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 $\times$ SuperCOSMOS public catalogues, covering the redshift range $z\lesssim0.4$. 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 $1-b_{\rm H}$. These results can also be interpreted as measurements of the bias-weighted average gas pressure $\langle bP_e\rangle$ 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 $1-b_{\rm H}$ with $\sim13\%$ precision in 6 equispaced redshift bins, and find no evidence for a redshift-dependent mass bias parameter, in agreement with previous analyses. Our mean value of $1-b_{\rm H} = 0.59\pm0.03$ is also in good agreement with the one estimated by the joint analysis of Planck cluster counts and CMB anisotropies. Our measurements of $\langle bP_e\rangle$, at the level of $\sim10\%$ 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.

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