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 Mpc/h. The second traces preferentially 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 (tSZ) 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 muK. The correlation extends out to ~6 deg, which at the median
depth of our template corresponds to a physical length of ~ 6-8 Mpc/h. On the
same fraction of the sky, the cross-correlation of the CMB data with the second
template is <0.17 muK (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. (2014).
