On the α formalism for the common envelope interaction

By O. De Marco, Jean-Claude Passy, M. Moe, Falk Herwig, M. Mac Low, B. Paxton. 2010

153 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/ff37bb1270f24be2e6bd863b81caa011f97df592

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Citations in the corpus

Delay-time distribution of core-collapse supernovae with late events resulting from binary interaction (2017, background): “Values of αCE > 1 account for possible extra energy sources used to unbind the envelope apart from the orbital energy (e.g., De Marco et al. 2011; Ivanova & Nandez 2016).”
Doing Science with eLISA: Astrophysics and Cosmology in the Millihertz Regime (2012, background): “Theoretical progress to understand the phase from first physical principles is slow (e.g. Taam and Ricker, 2010, Taam and Sandquist, 2000) and the standard formalism described above has been challenged by observational tests (De Marco et al., 2011, Nelemans and Tout, 2005).”
Common envelope evolution: where we stand and how we can move forward (2012, methodology): “…plus a condition on the mass of the remaining envelope, which itself is a function of the evolutionary status of the donor (for low mass red giants and asymptotic giant branch stars, De Marco et al. 2011), – where the nuclear energy generation falls below some threshold (De Marco et al. 2011).”
THE ROTATION RATES OF MASSIVE STARS: THE ROLE OF BINARY INTERACTION THROUGH TIDES, MASS TRANSFER, AND MERGERS (2012, methodology): “To treat common envelope situations we follow Hurley et al. (2002) we use choose a common envelope ejection efficiency parameter αCE = 0.2 in agreement with studies of binary systems in planetary nebulae (Zorotovic et al. 2010; Davis et al. 2010; De Marco et al. 2011).”
A circumbinary disc in the final stages of common envelope and the core-degenerate scenario for Type Ia supernovae (2011, methodology): “De Marco et al. (2011) suggest that if the spiral-in of the companion takes longer than the dynamical time, as in that case of long time energy release, the thermal energy of the AGB will be used to help unbind the envelope.”
SIMULATING THE COMMON ENVELOPE PHASE OF A RED GIANT USING SMOOTHED-PARTICLE HYDRODYNAMICS AND UNIFORM-GRID CODES (2011, methodology): “Using either the α-formalism (Webbink 1984, but see De Marco et al. 2011) or the γ-formalism (Nelemans et al. 2000) the relevant parameters can be constrained and the CE ejection efficiency can be predicted.”
Dawes Review 6: The Impact of Companions on Stellar Evolution (2016, methodology): “…of the CE might be have used known post-CE systems for which the pre-CE configuration could be reconstructed (e.g., Zorotovic et al., 2010; De Marco et al., 2011) or have used population synthesis codes with different CE efficiency prescriptions in the hope of using population constraints to…”
Theoretical uncertainties of the Type Ia supernova rate (2014, background): “Different groups determine a CE efficiency smaller than 1 after fitting theαce-prescription to a population of observed post-CE binaries (Zorotovic et al. 2010; De Marco et al. 2011; Davis et al. 2012).”