Tomographic measurement of the intergalactic gas pressure through galaxy-tSZ cross-correlations

We cross-correlate maps of the thermal Sunyaev-Zeldovich (tSZ) Compton-y parameter published by Planck with the projected distribution of galaxies in a set of low-redshift tomographic bins. We use the nearly full-sky 2MASS Photometric Redshift and WISE x SuperCOSMOS public catalogues, covering the redshift range z less than or similar to 0.4. Our measurements allow us to place constraints on the redshift dependence of the mass-observable relation for tSZ cluster count analyses in terms of the so-called hydrostatic mass bias parameter 1 - b(H). These results can also be interpreted as measurements of the bias-weighted average gas pressure < bP(e)> as a function of redshift, a quantity that can be related to the thermodynamics of gas inside haloes and used to constrain energy injection processes. We measure 1 - b(H) with similar to 13 per cent precision in six equispaced redshift bins, and find no evidence for a redshift-dependent mass bias parameter, in agreement with previous analyses. Our mean value of 1 - b(H) = 0.59 +/- 0.03 is also in good agreement with the one estimated by the joint analysis of Planck cluster counts and cosmic microwave background anisotropies. Our measurements of < bP(e)>, at the level of similar to 10 per cent in each bin, are the most stringent constraints on the redshift dependence of this parameter to date, and agree well both with previous measurements and with theoretical expectations from shock-heating models.