Heating of the intergalactic medium due to structure formation

We estimate the heating of the intergalactic medium due to shocks arising from structure formation. Heating of the gas outside the collapsed regions, with small overdensities (${n_b \over {\bar n_b}}\ll 200$) is considered here, with the aid of Zel'dovich approximation. We estimate the equation of state of this gas, relating the density with its temperature, and its evolution in time, considering the shock heating due to one-$\sigma$ density peaks as being the most dominant. We also estimate the mass fraction of gas above a given temperature as a function of redshift. We find that the baryon fraction above $10^6$ K at $z=0$ is $\sim 10$. We estimate the integrated Sunyaev-Zel'dovich distortion from this gas at present epoch to be of order $10^{-6}$.