Beyond the standard accretion disc model: coupled magnetic disc--corona solutions with a physically motivated viscosity law

We present a systematic, analytical study of geometrically thin, optically thick accretion disc solutions for magnetized turbulent flows, with an alpha-like viscosity prescription. Under the only assumptions that (1) Magneto-Rotational instability (MRI) generates the turbulence that produces the anomalous viscosity needed for accretion to proceed, and that (2) the magnetic field amplified by the instability saturates due to buoyant vertical escape, we are able to self-consistently solve the disc structure equations including the fraction of power, f, that is carried off by vertical Poynting flux (and likely dissipated outside the optically thick disc). For low-viscosity discs, we obtain stable high-f solutions at low accretion rates, when gas pressure dominates, and unstable, low-f, radiation pressure dominated solutions at high accretion rates. For high viscosity discs, instead, a new thermally and viscously stable, radiation pressure dominated solution is found, characterized by f~1 and appearing only above a critical accretion rate (of the order of few tenths of the Eddington one). We discuss the regimes of validity of our assumptions, and the astrophysical relevance of our solutions. We conclude that our newly discovered thin disc solutions, possibly accompanied by powerful, magnetically dominated coronae and outflows, should be seriously considered as models for black holes accreting at super-Eddington rates.