Probing the cluster pressure profile with thermal Sunyaev-Zeldovich
  effect and weak lensing cross-correlation
  We confront the universal pressure profile (UPP) proposed by~\citet{Arnaud10}
with the recent measurement of the cross-correlation function of the thermal
Sunyaev-Zeldovich (tSZ) effect from Planck and weak gravitational lensing
measurement from the Red Cluster Sequence lensing survey (RCSLenS). By using
the halo model, we calculate the prediction of $\xi^{y-\kappa}$ (lensing
convergence and Compton-$y$ parameter) and $\xi^{y-\gamma_{\rm t}}$ (lensing
shear and Compton-$y$ parameter) and fit the UPP parameters by using the
observational data. We find consistent UPP parameters when fixing the cosmology
to either WMAP 9-year or Planck 2018 best-fitting values. The best constrained
parameter is the pressure profile concentration $c_{500}=r_{500}/r_{\rm s}$,
for which we find $c_{500} = 2.68^{+1.46}_{-0.96}$ (WMAP-9) and $c_{500} =
1.91^{+1.07}_{-0.65}$ (Planck-2018) for the $\xi^{y-\gamma_t}$ estimator. The
shape index for the intermediate radius region $\alpha$ parameter is
constrained to $\alpha=1.75^{+1.29}_{-0.77}$ and $\alpha = 1.65^{+0.74}_{-0.5}$
for WMAP-9 and Planck-2018 cosmologies, respectively. Propagating the
uncertainties of the UPP parameters to pressure profiles results in a factor of
$3$ uncertainty in the shape and magnitude. Further investigation shows that
most of the signal of the cross-correlation comes from the low-redshift, inner
halo profile ($r \leqslant r_{\rm vir}/2$) with halo mass in the range of
$10^{14}$--$10^{15}\,{\rm M}_{\odot}$, suggesting that this is the major regime
that constitutes the cross-correlation signal between weak lensing and tSZ.
