Thermal energy census with the Sunyaev-Zel'dovich effect of DESI galaxy
  clusters/groups and its implication on the weak lensing power spectrum
  We carry out a thermal energy census of hot baryons at $z < 1$, by
cross-correlating the Planck MILCA y-map with over 40 DESI galaxy cluster/group
subsamples constructed from the Yang et. al (2021) catalog. In our
investigation, we select 0.8 million clusters/groups with richness $\geq 5$ and
estimated halo mass $\geq 10^{13} M_\odot/h$. The detection of the thermal
Sunyaev-Zel'dovich (tSZ) effect is significant in the investigated
clusters/groups. (1) The total measurement S/N of the one-halo term is 65. We
constrain the $Y-M$ relation over the halo mass range of $10^{13}-10^{15}
M_\odot/h$. We find $Y\propto M^{\alpha}$ with $\alpha= 1.8$ at $z=0.14$ and
$\alpha=2.1$ at $z=0.75$. The total thermal energy of gas bound to
clusters/groups increases from $0.11 \rm meV/cm^3$ at $z=0.14$ to $0.23 \rm
meV/cm^3$ at $z=0.75$. (2) The two-halo term measurement constrains the
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 $0.25\pm 0.03$ at
$z=0.14$ to $0.55\pm 0.04$ at $z=0.75$. These results lead to several
implications. (i) The hot gas fraction $f_{\rm gas}$ in clusters/groups
monotonically increase with halo mass, where $f_{\rm gas}$ of a $10^{14}
M_\odot/h$ halo is $\sim 50\%$ ($20\%$) of the cosmic mean at $z=0.14\ (0.75)$.
(ii) By comparing the 1h- and 2h-terms, we constrain the thermal energy of
unbound gas. (iii) The above results lead to a suppression of matter and weak
lensing power spectrum. At $l=10^3 \ (10^4)$, the suppression is $\sim 7\%\
(17\%)$ for source galaxies at $z_s=1$. These implications are potentially
important for gastrophysics and cosmology, although they suffer from
uncertainties in measurements (Planck resolution, cluster mass/redshift
determination, etc) and gas modeling to be further investigated.
