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Assuming self-similarity of the first kind, we get three possible valuesp=1/2, 1, 3/2 for the exponent describing the density profile, rho r^{-p}, of anon-radiative (and hence quasi-spherical) accretion flow. The high and low pcases are known as Bondi and Convection-Dominated accretion flows. The 1-lawflow we tentatively identify with the so-called Magnetically-Frustratedaccretion 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 (incollisionless plasma).

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