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.
