Paper detail

An analytic relation for the thickness of accretion flows

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 Θ) = [(γ-1)/(2γ)]^{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, Θis the half-opening angle of the flow, and γis the adiabatic index.