AGN-driven outflows and the formation of Ly$\alpha$ nebulae around
  high-z quasars
  The detection of Ly$\alpha$ nebulae around $z\gtrsim 6$ quasars provides
evidence for extended gas reservoirs around the first rapidly growing
supermassive black holes. Observations of $z > 6$ quasars can be explained by
cosmological models provided that the black holes by which they are powered
evolve in rare, massive dark matter haloes. Whether these theoretical models
also explain the observed extended Ly$\alpha$ emission remains an open
question. We post-process a suite of cosmological, radiation-hydrodynamic
simulations targeting a quasar host halo at $z>6$ with the Ly$\alpha$ radiative
transfer code RASCAS. A combination of recombination radiation from
photo-ionised hydrogen and emission from collisionally excited gas powers
Ly$\alpha$ nebulae with a surface brightness profile in close agreement with
observations. We also find that, even on its own, resonant scattering of the
Ly$\alpha$ line associated to the quasar's broad line region can also generate
Ly$\alpha$ emission on $\sim 100 \, \rm kpc$ scales, resulting in comparable
agreement with observed surface brightness profiles. Even if powered by a broad
quasar Ly$\alpha$ line, Ly$\alpha$ nebulae can have narrow line-widths
$\lesssim 1000 \, \rm km \, s^{-1}$, consistent with observational constraints.
Even if there is no quasar, we find that halo gas cooling produces a faint,
extended Ly$\alpha$ glow. However, to light-up extended Ly$\alpha$ nebulae with
properties in line with observations, our simulations unambiguously require
quasar-powered outflows to clear out the galactic nucleus and allow the
Ly$\alpha$ flux to escape and still remain resonant with halo gas. The close
match between observations and simulations with quasar outflows suggests that
AGN feedback already operates before $z \, = \, 6$ and confirms that high-$z$
quasars reside in massive haloes tracing overdensities.
