Post-common-envelope binaries from SDSS. IX: Constraining the common-envelope efficiency

TL;DR

This study constrains the common-envelope efficiency parameter alpha in post-common-envelope binaries using new observational data, finding a likely universal value between 0.2 and 0.3, and compares energy and angular momentum models.

Contribution

It provides the first comprehensive constraint on alpha using a large sample of PCEBs and compares different CE evolution models with realistic parameters.

Findings

All PCEBs can be reconstructed with the energy equation including internal energy.

Alpha values between 0.2 and 0.3 fit all systems simultaneously.

Classical energy equation constrains CE outcomes more effectively than angular momentum models.

Abstract

Reconstructing the evolution of post-common-envelope binaries (PCEBs) can constrain current prescriptions of common-envelope (CE) evolution. Analyzing a new sample of PCEBs we derive constraints on one of the most important parameters in the field of close compact binary formation, i.e. the CE efficiency alpha. After reconstructing the post-CE evolution and based on fits to stellar evolution calculations as well as a parametrized energy equation for CE evolution that incorporates realistic approximations of the binding energy parameter lambda, we determine the possible evolutionary histories of the observed PCEBs. We also reconstruct CE evolution replacing the classical energy equation with a scaled angular momentum equation and compare the results obtained with both algorithms. We find that all PCEBs in our sample can be reconstructed with the energy equation if the internal energy of the envelope is included. Although most individual systems have solutions for a broad range of values for alpha, only for alpha=0.2-0.3 do we find simultaneous solutions for all PCEBs in our sample. If we adjust alpha to this range of values, the values of the angular momentum parameter gamma cluster in a small range of values. In contrast if we fix gamma to a small range of values that allows us to reconstruct all our systems, the possible ranges of values for alpha remains broad for individual systems. The classical parametrized energy equation seems to be an appropriate prescription of CE evolution and turns out to constrain the outcome of the CE evolution much more than the alternative angular momentum equation. If there is a universal value of the CE efficiency, it should be in the range of alpha=0.2-0.3. We do not find any indications for a dependence of alpha on the mass of the secondary star or the final orbital period.