Adiabatic mass loss in binary stars. I. Computational method

Hongwei Ge, Michael S. Hjellming, Ronald F. Webbink, Xuefei Chen, Zhanwen Han

Research output: Contribution to journalArticlepeer-review


The asymptotic response of donor stars in interacting binary systems to very rapid mass loss is characterized by adiabatic expansion throughout their interiors. In this limit, energy generation and heat flow through the stellar interior can be neglected. We model this response by constructing model sequences, beginning with a donor star filling its Roche lobe at an arbitrary point in its evolution, holding its specific entropy and composition profiles fixed as mass is removed from the surface. The stellar interior remains in hydrostatic equilibrium. Luminosity profiles in these adiabatic models of mass-losing stars can be reconstructed from the specific entropy profiles and their gradients. These approximations are validated by comparison with time-dependent binary mass transfer calculations. We describe how adiabatic mass-loss sequences can be used to quantify threshold conditions for dynamical timescale mass transfer, and to establish the range of post-common envelope binaries that are allowed energetically. In dynamical timescale mass transfer, the adiabatic response of the donor star drives it to expand beyond its Roche lobe, leading to runaway mass transfer and the formation of a common envelope with its companion star. For donor stars with surface convection zones of any significant depth, this runaway condition is encountered early in mass transfer, if at all; but for main-sequence stars with radiative envelopes, it may be encountered after a prolonged phase of thermal timescale mass transfer, a so-called delayed dynamical instability. We identify the critical binary mass ratio for the onset of dynamical timescale mass transfer as that ratio for which the adiabatic response of the donor star radius to mass loss matches that of its Roche lobe at some point during mass transfer; if the ratio of donor to accretor masses exceeds this critical value, dynamical timescale mass transfer ensues. In common envelope evolution, the dissipation of orbital energy of the binary provides the energy to eject the common envelope; the energy budget for this process consists essentially of the initial orbital energy of the binary and the initial self-energies of the binary components. We emphasize that, because the stellar core and envelope contribute mutually to each other's gravitational potential energy, proper evaluation of the total energy of a star requires integration over the entire stellar interior, and not just over the ejected envelope alone as commonly assumed. We show that the change in total energy of the donor star, as a function of its remaining mass along an adiabatic mass-loss sequence, can be calculated either by integration over initial and final models, or by a path integral along the mass-loss sequence. That change in total energy of the donor star, combined with the requirement that both remnant donor and its companion star fit within their respective Roche lobes, then circumscribes energetically possible survivors of common envelope evolution.

Original languageEnglish (US)
Pages (from-to)724-738
Number of pages15
JournalAstrophysical Journal
Issue number2
StatePublished - 2010


  • binaries: close
  • stars: evolution
  • stars: interiors
  • stars: mass-loss

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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