Quasi-linear theory of the Jeans instability in disk-shaped galaxies

¹ Department of Physics, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel
² Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), PO Box 23, Taipei 106, Taiwan

Corresponding author: E. Griv, griv@bgumail.bgu.ac.il

Received: 4 September 2001
Accepted: 29 November 2001

Abstract

We analyse the reaction between almost aperiodically growing Jeans-unstable gravity perturbations and stars of a rotating and spatially inhomogeneous disk of flat galaxies. A mathematical formalism in the approximation of weak turbulence (a quasi-linearization of the Boltzmann collisionless kinetic equation) is developed. A diffusion equation in configuration space is derived which describes the change in the main body of equilibrium distribution of stars. The distortion in phase space resulting from such a wave–star interaction is studied. The theory, applied to the Solar neighborhood, accounts for the observed Schwarzschild shape of the velocity ellipsoid, the increase in the random stellar velocities with age, and the essential radial migration of the Sun from its birth-place in the inner part of the Galaxy outwards during its lifetime.