Phase separation of bacterial colonies in a limit of high degradation. Analogy with Jupiter's great red spot

We discuss the structure of the equilibrium states of a regularized Keller-Segel model describing the chemotaxis of bacterial populations. We consider the limit of high degradation of the secreted chemical where analytical results can be obtained. Below a critical effective temperature, the system experiences a second order phase transition from a homogeneous phase to an inhomogeneous phase formed by two domains with uniform concentration separated by a thin interface (domain wall). We study the properties of the interface and determine the bifurcation between a circular shape (spot) and a stripe as a function of the control parameters. We show the analogy with the structure of Jupiter's Great red spot which also consists of two phases with uniform potential vorticity separated by a thin annular jet.