The conductive propagation of nuclear flames. II. Convectively bounded flames in C + O and O + Ne + Mg cores

F. X. Timmes, S. E. Woosley, Ronald E. Taam

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


We determine the speeds, and many other physical properties, of flame fronts that propagate inward into degenerate and semidegenerate cores of carbon and oxygen (CO) and neon and oxygen (NeOMg) white dwarfs when such flames are bounded on their exterior by a convective region. Combustion in such fronts, per se, is incomplete, with only a small part of the initial mass fraction burned. A condition of balanced power is set up in the star where the rate of energy emitted as neutrinos from the convective region equals the power available from the unburned fuel that crosses the burning front. The propagation of the burning front itself is in turn limited by the temperature at the base of the convective shell, which cannot greatly exceed the adiabatic value. Solving for consistency between these two conditions gives a unique speed for the flame. Typical values for CO white dwarfs are a few hundredths of a centimeter per second. Flames in NeOMg mixtures are slower. Tables are presented in a form that can easily be implemented in stellar evolution codes and yield the rate at which the convective shell advances into the interior. Combining these velocities with the local equations for stellar structure, we find a minimum density for each gravitational potential below which the flame cannot propagate, and must die. Although detailed stellar models will have to be constructed to resolve some issues conclusively, our results suggest that a CO white dwarf ignited at its edge will not burn carbon all the way to its center unless the mass of the white dwarf exceeds 0.8 M. On the other hand, it is difficult to ignite carbon burning by compression alone anywhere in a white dwarf whose mass does not exceed 1.0 M. Thus, compressionally ignited shell carbon burning in an accreting CO dwarf almost certainly propagates all the way to the center of the star. Implications for neutron star formation, and Type Ia supernova models, are briefly discussed. These are also applicable to massive stars in the ∼ 10-12 M⊙ range which ignite neon burning off center.

Original languageEnglish (US)
Pages (from-to)348-363
Number of pages16
JournalAstrophysical Journal
Issue number1
StatePublished - Jan 1 1994
Externally publishedYes


  • Conduction
  • Nuclear reactions, nucleosynthesis, abundances
  • Stars: interiors
  • Supernovae: general
  • White dwarfs

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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