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We carry out a thermal energy census of hot baryons at $z < 1$, bycross-correlating the \emph{Planck} MILCA y-map with 0.8 millionclusters/groups selected from the Yang et.al (2021) catalog. The thermalSunyaev-Zel'dovich (tSZ) effect around these clusters/groups are reliablyobtained, which enables us to make our model constraints based on one-halo (1h)and two-halo (2h) contributions, respectively. (1) The total measurement S/N ofthe one-halo term is 63. We constrain the $Y$-$M$ relation over the halo massrange of $10^{13}$-$10^{15} M_\odot/h$, and find $Y\propto M^{\alpha}$ with$\alpha= 1.8$ at $z=0.14$ ($\alpha=2.1$ at $z=0.75$). The total thermal energyof gas bound to clusters/groups increases from $0.1\ \rm meV/cm^3$ at $z=0.14$to $0.22\ \rm meV/cm^3$ at $z=0.75$. (2) The two-halo term is used to constrainthe bias-weighted electron pressure $\langle b_yP_e \rangle$. We find that$\langle b_yP_e \rangle$ (in unit of $\rm meV/cm^3$) increases from $0.24\pm0.02$ at $z=0.14$ to $0.45\pm 0.02$ at $z=0.75$. These results lead to severalimplications. (i) The hot gas fraction $f_{\rm gas}$ in clusters/groupsmonotonically increase with halo mass, where $f_{\rm gas}$ of a $10^{14}M_\odot/h$ halo is $\sim 50\%$ ($25\%$) of the cosmic mean at $z=0.14\ (0.75)$.(ii) By comparing the 1h- and 2h-terms, we obtain tentative constraint on thethermal energy of unbound gas. (iii) The above results lead to significantsuppression of matter and weak lensing power spectrum at small scales. Theseimplications are important for astrophysics and cosmology, and we will furtherinvestigate them with improved data and gas modeling.

Thermal energy census with the Sunyaev-Zel'dovich effect of DESI galaxy clusters/groups and its implication on the weak lensing power spectrum