Constraints on Radial Migration in Spiral Galaxies I. Analytic Criterion for Capture at Corotation

TL;DR

This paper develops an analytic criterion to determine if stars in spiral galaxies are in trapped orbits at corotation, which is crucial for understanding radial migration and galaxy evolution.

Contribution

It introduces a new analytic criterion for star trapping at corotation that accounts for finite orbital energy, advancing previous zero-energy models.

Findings

Criterion depends mainly on stellar angular momentum.

Applicable to stars with finite random orbital energy.

Useful for interpreting N-body simulation results.

Abstract

Near the corotation resonance of a transient spiral arm, stellar orbital angular momenta may be changed without inducing significant kinematic heating, resulting in what has come to be known as radial migration. When radial migration is very efficient, a large fraction of disk stars experiences significant, permanent changes to their individual orbital angular momenta over the lifetime of the disk, having strong implications for the evolution of disk galaxies. The first step for a star in a spiral disk to migrate radially is to be captured in a "trapped" orbit, associated with the corotation resonance of the spiral pattern. An analytic criterion for determining whether or not a star is in a trapped orbit has previously been derived only for stars with zero random orbital energy in the presence of a spiral with fixed properties. In this first paper in a series, we derive an analytic criterion appropriate for a star that is on an orbit of finite random orbital energy. Our new criterion demonstrates that whether or not a star is in a "trapped" orbit primarily depends on the star's orbital angular momentum. This criterion could be a powerful tool in the interpretation of the results of N-body simulations. In future papers of this series, we apply our criterion to explore the physical parameters important to determining the efficiency of radial migration and its potential importance to disk evolution.