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Lars Bildsten - One of the best experts on this subject based on the ideXlab platform.
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a new class of large amplitude radial mode hot subdwarf pulsators
The Astrophysical Journal, 2019Co-Authors: T Kupfer, Evan B Bauer, Kevin B Burdge, Eric C Bellm, Lars Bildsten, Jim Fuller, J J Hermes, S R Kulkarni, Thomas A PrinceAbstract:Using high-cadence observations from the Zwicky Transient Facility at low Galactic latitudes, we have discovered a new class of pulsating, hot compact stars. We have found four candidates, exhibiting blue colors (g − r ≤ −0.1 mag), pulsation amplitudes of >5%, and pulsation periods of 200–475 s. Fourier transforms of the light curves show only one dominant frequency. Phase-resolved spectroscopy for three objects reveals significant radial velocity, T_(eff), and log(g) variations over the pulsation cycle, which are consistent with large-amplitude radial oscillations. The mean T_(eff) and log(g) for these stars are consistent with hot subdwarf B (sdB) effective temperatures and surface gravities. We calculate evolutionary tracks using MESA and adiabatic pulsations using GYRE for low-mass, Helium-core pre-white dwarfs (pre-WDs) and low-mass Helium-Burning stars. Comparison of low-order radial oscillation mode periods with the observed pulsation periods show better agreement with the pre-WD models. Therefore, we suggest that these new pulsators and blue large-amplitude pulsators (BLAPs) could be members of the same class of pulsators, composed of young ≈0.25–0.35 M_⊙ Helium-core pre-WDs.
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modules for experiments in stellar astrophysics mesa pulsating variable stars rotation convective boundaries and energy conservation
arXiv: Solar and Stellar Astrophysics, 2019Co-Authors: Bill Paxton, Lars Bildsten, Matteo Cantiello, Josiah Schwab, R Farmer, R Smolec, A Gautschy, Aaron Dotter, Jared A GoldbergAbstract:We update the capabilities of the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). RSP is a new functionality in MESAstar that models the non-linear radial stellar pulsations that characterize RR Lyrae, Cepheids, and other classes of variable stars. We significantly enhance numerical energy conservation capabilities, including during mass changes. For example, this enables calculations through the He flash that conserve energy to better than 0.001 %. To improve the modeling of rotating stars in MESA, we introduce a new approach to modifying the pressure and temperature equations of stellar structure, and a formulation of the projection effects of gravity darkening. A new scheme for tracking convective boundaries yields reliable values of the convective-core mass, and allows the natural emergence of adiabatic semiconvection regions during both core hydrogen- and Helium-Burning phases. We quantify the parallel performance of MESA on current generation multicore architectures and demonstrate improvements in the computational efficiency of radiative levitation. We report updates to the equation of state and nuclear reaction physics modules. We briefly discuss the current treatment of fallback in core-collapse supernova models and the thermodynamic evolution of supernova explosions. We close by discussing the new MESA Testhub software infrastructure to enhance source-code development.
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modules for experiments in stellar astrophysics mesa convective boundaries element diffusion and massive star explosions
Astrophysical Journal Supplement Series, 2018Co-Authors: Bill Paxton, Evan B Bauer, Lars Bildsten, Josiah Schwab, S I Blinnikov, Paul C Duffell, R FarmerAbstract:We update the capabilities of the software instrument Modules for Experiments in Stellar Astrophysics (MESA) and enhance its ease of use and availability. Our new approach to locating convective boundaries is consistent with the physics of convection, and yields reliable values of the convective-core mass during both hydrogen- and Helium-Burning phases. Stars with become white dwarfs and cool to the point where the electrons are degenerate and the ions are strongly coupled, a realm now available to study with MESA due to improved treatments of element diffusion, latent heat release, and blending of equations of state. Studies of the final fates of massive stars are extended in MESA by our addition of an approximate Riemann solver that captures shocks and conserves energy to high accuracy during dynamic epochs. We also introduce a 1D capability for modeling the effects of Rayleigh–Taylor instabilities that, in combination with the coupling to a public version of the radiation transfer instrument, creates new avenues for exploring Type II supernova properties. These capabilities are exhibited with exploratory models of pair-instability supernovae, pulsational pair-instability supernovae, and the formation of stellar-mass black holes. The applicability of MESA is now widened by the capability to import multidimensional hydrodynamic models into MESA. We close by introducing software modules for handling floating point exceptions and stellar model optimization, as well as four new software tools— , -Docker, , and mesastar.org—to enhance MESA's education and research impact.
