Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars

Details Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars

2007-05-30

arxiv.org/abs/0705.4366v2

Physica A, 387, 1999 (2008)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.physa.2007.10.075

We point out a remarkable analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in a generalized Keller-Segel model of chemotaxis [Chavanis & Sire, PRE, 69, 016116 (2004)]. This model is based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations similar to gaseous polytropes in astrophysics. For the critical index n_3=d/(d-2) (where d is the dimension of space), the theory of polytropes leads to a unique value of the mass M_c that we interpret as a limiting mass. In d=3, we find M_c=202.8956... and in d=2, we recover the well-known result M_c=8 pi (in suitable units). For MM_c, the system collapses and forms a Dirac peak containing a mass M_c surrounded by a halo. This paper exposes the model and shows, by simple considerations, the origin of the critical mass. A detailed description of the critical dynamics of the generalized Keller-Segel model will be given in a forthcoming paper.

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