The halo mass of optically-luminous quasars at z=1-2 measured via gravitational deflection of the cosmic microwave background

We measure the average deflection of cosmic microwave background photons by quasars at $\langle z \rangle =1.7$. Our sample is selected from the Sloan Digital Sky Survey to cover the redshift range $0.9\leq z\leq2.2$ with absolute i-band magnitudes of $M_i\leq-24$ (K-corrected to z=2). A stack of nearly 200,000 targets reveals an 8$\sigma$ detection of Planck's estimate of the lensing convergence towards the quasars. We fit the signal with a model comprising a Navarro-Frenk-White density profile and a 2-halo term accounting for correlated large scale structure, which dominates the observed signal. The best-fitting model is described by an average halo mass $\log_{10}(M_{\rm h}/h^{-1}M_\odot)=12.6\pm0.2$ and linear bias $b=2.7\pm0.3$ at $z=1.7$, in excellent agreement with clustering studies. We also report of a hint, at a 90% confidence level, of a correlation between the convergence amplitude and luminosity, indicating that quasars brighter than $M_i\lesssim -26$ reside in halos of typical mass ${M_{\rm h}\approx 10^{13}\,h^{-1}M_\odot}$, scaling roughly as ${M_{\rm h}\propto L_{\rm opt}^{3/4}}$ at ${M_i\lesssim-24}$, in good agreement with physically-motivated quasar demography models. Although we acknowledge this luminosity dependence is a marginal result, the observed $M_{\rm h}$-$L_{\rm opt}$ relationship could be interpreted as a reflection of the cutoff in the distribution of black hole accretion rates towards high Eddington ratios: the weak trend of $M_{\rm h}$ with $L_{\rm opt}$ observed at low luminosity becomes stronger for the most powerful quasars, which tend to be accreting close to the Eddington limit.