Monte Carlo simulations of post-common-envelope white dwarf + main sequence binaries: The effects of including recombination energy

¹ Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Casilla 5030, Valparaíso, Chile
e-mail: mzorotovic@dfa.uv.cl
² Millennium Nucleus “Protoplanetary Disks in ALMA Early Science”, Universidad de Valparaíso, Casilla 36-D Santiago, Chile
³ Departament de Física Aplicada, Universitat Politècnica de Catalunya, c/Esteve Terrades 5, 08860 Castelldefels, Spain
⁴ Institute for Space Studies of Catalonia, c/Gran Capità 2−4, Edif. Nexus 104, 08034 Barcelona, Spain
⁵ Kavli Institute for Astronomy and Astrophysics, Peking University, 100871 Beijing, PR China
⁶ Department of Physics, University of Warwick, Coventry CV4 7AL, UK

Received: 12 November 2013
Accepted: 20 June 2014

Abstract

Context. Detached white dwarf + main sequence (WD+MS) post-common-envelope binaries (PCEBs) are perhaps the most suitable objects for testing predictions of close-compact binary-star evolution theories, in particular, common-envelope (CE) evolution. Consequently, the population of WD+MS PCEBs has been simulated by several authors in the past and the predictions have been compared with the observations. However, most of those theoretical predictions did not take into account the possible contributions to the envelope ejection from additional sources of energy (mostly recombination energy) stored in the envelope.

Aims. Here we update existing binary population models of WD+MS PCEBs by assuming that in addition to a fraction α_CE of the orbital energy, a fraction α_rec of the recombination energy available within the envelope contributes to ejecting the envelope.

Methods. We performed Monte Carlo simulations of 10⁷ MS+MS binaries for 9 different combinations of α_CE and α_rec using standard assumptions for the initial primary mass function, binary separations, and initial-mass-ratio distribution and evolved these systems using the publicly available binary star evolution (BSE) code.

Results. Including a fraction of the recombination energy leads to a clear prediction of a large number of long orbital period (≳10 days) systems mostly containing high-mass WDs. The fraction of systems with He-core WD primaries (M_WD ≲ 0.5 M_⊙) increases with the CE efficiency and the existence of very low-mass He WDs (≲0.3 M_⊙) is only predicted for high values of the CE efficiency, i.e. α_CE ≳ 0.5. All models predict on average longer orbital periods for PCEBs containing C/O-core WDs (M_WD ≳ 0.5 M_⊙) than for PCEBs containing He WDs. This effect increases with increasing values of both efficiencies, i.e., α_CE and α_rec. Longer periods after the CE phase are also predicted for systems containing more massive secondary stars. The initial-mass-ratio distribution affects the distribution of orbital periods, especially the distribution of secondary star masses.

Conclusions. Our simulations, in combination with a large and homogeneous observational sample, can provide constraints on the values of α_CE and α_rec, as well as on the initial-mass-ratio distribution for MS+MS binary stars.