Standard thin-disk dissipation flux

For a steady Keplerian disk with a zero-torque inner edge

R_{in}

, the flux summed over both faces is

F_{diss} (R) = \frac{3 GM M ˙}{4 π R ^{3}} [1 - (\frac{R _{in}}{R})^{1/2}] .

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- Standard thin-disk luminosity Standard thin-disk dissipation flux

Standard thin-disk luminosity

Integrating the standard thin-disk dissipation flux gives

L_{thin} = \frac{GM M ˙}{2 R _{in}} = \frac{1}{2} \dot{M} R_{in}^{2} Ω_{K, in}^{2} .

Half of the Newtonian potential-energy decrease remains as orbital kinetic energy until the inner edge.

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