On the Evolution of Stars that Form Electron-Degenerate Cores Processed by Carbon Burning. III. The Inward Propagation of a Carbon-Burning Flame and Other Properties of a 9 M_☉ 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 ~1.066 M_☉ and an outer carbon-oxygen (CO) layer of mass ~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 ~0.03 M_☉ of the helium-burning shell. After carbon burning is completed,¹²C remains at a finite abundance throughout the electron-degenerate core of mass ~1.116 M_☉ and is more abundant than ²⁰Ne in the outer ~0.05 M_☉ of this core. Over most of the ONe interior of both the 9 and 10 M_☉ models,²³Na is more abundant than ²⁴Mg, but the maximum ¹²C abundance in the 9 M_☉ model ONe interior (X[¹²C] ~ 0.048) is significantly larger than in the 10 M_☉ model (X[¹²C] ~ 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 ¹²C abundance) and collapse to neutron-star dimensions (small ¹²C 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 ~0.014 M_☉ of the CO part of the core, the abundances of all neon isotopes are much less than solar, and ²⁵Mg and the neutron-rich isotopes made during the formation of ²⁵Mg 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 ~100 L_☉. The time between pulses is ~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 ~1.15 M_☉, the outer ~0.08 M_☉ of which is composed of carbon and oxygen.