Spiral galaxy evolution is frequently considered in the context of environment, but internal processes may also play an important role. One such process, called \lq\lq radial migration", rearranges the angular momentum distribution of the disk without causing kinematic heating. Should radial migration be efficient, it could cause a substantial fraction of disk stars to move large radial distances over the lifetime of the disk, thus having significant impact on its kinematic, structural and chemical evolution. However, clues to its efficiency from observational and simulated data are inconclusive and insight from analytic studies is limited. We here aim to build an analytic framework for understanding the physics important to the efficiency of radial migration. In order for a star to migrate radially, it must first be in a “trapped” orbit (a family of orbits that occurs near corotation) due to a transient spiral pattern. The efficiency of radial migration depends on both the duty cycle for transient patterns and the RMS change in orbital angular momentum from each pattern, ^(1/2). This work focuses on the physics that determines the magnitude of ^(1/2), which increases with increasing fraction of and radial excursions for stars in trapped orbits.
In this work, we derive both an expression for the maximum radial excursion of a trapped orbit and an analytic “capture criterion” that predicts whether or not a disk star with finite random orbital energy is in a trapped orbit. We then use the capture criterion, in a series of disk galaxy models, to find the fraction of stars in trapped orbits.
We show it is primarily a star's orbital angular momentum that determines whether or not it is in a trapped orbit. For an ensemble of stars, the trapped fraction decreases with increasing radial velocity dispersion as e^(-sigma_R^2). Further, the maximum radial excursions for trapped orbits is smaller than excursions expected from the random motions of stars in MW-like spirals. We conclude that radial migration may play a role in the evolution of disk galaxies, but it is not important enough to form major structural components
