On the α formalism for the common envelope interaction
Abstract
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.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- March 2011
- DOI:
- 10.1111/j.1365-2966.2010.17891.x
- arXiv:
- arXiv:1010.4374
- Bibcode:
- 2011MNRAS.411.2277D
- Keywords:
-
- stars: evolution;
- binaries: close;
- stars: horizontal branch;
- white dwarfs;
- planetary nebulae: general;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 17 pages, 8 figures. Accepted by MNRAS