Measuring the equation of state of the high-z intergalactic medium using curvature statistics

TL;DR

This study uses hydrodynamical simulations to demonstrate that curvature statistics of the high-redshift intergalactic medium can effectively recover its temperature-density relation parameters, offering a new observational probe.

Contribution

The paper introduces a novel method using curvature distribution percentiles to simultaneously measure the IGM's temperature and equation of state parameters at high redshift.

Findings

Curvature statistics correlate tightly with IGM temperature at characteristic overdensities.

The method can recover temperature and gamma parameters with quantifiable errors.

Curvature-based measurements provide a complementary approach to existing IGM diagnostics.

Abstract

Using hydrodynamical simulations, we explore the use of the mean and percentiles of the curvature distribution function to recover the equation of state of the high-$z$ ($2 < z < 4$) intergalactic medium (IGM). We find that the mean and percentiles of the absolute curvature distribution exhibit tight correlation with the temperatures measured at respective characteristic overdensities $\bar{\Delta}_i$'s at each redshift. Hence, they provide complementary probes of the same underlying temperature-density distribution, and can in principle be used to simultaneously recover both parameters $T_0$ and $\gamma$ of the IGM effective equation of state. We quantify the associated errors in the recovered parameters $T_0$ and $\gamma$ from the intrinsic scatter in the characteristic overdensities and the uncertainties in the curvature measurement.