Hydrodynamic simulations of Lyman alpha clouds based on ab inito cosmological models have produced results that are in broad agreement with observations. However, further analyses have revealed that, with progressively higher numerical resolution, the median or cutoff line width of the simulated Lyman alpha clouds (i.e. the Doppler parameter) appears to converge to a value significantly below what is observed at z~3 (by about a factor of 1.5). These convergence test simulations do not include feedback from star formation. Given the observed metallicity in the Lyman alpha clouds we suggest that supernovae, which presumably polluted the IGM with metals, may have deposited a sufficient amount of energy in the IGM to reconcile the theory with observations. Simple arguments immediately narrow the redshift range of pollution down to 4=0.01Zsun. Finally, assuming the specific supernova heating energy is proportional to the metallicity of a gas, we note that the picture proposed here would be consistent with supernovae being the apparently needed heating source for the intra-cluster gas, if the required heating of the intra-cluster gas is no greater than 1 keV per particle.

accepted to ApJ Letters