The VST ATLAS Quasar Survey III: Halo mass function via quasar clustering and quasar-CMB lensing cross-clustering

Abstract: We exploit the VST ATLAS quasar/QSO catalogue to perform three measurements of the quasar halo mass profile. First, we make a new estimate of the angular auto-correlation function of $\approx230,000$ ATLAS quasars with $z_{photo}\lesssim 2.5$ and $17<g<22$. By comparing with the $\Lambda$CDM mass clustering correlation function, we measure the quasar bias to be $b_Q\approx2.1$, implying a quasar halo mass of $M_{halo}\approx8.5\times10^{11}$h$^{-1} M_\odot$. Second, we cross-correlate these $z\approx1.7$ ATLAS quasars with the Planck Cosmic Microwave Background (CMB) lensing maps, detecting a somewhat stronger signal at $4'<\theta<60'$ than previous authors. Scaling these authors' model fit to our data we estimate a quasar host halo mass of $M_{halo}\approx8.3\times10^{11}h^{-1}$M$_{\odot}$. Third, we fit Halo Occupation Distribution (HOD) model parameters to our quasar auto-correlation function and from the derived halo mass function we estimate a quasar halo mass of $M_{halo}\approx2.5\times10^{12}$h$^{-1} M_\odot$. We then compare our HOD model prediction to our quasar-CMB lensing result, confirming their consistency. We find that most ($\approx2/3$) QSOs have halo masses within a factor of $\approx3$ of this average mass. An analysis based on the probability of X-ray detections of AGN in galaxies and the galaxy stellar mass function gives a similarly small mass range. Finally, we compare the quasar halo mass and luminosity functions and suggest that gravitational growth may produce the constant space density with redshift seen in the quasar luminosity function.