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The common-envelope (CE) phase is an important stage in the evolution ofbinary stellar populations. The most common way to compute the change inorbital period during a CE is to relate the binding energy of the envelope ofthe Roche-lobe filling giant to the change in orbital energy. Especially inpopulation-synthesis codes, where the evolution of millions of stars must becomputed and detailed evolutionary models are too expensive computationally,simple approximations are made for the envelope binding energy. In this study,we present accurate analytic prescriptions based on detailed stellar-evolutionmodels that provide the envelope binding energy for giants with metallicitiesbetween Z = 10-4 and Z = 0.03 and masses between 0.8 Msun and 100 Msun, as afunction of the metallicity, mass, radius and evolutionary phase of the star.Our results are also presented in the form of electronic data tables andFortran routines that use them. We find that the accuracy of our fits is betterthan 15% for 90% of our model data points in all cases, and better than 10% for90% of our data points in all cases except the asymptotic giant branches forthree of the six metallicities we consider. For very massive stars (M > 50Msun), when stars lose more than ~20% of their initial mass due to stellarwinds, our fits do not describe the models as accurately. Our results are morewidely applicable - covering wider ranges of metallicity and mass - and are ofhigher accuracy than those of previous studies.

Analytical expressions for the envelope binding energy of giants as a function of basic stellar parameters