Sub-Keplerian rotation

Sub-Keplerian rotation has angular speed below that of a circular Keplerian orbit at the same radius. In a gaseous disk, an outwardly decreasing pressure supplies some radial support and makes the gas sub-Keplerian.

For test particles with linear drag, negligible radial gas flow and negligible dust feedback, Sub-Keplerian rotation removes solid-particle angular momentum. The displayed inward velocity uses Stokes number $\mathrm{St}={\Omega }_K{t}_s$ and the pressure-gradient parameter of a protoplanetary disk. Drift is fastest at $\mathrm{St}=1$; the physical particle size at that point depends on the local gas and drag law.

A region that concentrates solids by opposing their loss through radial drift. Near a radial gas-pressure maximum, the pressure-support drift changes sign and carries particles toward the maximum from both sides. Gas advection and turbulent diffusion can limit retention.

A convention for the small fractional reduction of azimuthal gas speed due to radial pressure support. With $c_s^2=P_g/{\rho }_g$, radial balance gives $v_{g\varphi }^2=v_K^2(1-2\eta )$ and hence $v_{g\varphi }\simeq v_K(1-\eta )$. Other authors absorb the factor of two into the definition; the convention must accompany a drift formula.