Rethinking mass transfer: a unified semi-analytical framework for circular and eccentric binaries.II. Orbital evolution due to non-conservative mass transfer

TL;DR

This paper extends the General Mass Transfer (GeMT) framework to non-conservative mass transfer in eccentric binaries, introducing four AML modes and a Global-$L_2$ fit to quantify angular-momentum loss. It shows that $L_2$ mass loss is the most efficient AML channel across broad parameter space and that eccentric RLOF can naturally produce gravitational-wave source progenitors by yielding compact post-MT binaries within a Hubble time, unlike traditional instantaneous circularization assumptions. The work highlights how donor spin, mass ratio, and eccentricity shape the orbital evolution, with eccentricity driving phase-dependent MT and correlated changes in $a$ and $e$ that depend on the AML mode. By providing a self-consistent, semi-analytic treatment of both conservative and non-conservative MT across arbitrary eccentricities, the GeMT framework offers a robust tool for improving binary evolution and population-synthesis predictions, with implications for GW source formation and circumbinary-disc phenomena.

Abstract

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 non-conservative MT in eccentric orbits, a process especially relevant for binaries containing compact objects (COs). We examine four angular momentum loss (AML) modes; Jeans, isotropic re-emission, orbital-AML and $L_2$ mass loss -- the latter is the most efficient AML mode. For 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 re-emission and orbital-AML show intermediate behavior. Adopting isotropic re-emission, 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 large range of mass ratios and eccentricities, naturally linking eccentricity to $L_2$ mass loss. 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 non-conservative MT in arbitrary eccentricities with applications ranging from MT on the main sequence to GW progenitors.

Figures (17)

• Figure 1: A schematic of mass loss via isotropic re-emission. The equipotential surface (dotted curve) is shown in the corotating frame of the binary system. The thick black cross represents the system's center of mass, and the thick x-symbol represents the location of the $L_1$ point through which the donor transfers mass to the accretor. The mass that is not accreted is ejected isotropically from the vicinity of the accretor as indicated by the red arrows.
• Figure 2: A schematic of mass loss through the $L_2$ Lagrangian point. Two equipotential surfaces (dotted and dashed-dotted curves) are shown in the corotating frame of the binary system. The thick black cross represents the system's center of mass, and the thick x-symbols represent the locations of the $L_1$, through which the donor transfers mass to the accretor, and $L_2$ points, respectively. The mass that is not accreted is lost through the $L_2$ point indicated by the pink thick line. The red arrows pointing from the accretor to the $L_2$ point are only for schematic purposes.
• Figure 3: AML-parameter $\gamma$ for different angular momentum loss modes. From top to bottom, the subfigures correspond to $f_{\rm don}=0.8,1.0,1.2$, respectively. Dashed blue, orange and black lines corresponds to Jeans, isotropic re-emission and orbital-AML modes, respectively. Solid lines represent the $L_2$ mass loss mode (Eq. \ref{['eq:gamma_L2']}). Blue, orange, green, and red colors correspond to $e=0.0,0.3,0.6,0.9$, respectively. The blue dotted line corresponds to $L_2$ mass loss mode for circular orbits 1998CoSka..28..101P.
• Figure 4: Secular rate of change of the semimajor axis as a function of mass ratio $q$ and fraction of accreted mass $\beta$, in the limit of circular orbits for different AML modes. From top to bottom: the GeMT-model assuming Jeans mode, isotropic re-emission, orbital-AML, and $L_2$ mass loss. The values of the relevant parameters are provided in Table \ref{['tab:colormaps_parameters']}.
• Figure 5: Secular rate of change of the semimajor axis as a function of mass ratio $q$ and eccentricity $e$ in the limit of fully non-conservative MT for different AML modes. From top to bottom: the GeMT-model assuming Jeans mode, isotropic re-emission, orbital-AML, and $L_2$ mass loss. The values of the relevant parameters are provided in Table \ref{['tab:colormaps_parameters']}.