On the evolution of stars that form electron-degenerate cores processed by carbon burning .3. The inward propagation of a carbon-burning flame and other properties of a 9 M-circle dot model star

A 9 M. stellar model of Population I composition is evolved from the hydrogen-burning main sequence to the thermally pulsing ''super'' asymptotic giant branch stage, where it has an electron-degenerate core composed of an inner oxygen-neon (ONe) part of mass similar to 1.066 M. and an outer carbon-oxygen (GO) layer of mass similar to 0.05 M. and is experiencing thermal pulses driven by helium-burning thermonuclear flashes. The carbon-burning phase of the 9 M. model is in many respects similar to, but differs importantly from that of a 10 M. model studied earlier. In both cases, carbon is ignited off center, and a series of carbon flashes accompanied by a convective shell occur. In contrast to the 10 M. model, the 9 M. model experiences the second dredge-up phenomenon (the penetration of the base of the hydrogen-rich convective envelope inward into helium-and carbon-rich material) near the beginning rather than near the end of the carbon-burning phase. The first carbon-burning flash causes helium burning to shut down and the release of gravothermal energy (compressional and thermal energy) between the helium-carbon discontinuity and the base of the convective envelope plays a dominant role in the dredge-up event. Beginning with the third carbon-burning shell flash, the ''flame front,'' defined as being coincident with the base of the convective shell, propagates inward with a speed close to theoretical predictions that relate flame speed to local thermodynamic, opacity, and energy-generation rate characteristics. Ahead of the inward moving front, most of the nuclear energy released in a ''precursor flame'' goes into heating and expanding matter. As the precursor flame moves toward the center, its radial thickness decreases and, to follow the progress of the front with standard techniques, both the spatial grid size and the time step must be continually decreased. Following the front gives one the opportunity to ponder Zeno's paradox, which is averted because the thickness of the precursor flame remains finite. On reaching the center, the carbon-burning flame reverses direction and continues moving outward until it is within similar to 0.03 M. of the helium-burning shell. After carbon burning is completed, C-12 remains at a finite abundance throughout the electron-degenerate core of mass similar to 1.116 M. and is more abundant than Ne-20 in the outer similar to 0.05 M. of this core. Over most of the ONe interior of both the 9 and 10 M. models, Na-23 is more abundant than Mg-24: but th, maximum C-12 abundance in the 9 M. model ONe interior (X[C-12] similar to 0.048) is significantly larger than in the 10 M. model (X[C-12] similar to 0.012). For an ONe white dwarf that accretes enough matter to reach the Chandrasekhar limiting mass, this may make the difference between total explosive disruption (large C-12 abundance) and collapse to neutron-star dimensions (small C-12 abundance). The abundances in the CO part of the core have relevance for understanding the abundances in the ejecta of classical novae produced by massive ONe white dwarfs in close binaries. In the outer similar to 0.014 M. of the CO part of the core, the abundances of all neon isotopes are much less than solar, and Mg-25 and the neutron-rich isotopes made during the formation of Mg-25 are at a total abundance equal to the initial abundance of CNO elements in the model. As in the 10 M. case, thermal pulses occasioned by helium shell flashes begin after hydrogen is reignited and the carbon-burning luminosity drops below similar to 100 L.. The time between pulses is similar to 400 yr, roughly twice as large as in the 10 M. model. After the ejection of the hydrogen-rich envelope as a planetary nebula, the remnant of the 9 M. model is expected to evolve into a white dwarf of mass similar to 1.15 M., the outer similar to 0.08 M. of which is composed of carbon and oxygen.