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

Abstract

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 $0.9\le z\le 2.2$ with absolute i-band magnitudes of $M_i\le -24$ (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 ${\log }_{10}(M_{\mathrm{h}}/h^{-1}{M}_{\odot })=12.6\pm 0.2$ and linear bias $b=2.7\pm 0.3$ 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 $M_{\mathrm{h}}\approx 10^{13}{h}^{-1}{M}_{\odot }$, scaling roughly as $M_{\mathrm{h}}\propto L_{\mathrm{opt}}^{3/4}$ 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 $M_{\mathrm{h}}$-$L_{\mathrm{opt}}$ 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 $M_{\mathrm{h}}$ with $L_{\mathrm{opt}}$ observed at low luminosity becomes stronger for the most powerful quasars, which tend to be accreting close to the Eddington limit.

arXiv commentAccepted for publication in ApJ

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