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 \sim 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 .