Cross-correlation between the thermal Sunyaev-Zeldovich effect and the Integrated Sachs-Wolfe effect

Abstract

We present a joint cosmological analysis of the power spectra measurement of the Planck Compton parameter and the integrated Sachs-Wolfe (ISW) maps. We detect the statistical correlation between the Planck Thermal Sunyaev-Zeldovich (tSZ) map and ISW data with a significance of a $3.6\ddot{I}ƒ$ confidence level~(CL), with the autocorrelation of the Planck tSZ data being measured at a $25\ddot{I}ƒ$ CL. The joint auto- and cross-power spectra constrain the matter density to be $\hat{I}{\text{c◯}}_{\mathrm{m}}=0.317_{-0.031}^{+0.040}$, the Hubble constant $H_0=66.5_{-1.9}^{+2.0}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and the rms matter density fluctuations to be $\ddot{I}{ƒ}_8=0.730_{-0.037}^{+0.040}$ at the 68% CL. The derived large-scale structure $S_8$ parameter is $S_8\equiv \ddot{I}{ƒ}_8(\hat{I}{\text{c◯}}_{\mathrm{m}}/0.3{)}^{0.5}=0.755\pm 0.060$. If using only the diagonal blocks of covariance matrices, the Hubble constant becomes $H_0=69.7_{-1.5}^{+2.0}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. In addition, we obtain the constraint of the product of the gas bias, gas temperature, and density as $b_{\mathrm{gas}}\left(T_{\mathrm{e}}/(0.1\mathrm{keV})\right)\left({\bar{n}}_{\mathrm{e}}/1{\mathrm{m}}^{-3}\right)=3.09_{-0.380}^{+0.320}$. We find that this constraint leads to an estimate on the electron temperature today as $T_{\mathrm{e}}=(2.40_{-0.300}^{+0.250})\times 10^6\mathrm{K}$, consistent with the expected temperature of the warm-hot intergalactic medium. Our studies show that the ISW-tSZ cross-correlation is capable of probing the properties of the large-scale diffuse gas.

25 pages, 15 figures, 2 tables