  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.
