On the Binding Energy Parameter $\lambda$ of Common Envelope Evolution

TL;DR

This paper systematically calculates the binding energy parameter λ for stars of 1-20 solar masses, considering internal energy, providing fitting formulas for improved binary evolution modeling.

Contribution

It offers new detailed calculations and fitting formulas for λ across different stellar populations, enhancing common envelope evolution simulations.

Findings

Calculated λ values for Population I and II stars.

Provided fitting formulas for λ as a function of stellar parameters.

Discussed applications in binary evolution modeling.

Abstract

The binding energy parameter $\lambda$ plays an important role in common envelope (CE) evolution. Previous works have already pointed out that $\lambda$ varies throughout the stellar evolution, though it has been adopted as a constant in most of the population synthesis calculations. We have systematically calculated the binding energy parameter $\lambda$ for both Population I and Population II stars of masses $1-20 M_{\sun}$, taking into account the contribution from the internal energy of stellar matter. We present fitting formulae for $\lambda$ that can be incorporated into future population synthesis investigations. We also briefly discuss the possible applications of the results in binary evolutions.