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Abstract Common envelope (CE) evolution is an outstanding open problem in stellar evolution, critical to the formation of compact binaries including gravitational-wave sources. In the “classical” isolated binary evolution scenario for double compact objects, the CE is usually the second mass transfer phase. Thus, the donor star of the CE is the product of a previous binary interaction, often stable Roche lobe overflow (RLOF). Because of the accretion of mass during the first RLOF, the main-sequence core of the accretor star grows and is “rejuvenated.” This modifies the core-envelope boundary region and decreases significantly the envelope binding energy for the remaining evolution. Comparing accretor stars from self-consistent binary models to stars evolved as single, we demonstrate that the rejuvenation can lower the energy required to eject a CE by ∼42%–96% for both black hole and neutron star progenitors, depending on the evolutionary stage and final orbital separation. Therefore, binaries experiencing first stable mass transfer may more easily survive subsequent CE events and result in possibly wider final separations compared to current predictions. Despite their high mass, our accretors also experience extended “blue loops,” which may have observational consequences for low-metallicity stellar populations and asteroseismology. 

We present LEGWORK (LISA Evolution and Gravitational Wave Orbit Kit), an open-source Python package for making predictions about stellar-origin gravitational-wave sources and their detectability in LISA or other space-based gravitational-wave detectors. LEGWORK can be used to evolve the orbits of sources due to gravitational-wave emission, calculate gravitational-wave strains (using post-Newtonian approximations), compute signal-to-noise ratios, and visualize the results. It can be applied to a variety of potential sources, including binaries consisting of white dwarfs, neutron stars, and black holes. Although we focus on double compact objects, in principle LEGWORK can be used for any system with a user-specified orbital evolution, such as those affected by a third object or gas drag. We optimized the package to make it efficient for use in population studies, which can contain tens of millions of sources. This paper describes the package and presents several potential use cases. We explain in detail the derivations of the expressions behind the package as well as identify and clarify some discrepancies currently present in the literature. We hope that LEGWORK will enable and accelerate future studies triggered by the rapidly growing interest in gravitational-wave sources.

 

Gravitational-wave (GW) detections are starting to reveal features in the mass distribution of double compact objects. The lower end of the black hole (BH) mass distribution is especially interesting as few formation channels contribute here and because it is more robust against variations in the cosmic star formation than the high-mass end. In this work we explore the stable mass transfer channel for the formation of GW sources with a focus on the low-mass end of the mass distribution. We conduct an extensive exploration of the uncertain physical processes that impact this channel. We note that, for fiducial assumptions, this channel reproduces the peak at ∼9M_☉in the GW-observed binary BH mass distribution remarkably well and predicts a cutoff mass that coincides with the upper edge of the purported neutron star–black hole (NS–BH) mass gap. The peak and cutoff mass are a consequence of the unique properties of this channel; namely (1) the requirement of stability during the mass transfer phases, and (2) the complex way in which the final compact object masses scale with the initial mass. We provide an analytical expression for the cutoff in the primary component mass and show that this adequately matches our numerical results. Our results imply that selection effects resulting from the formation channel alone can provide an explanation for the purported NS–BH mass gap in GW detections. This provides an alternative to the commonly adopted view that the gap emerges during BH formation.