The host dark matter haloes of the first quasars

If $z > 6$ quasars reside in rare, massive haloes, $\Lambda$CDM cosmology predicts they should be surrounded by an anomalously high number of bright companion galaxies. Here I show that these companion galaxies should also move unusually fast. Using a new suite of cosmological, `zoom-in' hydrodynamic simulations, I present predictions for the velocity distribution of quasar companion galaxies and its variation with quasar host halo mass at $z \, = \, 6$. Satellites accelerate as they approach the quasar host galaxy, producing a line-of-sight velocity profile that broadens with decreasing distance to the quasar host galaxy. This increase in velocity dispersion is particularly pronounced if the host halo mass is $\gtrsim 5 \times 10^{12} \, \rm M_\odot$. Typical line-of-sight speeds rise to $\approx 500 \, \rm km \, s^{-1}$ at projected radii $\sim 10 \, \rm kpc$. For about $10\%$ of satellites, they should exceed $800 \, \rm km \, s^{-1}$, with $\approx 5\%$ of companions reaching line-of-sight speeds $\sim 1000 \, \rm km \, s^{-1}$. For lower host halo masses $\approx 5 \times 10^{11} - 10^{12} \, \rm M_\odot$, the velocity profile of companion galaxies is significantly flatter. In this case, typical line-of-sight velocities are $\approx 250 \, \rm km \, s^{-1}$ and do not exceed $\approx 500 \, \rm km \, s^{-1}$. A comparison with existing ALMA, JWST and MUSE line-of-sight velocity measurements reveals that observed $z > 6$ quasar companions closely follow the velocity distribution expected for a host halo with mass $\gtrsim 5 \times 10^{12} \, \rm M_\odot$, ruling out a light host halo. Finally, through an estimate of UV and \oiii \, luminosity functions, I show that the velocity distribution more reliably discriminates between halo mass than companion number counts, which are strongly affected by cosmic variance.