The binding energy parameter for common envelope evolution

The binding energy parameter lambda plays a vital role in common envelope evolution. Though it is well known that lambda takes different values for stars with different masses and varies during stellar evolution, it has been erroneously adopted as a constant in most population synthesis calculations. We have systematically calculated the values of lambda for stars of masses 1 - 60 M-circle dot by use of an updated stellar evolution code, taking into account the contribution from both gravitational energy and internal energy to the binding energy of the envelope. We adopt the criterion for the core-envelope boundary advocated by Ivanova. A new kind of lambda with an enthalpy prescription is also investigated. We present fitting formulae for the calculated values of various kinds of lambda, which can be used in future population synthesis studies.