Global Slim Accretion Disk Solutions Revisited

TL;DR

This paper revisits the limits of slim accretion disk models, establishing a maximum accretion rate based on vertical force balance, and highlights the role of outflows in high-rate accretion flows.

Contribution

It introduces a new physical limit on accretion rates for slim disks based on vertical force balance, correcting previous overestimations.

Findings

Existence of a maximal accretion rate for slim disks.

Vertical motion reduces the maximum accretion rate.

Outflows are necessary at high accretion rates.

Abstract

We show that there exists a maximal possible accretion rate, beyond which global slim disk solutions cannot be constructed because in the vertical direction the gravitational force would be unable to balance the pressure force to gather the accreted matter. The principle for this restriction is the same as that for the Eddington luminosity and the corresponding critical accretion rate, which were derived for spherical accretion by considering the same force balance in the radial direction. If the assumption of hydrostatic equilibrium is waived and vertical motion is included, this restriction may become even more serious as the value of the maximal possible accretion rate becomes smaller. Previous understanding in the literature that global slim disk solutions could stand for any large accretion rates is due to the overestimation of the vertical gravitational force by using an approximate potential. For accretion flows with large accretion rates at large radii, outflows seem unavoidable in order for the accretion flow to reduce the accretion rate and follow a global solution till the central black hole.