Common envelope evolution (CEE) physics plays a fundamental role in the formation of binary systems, such as merging stellar gravitational wave sources, pulsar binaries, and Type Ia supernovae. A precisely constrained CEE has become more important in the age of large surveys and gravitational wave detectors. We use an adiabatic mass-loss model to explore how the total energy of the donor changes as a function of the remnant mass. This provides a more self-consistent way to calculate the binding energy of the donor. For comparison, we also calculate the binding energy through integrating the total energy from the core to the surface. The outcome of CEE is constrained by total energy conservation at the point at which both components’ radii shrink back within their Roche lobes. We apply our results to 142 hot subdwarf binaries. For shorter orbital period hot subdwarf B stars (sdBs), the binding energy is highly consistent. For longer orbital period sdBs in our samples, the binding energy can differ by up to a factor of 2. The common envelope (CE) efficiency parameter β _CE becomes smaller than α _CE for the final orbital period log 10 P orb / days > − 0.5 . We also find the mass ratios log 10 q and CE efficiency parameters log 10 α CE and log 10 β CE linearly correlate in sdBs, similarly to the findings of De Marco et al. for post-AGB binaries.

Common envelope evolution (CEE) is vital for forming short-orbital-period compact binaries. It covers many objects, such as double compact merging binaries, Type Ia supernovae progenitors, binary pulsars, and X-ray binaries. Knowledge of the common envelope (CE) ejection efficiency still needs to be improved, though progress has been made recently. Short-orbital-period hot subdwarf B star (sdB) plus white dwarf (WD) binaries are the most straightforward samples with which to constrain CEE physics. We apply the known orbital period–WD mass relation to constrain the sdB progenitors of seven sdB+WD binaries with a known inclination angle. The average CE efficiency parameter is 0.32. This is consistent with previous studies. However, the CE efficiency need not be constant, but a function of the initial mass ratio, based on well-constrained sdB progenitor mass and evolutionary stage. Our results can be used as physical inputs for binary population synthesis simulations of related objects. A similar method can also be applied to study other short-orbital-period WD binaries.

The stability criteria of rapid mass transfer and common-envelope evolution are fundamental in binary star evolution. They determine the mass, mass ratio, and orbital distribution of many important systems, such as X-ray binaries, type Ia supernovae, and merging gravitational-wave sources. We use our adiabatic mass-loss model to systematically survey intermediate-mass (IM) stars’ thresholds for dynamical timescale mass transfer. The impact of metallicity on the stellar responses and critical mass ratios is explored. Both tables (Z = 0.001) and fitting formulae (Z = 0.001 and Z = 0.02) of the critical mass ratios of IM stars are provided. An application of our results to intermediate-mass X-ray binaries (IMXBs) is discussed. We find that the predicted upper limit to mass ratios, as a function of orbital period, is consistent with the observed IMXBs that undergo thermal or nuclear timescale mass transfer. According to the observed peak X-ray luminosity, L _X, we predict the range of L _X for IMXBs as a function of the donor mass and the mass-transfer timescale.

Context. Mass transfer stability is a key issue in studies of binary evolution. Critical mass ratios for dynamically stable mass transfer have been analyzed on the basis of an adiabatic mass loss model, finding that the donor stars on the giant branches tend to be more stable than that based on the composite polytropic stellar model. Double white dwarfs (DWDs) are of great importance in many fields and their properties would be significantly affected under the new mass transfer stability criterion. Aims. We seek to investigate the influence of mass transfer stability on the formation and properties of DWD populations and discuss the implications in supernova Type Ia (SN Ia) and gravitational wave (GW) sources. Methods. We performed a series of binary population synthesis, adopting the critical mass ratios from the adiabatic mass loss model (i.e., Ge’s model) and that of the composite polytropic model, respectively. In each simulation, 5 × 10⁶ binaries were included and evolved from zero-age main sequence to the end of their evolution and the DWDs were gradually obtained. Results. For Ge’s model, most of the DWDs are produced from the stable non-conservative Roche lobe (RL) overflow, along with a common-envelope (CE) ejection channel (RL+CE channel), regardless of the CE ejection efficiency, α_CE. Conversely, the results of the polytropic model strongly depend on the adopted value of α_CE. We find DWDs produced from the RL+CE channel have comparable WD masses and the mass ratio distribution peaks at around 1. Based on the magnitude-limited sample of DWDs, the space densities for the detectable DWDs and those with extremely low-mass WD (ELM WD) companions in Ge’s model is: 1347 kpc⁻³ and 473 kpc⁻³, respectively, which is close to what has been shown in observations. On the other hand, the polytropic model overpredicts space density of DWDs by a factor of about 2−3. We also find that the results of DWD merger rate distribution per Galaxy in Ge’s model reproduce the observations better than that of the polytropic model, and the merger rate of DWDs with ELM WD companions in the Galaxy is about 1.8 × 10⁻³ yr⁻¹ in Ge’s model. This result is comparable to the observation estimation of 2 × 10⁻³ yr⁻¹. The findings from Ge’s model predict a Galactic SN Ia rate of ∼6 × 10⁻³ yr⁻¹ from DWDs, supporting observations of (5.4 ± 1.2)×10⁻³ yr⁻¹. For the fiducial model of α_CE = 1, the number of detectable GW sources in the polytropic model is larger than that in Ge’s model by about 35%. Conclusions. We confirm that mass transfer stability plays an important role in the formation and properties of DWD populations as well as in the progenitors of SNe Ia and detectable GW sources. The results of Ge’s model support the observational DWD merger rate distribution per Galaxy and the space density of DWDs in the Galaxy.

Binary stars are responsible for many unusual astrophysical phenomena, including some important explosive cosmic events. The stability criteria for rapid mass transfer and common-envelope evolution are fundamental to binary star evolution. They determine the mass, mass ratio, and orbital distribution of systems such as X-ray binaries and merging gravitational-wave sources. We use our adiabatic mass-loss model to systematically survey metal-poor and solar-metallicity donor thresholds for dynamical timescale mass transfer. The critical mass ratios q _ad are systematically explored and the impact of metallicity and nonconservative mass transfer are studied. For metal-poor radiative-envelope donors, q _ad are smaller than those for solar-metallicity stars at the same evolutionary stage. However, q _ad do the opposite for convective-envelope donors. Nonconservative mass transfer significantly decreases q _ad for massive donors. This is because it matters how conservative mass transfer is during the thermal timescale phase immediately preceding a delayed dynamical mass transfer. We apply our theoretical predictions to observed high-mass X-ray binaries that have overfilled their Roche lobes and find a good agreement with their mass ratios. Our results can be applied to study individual binary objects or large samples of binary objects with binary population synthesis codes.