An analytic relation for the thickness of accretion flows

TL;DR

This paper derives an analytic relation connecting the sound speed, flow opening angle, and Keplerian velocity in accretion flows, applicable to both thin and thick geometries, enhancing understanding of flow structure.

Contribution

It introduces a new analytic relation that accounts for the vertical velocity distribution in spherical coordinates, applicable to various accretion flow geometries.

Findings

The relation c_{s0}/(v_K heta) = [(γ -1)/(2γ)]^{1/2} holds for thin and thick flows.

The relation links sound speed, flow angle, and Keplerian velocity.

It improves modeling of accretion flow vertical structure.

Abstract

We take the vertical distribution of the radial and azimuthal velocity into account in spherical coordinates, and find that the analytic relation c_{s0}/(v_K \Theta) = [(\gamma -1)/(2\gamma)]^{1/2} is valid for both geometrically thin and thick accretion flows, where c_{s0} is the sound speed on the equatorial plane, v_K is the Keplerian velocity, \Theta is the half-opening angle of the flow, and \gamma is the adiabatic index.