Thermal-diffusional instability in white dwarf flames : Regimes of flame pulsation

Thermal-diffusional pulsation behaviors in planar as well as outwardly and inwardly propagating white dwarf carbon flames are systematically studied. It is shown that different equations of state in non-degenerate and degenerate matters in white dwarfs lead to different criterions of flame pulsation, with the critical Zel'dovich number in the later twice as large as in the former. For realistic physical conditions in white dwarf carbon flames, the asymptotic degenerate equation of state is adopted and the simplified one-step reaction rate for nuclear reactions are used to study the flame propagation. Flame front pulsation behaviors in different environmental densities and temperatures are obtained to form the regime diagram of pulsation, showing that carbon flames pulsate in the typical density and temperature. While being stable at higher temperatures, in relatively lower temperatures the amplitude of the flame pulsation becomes larger. In outwardly propagating spherical flames the pulsation instability is enhanced and flames are also easier to quench, while the inwardly propagating flames are more stable.
QC 20181214