Resolving the physics of Quasar Ly$α$ Nebulae (RePhyNe): I. Constraining Quasar host halo masses through Circumgalactic Medium kinematics
Ly$α$ nebulae ubiquitously found around z>2 quasars can supply unique constraints on the properties of the Circumgalactic Medium, such as its density distribution, provided the quasar halo mass is known. We present a new method to constrain quasar halo masses based on the line-of-sight velocity dispersion maps of Ly$α$ nebulae. By using MUSE-like mock observations obtained from cosmological hydrodynamic simulations under the assumption of maximal quasar fluorescence, we show that the velocity dispersion radial profiles of Ly$α$-emitting gas are strongly determined by gravity and that they are thus self-similar with respect to halo mass when rescaled by the virial radius. Through simple analytical arguments and by exploiting the kinematics of HeII1640Ȧ emission for a set of observed nebulae, we show that Ly$α$ radiative transfer effects plausibly do not change the shape of the velocity dispersion profiles but only their normalisation without breaking their self-similarity. Taking advantage of these results, we define the variable $η^{140-200}_{40-100}$ as the ratio of the median velocity dispersion in two specifically selected annuli and derive an analytical relation between $η^{140-200}_{40-100}$ and the halo mass which can be directly applied to observations. We apply our method to 37 observed quasar Ly$α$ nebulae at 3<z<4.7 and find that their associated quasars are typically hosted by ~$10^{12.16 \pm 0.14}$ M$_{\odot}$ haloes independent of redshift within the explored range. This measurement, which is completely independent of clustering methods, is consistent with the lowest mass estimates based on quasar auto-correlation clustering at z~3 and with quasar-galaxies cross-correlation results.