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angular momentum transport within evolved low mass stars
The Astrophysical Journal, 2014Co-Authors: Matteo Cantiello, Lars Bildsten, Christopher Mankovich, J Christensendalsgaard, Bill PaxtonAbstract:Asteroseismology of 1.0-2.0 M {sub ☉} red giants by the Kepler satellite has enabled the first definitive measurements of interior rotation in both first ascent red giant branch (RGB) stars and those on the Helium Burning clump. The inferred rotation rates are 10-30 days for the ≈0.2 M {sub ☉} He degenerate cores on the RGB and 30-100 days for the He Burning core in a clump star. Using the Modules for Experiments in Stellar Evolution code, we calculate state-of-the-art stellar evolution models of low mass rotating stars from the zero-age main sequence to the cooling white dwarf (WD) stage. We include transport of angular momentum due to rotationally induced instabilities and circulations, as well as magnetic fields in radiative zones (generated by the Tayler-Spruit dynamo). We find that all models fail to predict core rotation as slow as observed on the RGB and during core He Burning, implying that an unmodeled angular momentum transport process must be operating on the early RGB of low mass stars. Later evolution of the star from the He Burning clump to the cooling WD phase appears to be at nearly constant core angular momentum. We also incorporate the adiabatic pulsation code, ADIPLS, tomore » explicitly highlight this shortfall when applied to a specific Kepler asteroseismic target, KIC8366239.« less
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angular momentum transport within evolved low mass stars
arXiv: Solar and Stellar Astrophysics, 2014Co-Authors: Matteo Cantiello, Lars Bildsten, Christopher Mankovich, J Christensendalsgaard, Bill PaxtonAbstract:Asteroseismology of 1.0-2.0 Msun red giants by the Kepler satellite has enabled the first definitive measurements of interior rotation in both first ascent red giant branch (RGB) stars and those on the Helium Burning clump. The inferred rotation rates are 10-30 days for the ~0.2Msun He degenerate cores on the RGB and 30-100 days for the He Burning core in a clump star. Using the MESA code we calculate state-of-the-art stellar evolution models of low mass rotating stars from the zero-age main sequence to the cooling white dwarf (WD) stage. We include transport of angular momentum due to rotationally induced instabilities and circulations, as well as magnetic fields in radiative zones (generated by the Tayler-Spruit dynamo). We find that all models fail to predict core rotation as slow as observed on the RGB and during core He Burning, implying that an unmodeled angular momentum transport process must be operating on the early RGB of low mass stars. Later evolution of the star from the He Burning clump to the cooling WD phase appears to be at nearly constant core angular momentum. We also incorporate the adiabatic pulsation code, ADIPLS, to explicitly highlight this shortfall when applied to a specific Kepler asteroseismic target, KIC8366239. The MESA inlist adopted to calculate the models in this paper can be found at \url{this https URL} (bottom of the document).
Miguel Aguilar - One of the best experts on this subject based on the ideXlab platform.
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variability in the massive open cluster ngc 1817 from k2 a rich population of asteroseismic red clump eclipsing binary and main sequence pulsating stars
The Astronomical Journal, 2020Co-Authors: Eric L Sandquist, D Stello, T Arentoft, Karsten Brogaard, F Grundahl, Andrew Vanderburg, Anne Hedlund, Ryan Dewitt, Taylor R Ackerman, Miguel AguilarAbstract:: We present a survey of variable stars detected in K2 Campaign 13 within the massive intermediate-age (~1 Gyr) open cluster NGC 1817. We identify a complete sample of 44 red clump stars in the cluster, and have measured asteroseismic quantities (νmax and/or Δν) for 29 of them. Five stars showed suppressed dipole modes, and the occurrence rates indicate that mode suppression is unaffected by evolution through core Helium Burning. A subset of the giants in NGC 1817 (and in the similarly aged cluster NGC 6811) have νmax and Δν values at or near the maximum observed for core Helium-Burning stars, indicating they have core masses near the minimum for fully nondegenerate Helium ignition. Further asteroseismic study of these stars can constrain the minimum Helium core mass in red clump stars and the physics that determines this limit. Two giant stars show photometric variations on timescales similar to previously measured spectroscopic orbits. Thirteen systems in the field show eclipses, but only five are probable cluster members. We identify 32 δ Sct pulsators, 27 γ Dor candidates, and 7 hybrids that are probable cluster members, with most being new detections. We used the ensemble properties of the δ Sct stars to identify stars with possible radial pulsation modes. Among the oddities we have uncovered are: an eccentric orbit for a short-period binary containing a δ Sct pulsating star; a rare subgiant within the Hertzsprung gap showing δ Sct pulsations; and two hot γ Dor pulsating star candidates.
