On the energy equation and efficiency parameter of the common envelope evolution
J.D.M. Dewi 1,3,4 and
T.M. Tauris 2,1
Received 22 February 2000 / Accepted 23 June 2000
We have investigated the structure of evolved giant stars with masses 3 - 10 in order to evaluate the binding energy of the envelope to the core prior to mass transfer in close binary systems. This binding energy is expressed by a parameter which is crucial for determining the outcome of binaries evolving through a common envelope (CE) and spiral-in phase. We discuss the -parameter and the efficiency of envelope ejection in the CE-phase, and show that depends strongly on the evolutionary stage (i.e. stellar radius) of the donor star at the onset of the mass transfer. The existence of this relation enables us to introduce a new approach for solving the energy equation. For a given observed binary system we can derive a unique solution for the original mass and age of the donor star, as well as the pre-CE orbital period.
We find that the value of is typically between 0.2 and 0.8. But in some cases, particularly on the asymptotic giant branch of lower-mass stars, it is possible that . A high value of (rather than assuming a high efficiency parameter, ) is sufficient to explain the long final orbital periods observed among those binary millisecond pulsars which are believed to have evolved through a CE-phase.
We also present a tabulation of as a function of stellar radius and mass, which is useful for a quick estimation of the orbital decay during a common envelope and spiral-in phase.
Key words: stars: binaries: general stars: evolution stars: mass-loss methods: numerical stars: pulsars: individual: PSR J1454-5846
Send offprint requests to: J.D.M. Dewi (email@example.com)
© European Southern Observatory (ESO) 2000
Online publication: August 23, 2000