Outflows in super-Eddington quasars drive clumpy circumgalactic medium and extended H$\alpha$ nebulae at $z \gtrsim 6$

The discovery of gargantuan black holes with masses exceeding a billion solar masses at $z\gtrsim6$ suggests rapid black hole growth and significant energy input into their host galaxies in the early Universe. With JWST probing previously unseen phases of the interstellar (ISM) and circumgalactic (CGM) medium around $z > 6$ quasars, detailed theoretical studies can now be directly confronted with observations. We use zoom-in simulations of a massive protocluster at $z\sim6$, employing both the fiducial FABLE galaxy formation model and modifications that allow earlier black hole seeding and mildly super-Eddington accretion. The central quasar remains Compton-thick throughout most of its evolution, with the obscuration arising from the ISM of its compact host galaxy. The onset of sufficiently strong quasar feedback drives a 'blow-out' episode, clearing out escape channels for ionizing radiation and leaving the central engine unobscured. This leads to a complete transformation of the CGM, whereby powerful, metal-enriched outflows produce a population of cold, fast, neutral clumps, significantly increasing the covering fraction of neutral hydrogen in the host halo. Radiative transfer calculations performed with a new ray-tracing code show that the CGM responds to quasar activity through the formation of H$\alpha$ nebulae, whose size and luminosity increase with the strength of quasar feedback and decrease with obscuration level. Enhanced early black hole growth thus fundamentally reshapes the ISM and CGM of $z\sim6$ quasars, leaving clear observable signatures in their obscuration, neutral hydrogen distribution, and extended H$\alpha$ emission.