Probing galaxy bias and intergalactic gas pressure with KiDS
  Galaxies-tSZ-CMB lensing cross-correlations
  We constrain the redshift dependence of gas pressure bias $\left\langle b_{y}
P_{\mathrm{e}}\right\rangle$ (bias-weighted average electron pressure), which
characterises the thermodynamics of intergalactic gas, through a combination of
cross-correlations between galaxy positions and the thermal Sunyaev-Zeldovich
(tSZ) effect, as well as galaxy positions and the gravitational lensing of the
cosmic microwave background (CMB). The galaxy sample is from the fourth data
release of the Kilo-Degree Survey (KiDS). The tSZ $y$ map and the CMB lensing
map are from the {\textit{Planck}} 2015 and 2018 data releases, respectively.
The measurements are performed in five redshift bins with $z\lesssim1$. With
these measurements, combining galaxy-tSZ and galaxy-CMB lensing
cross-correlations allows us to break the degeneracy between galaxy bias and
gas pressure bias, and hence constrain them simultaneously. In all redshift
bins, the best-fit values of $\bpe$ are at a level of $\sim 0.3\,
\mathrm{meV/cm^3}$ and increase slightly with redshift. The galaxy bias is
consistent with unity in all the redshift bins. Our results are not sensitive
to the non-linear details of the cross-correlation, which are smoothed out by
the {\textit{Planck}} beam. Our measurements are in agreement with previous
measurements as well as with theoretical predictions. We also show that our
conclusions are not changed when CMB lensing is replaced by galaxy lensing,
which shows the consistency of the two lensing signals despite their radically
different redshift ranges. This study demonstrates the feasibility of using CMB
lensing to calibrate the galaxy distribution such that the galaxy distribution
can be used as a mass proxy without relying on the precise knowledge of the
matter distribution.
