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.
