Lensing and the Warm-hot Intergalactic Medium

The correlation of weak lensing and Cosmic Microwave Anisotropy (CMB) data traces the pressure distribution of the hot, ionized gas and the underlying matter density field. The measured correlation is dominated by baryons residing in halos. Detecting the contribution from unbound gas by measuring the residual cross-correlation after masking all known halos requires a theoretical understanding of this correlation and its dependence with model parameters. Our model assumes that the gas in filaments is well described by a log-normal probability distribution function, with temperatures $10^{5-7}$K and overdensities $\xi\le 100$. The lensing-comptonization cross-correlation is dominated by gas with overdensities in the range $\xi\approx[3-33]$; the signal is generated at redshifts $z\le 1$. If only 10\% of the measured cross-correlation is due to unbound gas, then the most recent measurements set an upper limit of $\bar{T}_e\lesssim 10^6$K on the mean temperature of Inter Galactic Medium. The amplitude is proportional to the baryon fraction stored in filaments. The lensing-comptonization power spectrum peaks at a different scale than the gas in halos making it possible to distinguish both contributions. To trace the distribution of the low density and low temperature plasma on cosmological scales, the effect of halos will have to be subtracted from the data, requiring observations with larger signal-to-noise ratio than currently available.