Constraints on radial migration in spiral galaxies - I. Analytic criterion for capture at corotation

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 disc stars experiences significant, permanent changes to their individual orbital angular momenta over the lifetime of the disc, having strong implications for the evolution of disc galaxies. The first step for a star in a spiral disc 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 disc evolution.