The host dark matter haloes of the first quasars.

If z > 6 quasars reside in rare, massive haloes, ΛCDM 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 per cent of satellites, they should exceed |$800 \, \rm km \, s^{-1}$|⁠ , with |$\approx 5~{{\ \rm per\ cent}}$| 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 Atacama Large Millimeter/submillimeter Array (ALMA), JWST and Multi-Unit Spectroscopic Explorer (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 ultraviolet and [ |$\rm O \, {\small III}$| ] 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. [ABSTRACT FROM AUTHOR]