The Halo Mass of Optically Luminous Quasars at z ,F≈ ,F1-2 Measured via Gravitational Deflection of the Cosmic Microwave Background

We measure the average deflection of cosmic microwave background photons by quasars at 〈Z〉= 1.7. Our sample is selected from the Sloan Digital Sky Survey to cover the redshift range 0.9 ≤z≤2.2 with absolute i-band magnitudes of M i ≤-24 (K-corrected to z = 2). A stack of nearly 200,000 targets reveals an 8δ detection of Planck's estimate of the lensing convergence toward the quasars. We fit the signal with a model comprising a Navarro-Frenk-White density profile and a two-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 h h -1 M)12.6 ±0.2 = and linear bias b=2.7±0.3 at 〈Z 〉= 1.7, in excellent agreement with clustering studies. We also report a hint, at a 90% confidence level, of a correlation between the convergence amplitude and luminosity, indicating that quasars brighter than Mi≲ -26 reside in halos of typical mass M h ≈ 10 13 h -1 M, scaling roughly as M h ∞ L opt 3/4 at M i ≲-24 mag, in good agreement with physically motivated quasar demography models. Although we acknowledge that this luminosity dependence is a marginal result, the observed Mh-L opt relationship could be interpreted as a reflection of the cutoff in the distribution of black hole accretion rates toward high Eddington ratios: the weak trend of Mh with Lopt observed at low luminosity becomes stronger for the most powerful quasars, which tend to be accreting close to the Eddington limit.