Collisional dynamics of the Milky Way

The effect of gravitational (elastic) encounters between stars and giant molecular clouds on the stability of small-amplitude perturbations of the Milky Way's self-gravitating disk is considered, using the exact Landau (Fokker-Planck type) collision integral, and compared with the results obtained by Griv & Peter (1996), who used the simple phenomenological Bhatnagar-Gross-Krook (Bhatnagar et al. 1954) collisional model. The present analysis is carried out for the case of a spatially inhomogeneous, highly flattened system, i.e., an inhomogeneous system in which the thickness is very small in comparison with the disk's radial extension. According to observations (Grivnev & Fridman 1990), the dynamics of a system with rare, κ² ≫ ν²_c (and weak, ω² ≫ ν²_c), interparticle encounters is considered, where κ is the epicyclic frequency, ω is the frequency of excited waves, and ν_c ∼ 10^-9 yr^-1 is the effective frequency of star-cloud encounters. The evolution of the stellar distribution is determined primarily by interactions with collective modes of oscillations - gravitational Jeans-type and gradient-dissipative modes - rather than by ordinary ("close") star-cloud encounters. On the basis of a local kinetic theory, it is shown that the Landau integral and the Bhatnagar et al. model give practically identical results in the case of perturbations with the wavelength λ that is comparable to the mean epicyclic radius of stars ρ, that is, in the case of the most dangerous, in the sense of the loss of stability, gravitational Jeans-type perturbations. The models, however, have essentially different qualitative and quantitative behaviors in the extreme limits of long-wavelength perturbations, (πρ/λ)² ≪ 1, and of short-wavelength perturbations, (πρ/λ)² ≫ 1. Certain observational implications of the present theory are discussed.