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

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 approximate to 230 000 ATLAS quasars with z(photo)less than or similar to 2.5 and 17<g<22. By comparing with the Lambda CDM mass clustering correlation function, we measure the quasar bias to be bQ approximate to 2.1, implying a quasar halo mass of M-halo approximate to 8.5x10(11)h(-1)M(circle dot). Second, we cross-correlate these z approximate to 1.7 ATLAS quasars with the Planck cosmic microwave background (CMB) lensing maps, detecting a somewhat stronger signal at 4arcmin<theta<60arcmin than previous authors. Scaling these authors' model fit to our data, we estimate a quasar host halo mass of M-halo approximate to 8.3x10(11)h-1M(circle dot). 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-halo approximate to 2.5x10(12)h(-1)M(circle dot). We then compare our HOD model prediction to our quasar-CMB lensing result, confirming their consistency. We find that most (approximate to 2/3) QSOs have halo masses within a factor of approximate to 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.