Cross-correlating Planck CMB lensing with SDSS: Lensing-lensing and galaxy-lensing cross-correlations

Abstract: We present results from cross-correlating Planck CMB lensing maps with the Sloan Digital Sky Survey (SDSS) galaxy lensing shape catalog and BOSS galaxy catalogs. For galaxy position vs. CMB lensing cross-correlations, we measure the convergence signal around the galaxies in configuration space, using the BOSS LOWZ ($z\sim0.30$) and CMASS ($z\sim0.57$) samples. With fixed Planck 2015 cosmology, doing a joint fit with the galaxy clustering measurement, for the LOWZ (CMASS) sample we find a galaxy bias $b_g=1.75\pm0.04$ ($1.95\pm 0.02$) and galaxy-matter cross-correlation coefficient $r_{cc}=1.0\pm0.2$ ($0.8\pm 0.1$) using $20<r_p<70h^{-1}$Mpc, consistent with results from galaxy-galaxy lensing. Using the same scales and including the galaxy-galaxy lensing measurements, we constrain $\Omega_m=0.284\pm0.024$ and relative calibration bias between the CMB lensing and galaxy lensing to be $b_\gamma=0.82^{+0.15}_{-0.14}$. The combination of galaxy lensing and CMB lensing also allows us to measure the cosmological distance ratios (with $z_l\sim0.3$, $z_s\sim0.5$) $\mathcal R=\frac{D_s D_{l,}}{D_ D_{l,s}}=2.68\pm0.29$, consistent with predictions from the Planck 2015 cosmology ($\mathcal R=2.35$). We detect the galaxy position-CMB convergence cross-correlation at small scales, $r_p<1h^{-1}$Mpc, and find consistency with lensing by NFW halos of mass $M_h\sim10^{13}h^{-1}M_\odot$. Finally, we measure the CMB lensing-galaxy shear cross-correlation, finding an amplitude of $A=0.76\pm0.23$ ($z_\text{eff}=0.35$, $\theta<2^\circ$) with respect to Planck 2015 $\Lambda$CDM predictions ($1\sigma$-level consistency). We do not find evidence for relative systematics between the CMB and SDSS galaxy lensing.