Enrichment of the dust-to-gas mass ratio in Bondi/Jeans accretion/cloud systems due to unequal changes in dust and gas incoming velocities

The ratio of the Bondi and Jeans lengths is used to develop a cloud-accretion model that describes both an inner Bondi-type regime where gas pressure is balanced by the gravity of a central star and an outer Jeans-type regime where gas pressure is balanced by gas self-gravity. The gas density profile provided by this model makes a smooth transition from a wind-type inner solution to a Bonnor-Ebert type outer solution. It is shown that high-velocity dust impinging on this cloud will tend to pile-up due to having a different velocity profile than gas so that the dust-to-gas ratio is substantially enriched above the 1% ISM level.