The temperature of IGM at high redshifts: shock heating and high mach problem

The thermal history of cosmic gas in the Dark Ages remains largely unknown. It is important to quantify the impact of relevant physics on the IGM temperature between $z=10$ and $z \sim 30$, in order to interpret recent and oncoming observations, including results reported by EDGES. We revisit the gas heating due to structure formation shocks in this era, using a set of fixed grid cosmological hydrodynamical simulations performed by three different codes. In all our simulations, the cosmic gas is predicted to be in multiphase state since $z>30$. The gas surrounding high density peaks gradually develops a relation more sharp than $T \propto \rho^{2/3}$, approximately $T \propto \rho^{2}$, from $z=30$ to $z=11$, might due to shock heating. Meanwhile, the gas in void region tends to have a large local mach number, and their thermal state varies significantly from code to code. In the redshift range $11-20$, the mass fraction of gas shock heated above the CMB temperature in our simulations is larger than previous semi-analytical results by a factor of 2 to 8. At $z=15$, the fraction varies from $\sim 19\%$ to $52 \%$ among different codes. Between $z=11$ and $z=20$, the gas temperature $<1/T_{\rm{K}}>_M^{-1}$ is predicted to be $\sim 10-20$ K by two codes, much higher than the adiabatic cooling model and some previous works. However, in our simulations performed by RAMSES, $<1/T_{\rm{K}}>_M^{-1}$ is predicted to be even below the temperature required to explain result of the EDGES. Given the fact that different codes give different predictions, currently, it seems a challenge to make solid prediction on the temperature of gas at $z \sim 17$ in simulations.