Probing gravitational lensing of the CMB with SDSS-IV quasars

Abstract

We study the cross-correlation between the Planck CMB lensing convergence map and the eBOSS quasar overdensity obtained from the Sloan Digital Sky Survey (SDSS) IV, in the redshift range $0.9 < z < 2.2$. We detect the CMB lensing convergence-quasar cross power spectrum at $5.4 \sigma$ significance. The cross power spectrum provides a quasar clustering bias measurement that is expected to be particularly robust against systematic effects. The redshift distribution of the quasar sample has a median redshift $z \approx 1.55$, and an effective redshift about $1.51$. The best fit bias of the quasar sample is $b_q = 2.43 \pm 0.45$, corresponding to a host halo mass of $\log_{10}\left( \frac{M}{h^{-1} M_\odot} \right) = 12.54^{+0.25}_{-0.36}$. This is broadly consistent with the previous literature on quasars with a similar redshift range and selection. Since our constraint on the bias comes from the cross-correlation between quasars and CMB lensing, we expect it to be robust to a wide range of possible systematic effects that may contaminate the auto correlation of quasars. We checked for a number of systematic effects from both CMB lensing and quasar overdensity, and found that all systematics are consistent with null within $2 \sigma$. The data is not sensitive to a possible scale dependence of the bias at present, but we expect that as the number of quasars increases (in future surveys such as DESI), it is likely that strong constraints on the scale dependence of the bias can be obtained.