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

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.