Postcollapse dynamics of self-gravitating Brownian particles and bacterial populations

We address the postcollapse dynamics of a self-gravitating gas of Brownian particles in D dimensions in both canonical and microcanonical ensembles. In the canonical ensemble, the postcollapse evolution is marked by the formation of a Dirac peak with increasing mass. The density profile outside the peak evolves self-similarly with decreasing central density and increasing core radius. In the microcanonical ensemble, the postcollapse regime is marked by the formation of a "binarylike" structure surrounded by an almost uniform halo with high temperature. These results are consistent with thermodynamical predictions in astrophysics. We also show that the Smoluchowski-Poisson system describing the collapse of self-gravitating Brownian particles in a strong-friction limit is isomorphic to a simplified version of the Keller-Segel equations describing the chemotactic aggregation of bacterial populations. Therefore, our study has direct applications in this biological context.