### Abstract

The physical properties - speed, width, and density structure - of conductive burning fronts in degenerate carbon-oxygen (C + O) and oxygen-neon-magnesium (O + Ne + Mg) compositions are determined for a grid of initial densities and compositions. Assuming a subsonic, isobaric nuclear flame, these properties are computed by four independent methods : a numerical radiation transport code which includes implicit hydrodynamics ; a moving mesh diffusion code ; an eigenvalue method ; and a quasi-analytical, integral expression. The dependence of the physical properties of the flame on the assumed values of nuclear reaction rates, the nuclear reaction network employed, the thermal conductivity, and the choice of coordinate system are all investigated. The new results have implications for the formation of neutron stars by the accretion-induced collapse (AIC) of a white dwarf and for the production of Type Ia supernovae. The occurrence of AIC is critically dependent on the velocity of the nuclear conductive burning front and the growth rate of hydrodynamic instabilities. However, electron capture in nuclear statistical equilibrium behind the flame causes the density to increase (at constant pressure), restoring the density to its initial value some distance behind the front. There consequently exists a maximum length scale for the development of hydrodynamic instabilities. Treating the expanding area of the turbulent burning region as a fractal whose tile size is identical to the minimum unstable Rayleigh-Taylor wavelength, we find, for all reasonable values of the fractal dimension, that for initial C + O or O + Ne + Mg densities above about 9 × 10^{9} g cm^{-3} the white dwarf should collapse to a neutron star.

Original language | English (US) |
---|---|

Pages (from-to) | 649-667 |

Number of pages | 19 |

Journal | Astrophysical Journal |

Volume | 396 |

Issue number | 2 |

State | Published - 1992 |

Externally published | Yes |

### Fingerprint

### Keywords

- Conduction
- Nuclear reactions, nucleosynthesis, abundances
- Stars : neutron
- White dwarfs

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*396*(2), 649-667.

**The conductive propagation of nuclear flames. I. Degenerate C + O and O + Ne + Mg white dwarfs.** / Timmes, Francis; Woosley, S. E.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 396, no. 2, pp. 649-667.

}

TY - JOUR

T1 - The conductive propagation of nuclear flames. I. Degenerate C + O and O + Ne + Mg white dwarfs

AU - Timmes, Francis

AU - Woosley, S. E.

PY - 1992

Y1 - 1992

N2 - The physical properties - speed, width, and density structure - of conductive burning fronts in degenerate carbon-oxygen (C + O) and oxygen-neon-magnesium (O + Ne + Mg) compositions are determined for a grid of initial densities and compositions. Assuming a subsonic, isobaric nuclear flame, these properties are computed by four independent methods : a numerical radiation transport code which includes implicit hydrodynamics ; a moving mesh diffusion code ; an eigenvalue method ; and a quasi-analytical, integral expression. The dependence of the physical properties of the flame on the assumed values of nuclear reaction rates, the nuclear reaction network employed, the thermal conductivity, and the choice of coordinate system are all investigated. The new results have implications for the formation of neutron stars by the accretion-induced collapse (AIC) of a white dwarf and for the production of Type Ia supernovae. The occurrence of AIC is critically dependent on the velocity of the nuclear conductive burning front and the growth rate of hydrodynamic instabilities. However, electron capture in nuclear statistical equilibrium behind the flame causes the density to increase (at constant pressure), restoring the density to its initial value some distance behind the front. There consequently exists a maximum length scale for the development of hydrodynamic instabilities. Treating the expanding area of the turbulent burning region as a fractal whose tile size is identical to the minimum unstable Rayleigh-Taylor wavelength, we find, for all reasonable values of the fractal dimension, that for initial C + O or O + Ne + Mg densities above about 9 × 109 g cm-3 the white dwarf should collapse to a neutron star.

AB - The physical properties - speed, width, and density structure - of conductive burning fronts in degenerate carbon-oxygen (C + O) and oxygen-neon-magnesium (O + Ne + Mg) compositions are determined for a grid of initial densities and compositions. Assuming a subsonic, isobaric nuclear flame, these properties are computed by four independent methods : a numerical radiation transport code which includes implicit hydrodynamics ; a moving mesh diffusion code ; an eigenvalue method ; and a quasi-analytical, integral expression. The dependence of the physical properties of the flame on the assumed values of nuclear reaction rates, the nuclear reaction network employed, the thermal conductivity, and the choice of coordinate system are all investigated. The new results have implications for the formation of neutron stars by the accretion-induced collapse (AIC) of a white dwarf and for the production of Type Ia supernovae. The occurrence of AIC is critically dependent on the velocity of the nuclear conductive burning front and the growth rate of hydrodynamic instabilities. However, electron capture in nuclear statistical equilibrium behind the flame causes the density to increase (at constant pressure), restoring the density to its initial value some distance behind the front. There consequently exists a maximum length scale for the development of hydrodynamic instabilities. Treating the expanding area of the turbulent burning region as a fractal whose tile size is identical to the minimum unstable Rayleigh-Taylor wavelength, we find, for all reasonable values of the fractal dimension, that for initial C + O or O + Ne + Mg densities above about 9 × 109 g cm-3 the white dwarf should collapse to a neutron star.

KW - Conduction

KW - Nuclear reactions, nucleosynthesis, abundances

KW - Stars : neutron

KW - White dwarfs

UR - http://www.scopus.com/inward/record.url?scp=4243675794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243675794&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4243675794

VL - 396

SP - 649

EP - 667

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -