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Most studies of mass transfer in binary systems assume circular orbits at theonset of Roche lobe overflow. However, there are theoretical and observationalindications that mass transfer could occur in eccentric orbits. In particular,eccentricity could be produced via sudden mass loss and velocity kicks duringsupernova explosions, or Lidov-Kozai (LK) oscillations in hierarchical triplesystems, or, more generally, secular evolution in multiple-star systems.However, current analytic models of eccentric mass transfer are faced with theproblem that they are only well defined in the limit of very higheccentricities, and break down for less eccentric and circular orbits. Thisprovides a major obstacle to implementing such models in binary andhigher-order population synthesis codes, which are useful tools for studyingthe long-term evolution of a large number of systems. Here, we present a newanalytic model to describe the secular orbital evolution of binaries undergoingconservative mass transfer. The main improvement of our model is that the masstransfer rate is a smoothly varying function of orbital phase, rather than adelta function centered at periapsis. Consequently, our model is in principlevalid for any eccentricity, thereby overcoming the main limitation of previousworks. We implement our model in an easy-to-use and publicly available codethat can be used as a basis for implementations of our model into populationsynthesis codes. We investigate the implications of our model in a number ofapplications with circular and eccentric binaries, and triples undergoing LKoscillations.

An analytic model for mass transfer in binaries with arbitrary eccentricity, with applications to triple-star systems