Semi-Analytic Solutions For Warped, Super-Eddington Accretion Disks with Outflows

The discovery of billion solar mass black holes at high redshift challenges any standard Eddington-limited growth model. Previous work has shown that an advective accretion disk can account for these early black holes with episodic accretion. It has also been shown that if the accretion disk of a black hole is misaligned from the spin axis of the black hole, the disk can become advective within a certain radius. While warped and misaligned accretion disks have been explored in numerical simulations, there is no fully or semi-analytic framework that self-consistently connects disk warp, mass inflow, winds, and energy transport in the super-Eddington regime. In this work, we develop a first-principles semi-analytic model of a radiation-pressure-dominated, warped accretion disk, starting from the coupled conservation equations for mass, energy, and angular momentum. We find profiles for the radial velocity and surface density that explicitly account for disk warping and mass loss and determine the radius at which the disk becomes advective. We explore changes with black hole spin, misalignment angle and viscosity, reproducing relevant results from numerical studies.