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

## TL;DR

This paper introduces a new analytic model for mass transfer in binary systems with arbitrary eccentricity, enabling more accurate long-term evolution studies of such systems, including triples with Lidov-Kozai oscillations.

## Contribution

The authors develop a smooth, phase-dependent mass transfer model valid for any eccentricity, overcoming previous high-eccentricity limitations and facilitating population synthesis applications.

## Key findings

- Model valid for all eccentricities, including circular orbits.
- Implementation in a publicly available code for population synthesis.
- Application to systems with LK oscillations and eccentric binaries.

## Abstract

Most studies of mass transfer in binary systems assume circular orbits at the onset of Roche lobe overflow. However, there are theoretical and observational indications that mass transfer could occur in eccentric orbits. In particular, eccentricity could be produced via sudden mass loss and velocity kicks during supernova explosions, or Lidov-Kozai (LK) oscillations in hierarchical triple systems, or, more generally, secular evolution in multiple-star systems. However, current analytic models of eccentric mass transfer are faced with the problem that they are only well defined in the limit of very high eccentricities, and break down for less eccentric and circular orbits. This provides a major obstacle to implementing such models in binary and higher-order population synthesis codes, which are useful tools for studying the long-term evolution of a large number of systems. Here, we present a new analytic model to describe the secular orbital evolution of binaries undergoing conservative mass transfer. The main improvement of our model is that the mass transfer rate is a smoothly varying function of orbital phase, rather than a delta function centered at periapsis. Consequently, our model is in principle valid for any eccentricity, thereby overcoming the main limitation of previous works. We implement our model in an easy-to-use and publicly available code that can be used as a basis for implementations of our model into population synthesis codes. We investigate the implications of our model in a number of applications with circular and eccentric binaries, and triples undergoing LK oscillations.