-08-26 | Last updated 2026-08-25

Abstract

Recently initiated and upcoming spectroscopic surveys, such as DESI and WST, will provide more than $10^6$ high-$z$ quasar spectra, enabling dense sky coverage by the Ly$α$ forest. This is expected to establish the three-dimensional (3D) Ly$α$ forest power spectrum, $P_{\rm 3D,α}$, as a probe of the thermal and ionization history of the intergalactic medium (IGM). To exploit this opportunity, we quantify the imprints of reionization on the post-reionization IGM using high-fidelity numerical models. We use the Sherwood and Sherwood-Relics cosmological hydrodynamical simulations with box sizes up to $160\,h^{-1}\,\rm cMpc$ to investigate the impact of box size, mass resolution, and extracted grid resolution on $P_{\rm 3D,α}$ over $2.4\leq z\leq4.8$. After applying a Zel'dovich control variate correction, simulation volume has a modest impact over most scales and orientations, whereas degrading the mass resolution produces differences of up to $\sim13\%$. Insufficient resolution of the grid used for the optical-depth calculation can artificially enhance small-scale power by up to $\sim35\%$. The timing of $\mathrm{H\,I}$ reionization leaves only a percent-level imprint on $P_{\rm 3D,α}$ at $z=2.4$, whereas varying the photoheating rate by a factor of two changes the large-scale power by $\sim4-8\%$. Our results demonstrate that numerical effects can be comparable to, or exceed, the relic astrophysical signatures encoded in $P_{\rm 3D,α}$, making numerical convergence essential for interpreting precise Ly$α$ forest measurements. The strongest astrophysical imprint arises from spatially inhomogeneous $\mathrm{H\,I}$ reionization, which enhances the large-scale power by up to $\sim70\%$ at $z=4.2$. This highlights the potential of post-reionization Ly$α$ forest measurements as a probe of the thermal history and spatial morphology of cosmic reionization.

Short digest

Šoltinský et al. use Sherwood and Sherwood-Relics hydrodynamical simulations, spanning boxes up to 160 h⁻¹ cMpc, to map how numerical choices and IGM thermal histories shape the three-dimensional Lyα forest flux power spectrum over z=2.4–4.8. Mass-resolution losses can alter the signal by up to about 13%, while inadequate optical-depth grid resolution spuriously raises small-scale power by as much as about 35%, establishing convergence as a prerequisite for exploiting DESI- and WST-era measurements. Astrophysically, changing the H I reionization timing leaves only percent-level residuals by z=2.4, photoheating variations shift large-scale power by roughly 4–8%, and patchy H I reionization produces the standout signature: up to a 70% large-scale enhancement at z=4.2, linking post-reionization forest clustering to reionization morphology.

Key figures to inspect

• Figure 10. This convergence test isolates a key technical result: coarse grids used to calculate optical depths can create an artificial small-scale power excess, while degrading an already computed flux field largely avoids it. It makes the paper’s central warning about numerical systematics immediately concrete.
• Figure 12. This figure compares thermal and reionization-history variants against the fiducial Sherwood-Relics model, showing the modest residual sensitivity to reionization redshift and the scale- and angle-dependent response to factor-of-two photoheating changes. It is the clearest summary of the non-patchy astrophysical signal relative to the numerical requirements.
• Figure 14. This direct homogeneous-versus-patchy comparison presents the paper’s strongest physical conclusion: spatially inhomogeneous H I reionization substantially boosts large-scale 3D Lyα power, especially in transverse modes. It shows why the statistic can probe not merely reionization timing but its spatial morphology.
• Figure 15. This figure demonstrates how the Zel’dovich control-variate correction suppresses coherent large-scale offsets between simulations, particularly for larger volumes, while revealing remaining limitations in the smallest box. It supports the methodological basis for separating finite-volume artifacts from genuine thermal-history signatures.