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.
