[Paper Review] Forecasting constraints on the high-z IGM thermal state from the Lyman-$α$ forest flux auto-correlation function

Molly Wolfson, Joseph F. Hennawi+3 more|arXiv (Cornell University)|Sep 11, 2023

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This paper forecasts constraints on the high-redshift intergalactic medium (IGM) thermal state using the Lyman-α forest flux auto-correlation function from cosmological hydrodynamical simulations. It demonstrates that with 20 quasars and ideal data, $T_0$ can be constrained to 29% and $\gamma$ to 9% at $z=5.4$, establishing the auto-correlation function as a competitive tool for probing reionization physics via the IGM's thermal history.

ABSTRACT

The auto-correlation function of the Lyman-$α$ (Ly$α$) forest flux from high-z quasars can statistically probe all scales of the intergalactic medium (IGM) just after the epoch of reionization. The thermal state of the IGM, which is determined by the physics of reionization, sets the amount of small-scale power seen in the \lya forest. To study the sensitivity of the auto-correlation function to the thermal state of the IGM, we compute the auto-correlation function from cosmological hydrodynamical simulations with semi-numerical models of the thermal state of the IGM. We create mock data sets of 20 quasars to forecast constraints on $T_0$ and $γ$, which characterize a tight temperature-density relation in the IGM, at $5.4 \leq z \leq 6$. At $z = 5.4$ we find that an ideal data set constrains $T_0$ to 29\% and $γ$ to 9\%. In addition, we investigate four realistic reionization scenarios that combine temperature and ultra-violet background (UVB) fluctuations at $z = 5.8$. We find that, when using mock data generated from a model that includes temperature and UVB fluctuations, we can rule out a model with no temperature or UVB fluctuations at $>1σ$ level 50.5\% of the time.

Motivation & Objective

• To assess the sensitivity of the Lyman-α forest flux auto-correlation function to the thermal state of the high-redshift IGM.
• To forecast constraints on the temperature-density relation parameters $T_0$ and $\gamma$ at $5.4 \leq z \leq 6$ using mock quasar data.
• To investigate how temperature and UV background (UVB) fluctuations affect the auto-correlation function and distinguishability of reionization models.
• To evaluate the statistical robustness of likelihood inference using multi-variate Gaussian approximations for non-Gaussian data at high redshift.
• To identify the potential of the flux auto-correlation function as a competitive probe of reionization physics at $z > 5$.

Proposed method

• Simulated high-redshift IGM using cosmological hydrodynamical simulations with semi-numerical models of the thermal state.
• Generated mock quasar spectra for 20 high-redshift quasars to emulate observational data at $5.4 \leq z \leq 6$.
• Computed the 1D flux auto-correlation function from mock data to probe IGM structure across scales.
• Applied a multi-variate Gaussian likelihood with MCMC sampling and re-weighting to ensure posterior inference validity.
• Used likelihood ratio tests to compare models with and without temperature and UVB fluctuations.
• Conducted inference tests to assess the validity of Gaussian likelihood assumptions, correcting for non-Gaussianity in data.

Experimental results

Research questions

• RQ1 How precisely can the flux auto-correlation function constrain the IGM temperature-density relation parameters $T_0$ and $\gamma$ at $z \sim 5.4$?
• RQ2 How do temperature and UVB fluctuations jointly affect the flux auto-correlation function in high-redshift IGM simulations?
• RQ3 Can the auto-correlation function distinguish between reionization models with and without temperature and UVB fluctuations?
• RQ4 What are the limitations of using a multi-variate Gaussian likelihood for flux auto-correlation data at $z > 5$?
• RQ5 How does data quality and sample size (e.g., 20 quasars) impact the statistical power to constrain the IGM thermal state?

Key findings

• At $z = 5.4$, an ideal data set constrains $T_0$ to 29% and $\gamma$ to 9% precision, demonstrating strong sensitivity to the IGM thermal state.
• The auto-correlation function is sensitive to both temperature and UVB fluctuations, with the strongest signal in models including both physical effects.
• For mock data generated from a model with temperature and UVB fluctuations, a model without either fluctuation type is ruled out at $>1\sigma$ significance in 50.5% of realizations.
• The likelihood inference procedure failed initially due to non-Gaussianity in the auto-correlation function, highlighting the risk of using Gaussian likelihoods for high-redshift Ly$\alpha$ forest statistics.
• The use of re-weighted MCMC chains corrected for inference failure, validating the posterior estimates despite non-Gaussian data.
• UVB fluctuations are suppressed in small simulation boxes (40 cMpc h⁻¹), suggesting that larger boxes may improve distinguishability between models with and without UVB fluctuations.