1/2, 1, and 3/2--Law Non-Radiative Accretion Flows

Assuming self-similarity of the first kind, we get three possible values p=1/2, 1, 3/2 for the exponent describing the density profile, rho r^{-p}, of a non-radiative (and hence quasi-spherical) accretion flow. The high and low p cases are known as Bondi and Convection-Dominated accretion flows. The 1-law flow we tentatively identify with the so-called Magnetically-Frustrated accretion flow. If our interpretation is correct, the accretion flow must be, roughly speaking, a collection of Prandtl's turbulent jets. The 1-law flow, being a first-kind self-similar solution, may actually occur in nature (in collisionless plasma).