[Paper Review] The Impact of the WHIM on the IGM Thermal State Determined from the Low-$z$ Lyman-$α$ Forest

Teng Hu, Vikram Khaire+5 more|arXiv (Cornell University)|Aug 28, 2023

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy3 citations

TL;DR

This study demonstrates that the thermal state of the low-redshift intergalactic medium (IGM), parameterized by $T_0$ and $\gamma$, can be reliably measured from the Ly$\alpha$ forest despite significant shock heating from the warm-hot intergalactic medium (WHIM). Using machine learning-enabled simulation-based inference on Nyx, IllustrisTNG, and Illustris simulations, it shows that the $b$--$N_{\text{H\,{\tiny i}}}$ distribution remains insensitive to WHIM fraction differences, yielding biases of $|\Delta\log(T_0/\text{K})|\lesssim 0.05$ dex and $|\Delta\gamma|\lesssim 0.1$, smaller than typical observational uncertainties.

ABSTRACT

At $z \lesssim 1$, shock heating caused by large-scale velocity flows and possibly violent feedback from galaxy formation, converts a significant fraction of the cool gas ($T\sim 10^4$ K) in the intergalactic medium (IGM) into warm-hot phase (WHIM) with $T >10^5$K, resulting in a significant deviation from the previously tight power-law IGM temperature-density relationship, $T=T_0 (ρ/ {\barρ})^{γ-1}$. This study explores the impact of the WHIM on measurements of the low-$z$ IGM thermal state, $[T_0,γ]$, based on the $b$-$N_{H I}$ distribution of the Lyman-$α$ forest. Exploiting a machine learning-enabled simulation-based inference method trained on Nyx hydrodynamical simulations, we demonstrate that [$T_0$, $γ$] can still be reliably measured from the $b$-$N_{H I}$ distribution at $z=0.1$, notwithstanding the substantial WHIM in the IGM. To investigate the effects of different feedback, we apply this inference methodology to mock spectra derived from the IllustrisTNG and Illustris simulations at $z=0.1$. The results suggest that the underlying $[T_0,γ]$ of both simulations can be recovered with biases as low as $|Δ\log(T_0/ ext{K})| \lesssim 0.05$ dex, $|Δγ| \lesssim 0.1$, smaller than the precision of a typical measurement. Given the large differences in the volume-weighted WHIM fractions between the three simulations (Illustris 38\%, IllustrisTNG 10\%, Nyx 4\%) we conclude that the $b$-$N_{H I}$ distribution is not sensitive to the WHIM under realistic conditions. Finally, we investigate the physical properties of the detectable Lyman-$α$ absorbers, and discover that although their $T$ and $Δ$ distributions remain mostly unaffected by feedback, they are correlated with the photoionization rate used in the simulation.

Motivation & Objective

• To assess whether the presence of the warm-hot intergalactic medium (WHIM) at $z \lesssim 1$ distorts measurements of the IGM thermal state $[T_0, \gamma]$ from the Ly$\alpha$ forest.
• To evaluate the robustness of the $b$--$N_{\text{H\,{\tiny i}}}$ distribution as a probe of the IGM temperature-density relation under varying feedback models.
• To determine whether differences in WHIM fractions between cosmological simulations affect the inferred thermal parameters from observed Ly$\alpha$ forest statistics.
• To validate a machine learning-based inference framework for recovering $[T_0, \gamma]$ from mock Ly$\alpha$ forest spectra across simulations with distinct feedback prescriptions.

Proposed method

• Employed a machine learning-enabled simulation-based inference method trained on high-resolution Nyx hydrodynamical simulations to infer $[T_0, \gamma]$ from the $b$--$N_{\text{H\,{\tiny i}}}$ distribution at $z = 0.1$.
• Applied the same inference framework to mock Ly$\alpha$ forest spectra derived from IllustrisTNG and Illustris simulations, which differ significantly in feedback strength and resulting WHIM fractions.
• Used density-estimation likelihood-free inference (DELFI) to map observed $b$--$N_{\text{H\,{\tiny i}}}$ distributions to posterior distributions over $[T_0, \gamma]$, enabling parameter recovery despite complex non-linearities.
• Post-processed simulations to share the same photoionization rate $\Gamma_{\text{H\,{\tiny i}}}$, isolating the effects of feedback from those of ionization history.
• Compared the $T$--$\Delta$ distributions of simulated Ly$\alpha$ absorbers across simulations to assess sensitivity to feedback and WHIM content.
• Validated results by comparing recovered $[T_0, \gamma]$ to the true input values in each simulation, quantifying bias and precision.

Experimental results

Research questions

• RQ1 Does the presence of the WHIM at $z \lesssim 1$ significantly bias measurements of the IGM thermal state $[T_0, \gamma]$ from the Ly$\alpha$ forest?
• RQ2 Can the $b$--$N_{\text{H\,{\tiny i}}}$ distribution in the Ly$\alpha$ forest reliably recover $[T_0, \gamma]$ even when the IGM contains substantial WHIM ($T > 10^5$ K)?
• RQ3 How do different feedback models (e.g., Illustris vs. IllustrisTNG) affect the thermal state parameters $[T_0, \gamma]$ and the detectability of the WHIM in the Ly$\alpha$ forest?
• RQ4 To what extent do the physical properties of detectable Ly$\alpha$ absorbers correlate with the photoionization rate, independent of feedback mechanisms?
• RQ5 Is the $b$--$N_{\text{H\,{\tiny i}}}$ distribution sensitive to the volume-weighted WHIM fraction when the photoionization rate is held constant?

Key findings

• The machine learning-based inference framework successfully recovers the true $[T_0, \gamma]$ parameters in all three simulations (Nyx, IllustrisTNG, Illustris), with biases $|\Delta\log(T_0/\text{K})| \lesssim 0.05$ dex and $|\Delta\gamma| \lesssim 0.1$, which are smaller than typical measurement uncertainties.
• Despite large differences in volume-weighted WHIM fractions—4% in Nyx, 10% in IllustrisTNG, and 38% in Illustris—the $b$--$N_{\text{H\,{\tiny i}}}$ distribution remains largely insensitive to these variations under realistic conditions.
• The $T$--$\Delta$ distributions of simulated Ly$\alpha$ absorbers are nearly indistinguishable across simulations when the photoionization rate $\Gamma_{\text{H\,{\tiny i}}}$ is held constant, indicating that feedback effects are masked in the observed forest statistics.
• The WHIM fraction in the simulated Ly$\alpha$ absorbers is nearly identical across IllustrisTNG and Illustris (11.6% on average), despite their vastly different IGM WHIM fractions, suggesting that absorbers preferentially trace the same physical conditions regardless of feedback strength.
• The $b$--$N_{\text{H\,{\tiny i}}}$ distribution is not sensitive to the WHIM under realistic conditions, implying that standard thermal state measurements from the Ly$\alpha$ forest remain robust even in the presence of significant shock heating.
• The study confirms that the $T_0$--$\gamma$ relation remains a valid and measurable description of the IGM thermal state at $z \lesssim 1$, even when the IGM exhibits substantial dispersion due to shock heating and feedback.