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 autocorrelation function of ≈230 000 ATLAS quasars with $z_{\rm photo}\lesssim 2.5$ and $17 < g < 22$. By comparing with the $\Lambda$CDM mass clustering correlation function, we measure the quasar bias to be $b_{\rm Q}\approx 2.1$, implying a quasar halo mass of $M_{\rm halo} \approx 8.5\times 10^{11}\,h^{-1}\,{\rm M}_\odot$. Second, we cross-correlate these $z\approx 1.7$ ATLAS quasars with the Planck cosmic microwave background (CMB) lensing maps, detecting a somewhat stronger signal at $4\,{\rm arcmin} < \theta < 60\,{\rm arcmin}$ than previous authors. Scaling these authors’ model fit to our data, we estimate a quasar host halo mass of $M_{\rm halo}\approx 8.3\times 10^{11}\,h^{-1}\,{\rm M}_\odot$. Third, we fit halo occupation sistribution (HOD) model parameters to our quasar autocorrelation function and from the derived halo mass function, we estimate a quasar halo mass of $M_{\rm halo}\approx 2.5\times 10^{12}\,h^{-1}\,{\rm M}_\odot$. We then compare our HOD model prediction to our quasar-CMB lensing result, confirming their consistency. We find that most (≈2/3) QSOs have halo masses within a factor of ≈3 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.