Constraining the Baryon Fraction in the Warm Hot Intergalactic Medium at Low Redshifts with Planck Data

We cross-correlate foreground cleaned Planck Nominal cosmic microwave background (CMB) maps with two templates constructed from the Two-Micron All-Sky Redshift Survey of galaxies. The first template traces the large-scale filamentary distribution characteristic of the Warm-Hot Intergalactic Medium (WHIM) out to ∼ 90 {{h}^-1} Mpc. The second preferentially traces the virialized gas in unresolved halos around galaxies. We find a marginal signal from the correlation of Planck data and the WHIM template with a signal to noise from 0.84 to 1.39 at the different Planck frequencies, and with a frequency dependence compatible with the thermal Sunyaev-Zel’dovich effect. When we restrict our analysis to the 60% of the sky outside the plane of the Galaxy and known point sources and galaxy clusters, the cross-correlation at zero lag is 0.064+/- 0.051 μ K. The correlation extends out to ≈ 6{}^\circ , which at the median depth of our template corresponds to a physical length of ∼ 6--8 {{h}^-1} Mpc. On the same fraction of the sky, the cross-correlation of the CMB data with the second template is \lt 0.17 μ K (95% C.L.), providing no statistically significant evidence of a contribution from bound gas to the previous result. This limit translates into a physical constraint on the properties of the shock-heated WHIM of a log-normal model describing the weakly nonlinear density field. We find that our upper limit is compatible with a fraction of 45% of all baryons residing in filaments at overdensities ∼1-100 and with temperatures in the range {{10}^4.5}--{{10}^7.5} K, in agreement with the detection at redshift z∼ 0.5 of Van Waerbeke et al..