Analytical Approach to the Galactic Radial Migration Induced by Overlapping Perturbations

Many galaxies, including our Milky Way, exhibit a bar-like structure at their center. Within these galactic bars, millions of stars rotate and collectively spin as a solid body. Besides, there are a multitude of revolving galactic bodies with spiral (density) waves that exist in the galactic disk. Through resonant interactions, these bodies can effectively absorb energy from the bar and cause stars within the bar to migrate radially. The aim of this work is to establish a transport equation for the resonant relaxation of a distribution of galactic bodies due to the simultaneous action of multiple overlapping perturbing sources. The limiting case of dominant stochasticity, in which the effective background diffusion frequency ν_eff is faster than the libration (bounce) frequency Ω_b, is shown to lead to considerable analytic simplification. In this regime, the relaxation of the angle-averaged distribution can be cast as a quasilinear diffusion equation that can be analytically integrated to all orders in the small parameter 1/Δ ≡ ω_b²/ν_eff². This framework, which is a non-trivial extension of a previously treated case of single perturbations (Hamilton et al. Astrophys. J. 2022, in press, arxiv.org/abs/2208.03855), is relevant to formulating reduced models for the radial migration problem of the bar-spiral coupling as well as to galaxies with two bar structures. Analytical insights and simulation are then applied to better understand the N-body simulations of Minchev & Famaey [Astrophys. J. 722 112 (2010)].