We use three-dimensional hydrodynamical simulations to study the rapid infall phase of the common envelope interaction of a red giant branch star of mass equal to 0.88 M and a companion star of mass ranging from 0.9 down to 0.1 M . We first compare the results obtained using two different numerical techniques with different resolutions, and find overall very good agreement. We then compare the outcomes of those simulations with observed systems thought to have gone through a common envelope. The simulations fail to reproduce those systems in the sense that most of the envelope of the donor remains bound at the end of the simulations and the final orbital separations between the donor's remnant and the companion, ranging from 26.8 down to 5.9 R , are larger than the ones observed. We suggest that this discrepancy vouches for recombination playing an essential role in the ejection of the envelope and/or significant shrinkage of the orbit happening in the subsequent phase.
The α formalism is a common way to parametrize the common envelope interaction between a giant star and a more compact companion. The α parameter describes the fraction of orbital energy released by the companion that is available to eject the giant star's envelope. By using new, detailed stellar evolutionary calculations, we derive a user-friendly prescription for the λ parameter and an improved approximation for the envelope binding energy, thus revising the α equation. We then determine α both from simulations and from observations in a self-consistent manner. By using our own stellar structure models as well as population considerations to reconstruct the primary's parameters at the time of the common envelope interaction, we gain a deeper understanding of the uncertainties. We find that systems with very low values of q (the ratio of the companion's mass to the mass of the primary at the time of the common envelope interaction) have higher values of α. A fit to the data suggests that lower-mass companions are left at comparable or larger orbital separations to more massive companions. We conjecture that lower-mass companions take longer than a stellar dynamical time to spiral into the giant's core, and that this is key to allowing the giant to use its own thermal energy to help unbind its envelope. As a result, although systems with light companions might not have enough orbital energy to unbind the common envelope, they might stimulate a stellar reaction that results in the common envelope ejection.
Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability in the astrophysical community. This discussion relies largely on how the KHI test is posed and analyzed. We pose a stringent test of the initial growth of the instability. The goal is to provide a rigorous methodology for verifying a code on two dimensional Kelvin-Helmholtz instability. We ran the problem in the Pencil Code, Athena, Enzo, NDSPMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, though this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of Smoothed Particle Hydrodynamics. We then comment on the connection between this behavior to the underlying lack of zeroth-order consistency in Smoothed Particle Hydrodynamics interpolation. We comment on the tendency of some methods, particularly those with very low numerical diffusion, to produce secondary Kelvin-Helmholtz billows on similar tests. Though the lack of a fixed, physical diffusive scale in the Euler equations lies at the root of the issue, we suggest that in some methods an extra diffusion operator should be used to damp the growth of instabilities arising from grid noise. This statement applies particularly to moving-mesh tessellation codes, but also to fixed-grid Godunov schemes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.