Lognormal semi-numerical simulations of the Lyman-$\alpha$ forest: comparison with full hydrodynamic simulations

TL;DR

This study evaluates the effectiveness of a lognormal semi-numerical model in simulating the Lyman-alpha forest and accurately recovering intergalactic medium parameters by comparison with detailed hydrodynamic simulations.

Contribution

It demonstrates that the lognormal model can reliably estimate IGM parameters at z~2.5, matching results from high-resolution hydrodynamic simulations.

Findings

Parameters T0, γ, and Γ12 are recovered within 1σ of the true values.

The lognormal model remains valid across different simulation conditions.

Efficiently models Lyman-alpha transmitted flux at z~2.5.

Abstract

Observations of the Lyman-$\alpha$ (Ly$\alpha$) forest in spectra of distant quasars enable us to probe the matter power spectrum at relatively small scales. With several upcoming surveys, it is expected that there will be a many-fold increase in the quantity and quality of data, and hence it is important to develop efficient simulations to forward model these data sets. One such semi-numerical method is based on the assumption that the baryonic densities in the intergalactic medium (IGM) follow a lognormal distribution. In this work, we test the robustness of the lognormal model of the Ly$\alpha$ forest in recovering a set of IGM parameters by comparing with high-resolution Sherwood SPH simulations. We study the recovery of the parameters $T_0$ (temperature of the mean-density IGM), $\gamma$ (slope of the temperature-density relation) and $\Gamma_{12}$ (hydrogen photoionization rate) at $z \sim 2.5$ using a Markov Chain Monte Carlo (MCMC) technique for parameter estimation. Using three flux statistics, the probability distribution, the mean flux and the power spectrum, values of all three parameters, $T_0$, $\gamma$ and $\Gamma_{12}$ implied in the SPH simulations are recovered within $1 - \sigma$ ($\sim$ 9, 4 and 1% respectively) of the median (best-fit) values. We verify the validity of our results at different baryon smoothing filter, SNR, box size & resolution, and data seed and confirm that the lognormal model can be used as an efficient tool for modelling the Ly$\alpha$ transmitted flux at $z \sim 2.5$.