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We study the thermodynamical properties of a self-gravitating gas with two ormore types of particles. Using the method of linear series of equilibria, wedetermine the structure and stability of statistical equilibrium states in bothmicrocanonical and canonical ensembles. We show how the critical temperature(Jeans instability) and the critical energy (Antonov instability) depend on therelative mass of the particles and on the dimension of space. We then study thedynamical evolution of a multi-components gas of self-gravitating Brownianparticles in the canonical ensemble. Self-similar solutions describing thecollapse below the critical temperature are obtained analytically. We findparticle segregation, with the scaling profile of the slowest collapsingparticles decaying with a non universal exponent that we compute perturbativelyin different limits. These results are compared with numerical simulations ofthe two-species Smoluchowski-Poisson system. Our model of self-attractingBrownian particles also describes the chemotactic aggregation of amulti-species system of bacteria in biology

Self-gravitating Brownian systems and bacterial populations with two or more types of particles