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.