Rethinking mass transfer: A unified semianalytical framework for circular and eccentric binaries

Although mass transfer (MT) has been studied primarily in circular binaries, observations show that it also occurs in eccentric systems. We investigate orbital evolution during nonconservative MT in eccentric orbits, a process especially relevant for binaries containing compact objects (COs). We examined four angular momentum loss (AML) modes: Jeans, isotropic reemission, orbital-AML, and L 2 mass loss, with the last mode being the most efficient AML mode. For a fixed AML mode and accretion efficiency, orbital evolution is correlated: orbits either widen while becoming more eccentric, or shrink while circularizing. Jeans mode generally yields orbital widening and eccentricity pumping, whereas L 2 mass loss typically leads to orbital shrinkage and eccentricity damping. Isotropic reemission and orbital-AML show an intermediate behavior. Adopting isotropic reemission, we demonstrate that eccentric MT produces compact binaries that merge via gravitational waves (GW) within a Hubble time, whereas the same systems would instead merge during MT under traditional modeling. We further show that, in eccentric orbits, the gravitational potential at L 2 becomes lower than at L 1 across a wide range of mass ratios and eccentricities, naturally linking eccentricity to L 2 mass loss. Eccentric MT may therefore lead to the formation of the circumbinary disks observed around eccentric post-red-giant-branch and post-asymptotic-giant-branch systems. Since interacting binaries containing COs are frequently eccentric, L 2 mass loss offers a new robust pathway to orbital tightening during eccentric MT, contributing to the formation rate of GW sources. This model can treat orbital evolution due to conservative and nonconservative MT in arbitrary eccentricities, with applications ranging from MT on the main sequence to GW progenitors.