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variability in the massive open cluster ngc 1817 from k2 a rich population of asteroseismic red clump eclipsing binary and main sequence pulsating stars
arXiv: Solar and Stellar Astrophysics, 2020Co-Authors: Eric L Sandquist, D Stello, T Arentoft, Karsten Brogaard, F Grundahl, Andrew Vanderburg, Anne Hedlund, Ryan Dewitt, Taylor R Ackerman, Miguel AguilarAbstract:We present a survey of variable stars detected in K2 Campaign 13 within the massive intermediate age ($\sim1$ Gyr) open cluster NGC 1817. We identify a complete sample of 44 red clump stars in the cluster, and have measured asteroseismic quantities ($\nu_{\rm max}$ and/or $\Delta \nu$) for 29 of them. Five stars showed suppressed dipole modes, and the occurrence rates indicate that mode suppression is unaffected by evolution through core Helium Burning. A subset of the giants in NGC 1817 (and in the similarly aged cluster NGC 6811) have $\nu_{\rm max}$ and $\Delta \nu$ values at or near the maximum observed for core Helium Burning stars, indicating they have core masses near the minimum for fully non-degenerate Helium ignition. Further asteroseismic study of these stars can constrain the minimum Helium core mass in red clump stars and the physics that determines this limit. Two giant stars show photometric variations on timescales similar to previously measured spectroscopic orbits. Thirteen systems in the field show eclipses, but only five are probable cluster members. We identify 32 $\delta$ Sct pulsators, 27 $\gamma$ Dor candidates, and 7 hybrids that are probable cluster members, with most new detections. We used the ensemble properties of the $\delta$ Sct stars to identify stars with possible radial pulsation modes. Among the oddities we have uncovered are: an eccentric orbit for a short-period binary containing a $\delta$ Sct pulsating star; a rare subgiant within the Hertzsprung gap showing $\delta$ Sct pulsations; and two hot $\gamma$ Dor pulsating star candidates.
J Christensendalsgaard - One of the best experts on this subject based on the ideXlab platform.
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the treatment of mixing in core Helium Burning models i implications for asteroseismology
arXiv: Solar and Stellar Astrophysics, 2015Co-Authors: T Constantino, J Christensendalsgaard, Simon Campbell, John C Lattanzio, Dennis StelloAbstract:The detection of mixed oscillation modes offers a unique insight into the internal structure of core Helium Burning (CHeB) stars. The stellar structure during CHeB is very uncertain because the growth of the convective core, and/or the development of a semiconvection zone, is critically dependent on the treatment of convective boundaries. In this study we calculate a suite of stellar structure models and their non-radial pulsations to investigate why the predicted asymptotic g-mode $\ell = 1$ period spacing $\Delta\Pi_1$ is systematically lower than is inferred from Kepler field stars. We find that only models with large convective cores, such as those calculated with our newly proposed "maximal-overshoot" scheme, can match the average $\Delta\Pi_1$ reported. However, we also find another possible solution that is related to the method used to determine $\Delta\Pi_1$: mode trapping can raise the observationally inferred $\Delta\Pi_1$ well above its true value. Even after accounting for these two proposed resolutions to the discrepancy in average $\Delta\Pi_1$, models still predict more CHeB stars with low $\Delta\Pi_1$ ($ < 270$ s) than are observed. We establish two possible remedies for this: i) there may be a difficulty in determining $\Delta\Pi_1$ for early CHeB stars (when $\Delta\Pi_1$ is lowest) because of the effect that the sharp composition profile at the hydrogen Burning shell has on the pulsations, or ii) the mass of the Helium core at the flash is higher than predicted. Our conclusions highlight the need for the reporting of selection effects in asteroseismic population studies in order to safely use this information to constrain stellar evolution theory.
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on the asymptotic acoustic mode phase in red giant stars and its dependence on evolutionary state
Monthly Notices of the Royal Astronomical Society, 2014Co-Authors: J Christensendalsgaard, Y. Elsworth, Victor Silva Aguirre, Saskia HekkerAbstract:Asteroseismic investigations based on the wealth of data now available,in particular from the CoRoT and Kepler missions, require a good understanding of the relation between the observed quantities and the properties of the underlying stellar structure. Kallinger et al. 2012 found a relation between their determination of the asymptotic phase of radial oscillations in evolved stars and the evolutionary state, separating ascending-branch red giants from Helium-Burning stars in the `red clump'. Here we provide a detailed analysis of this relation, which is found to derive from differences between these two classes of stars in the thermodynamic state of the convective envelope. There is potential for distinguishing red giants and clump stars based on the phase determined from observations that are too short to allow distinction based on determination of the period spacing for mixed modes. The analysis of the phase may also point to a better understanding of the potential for using the Helium-ionization-induced acoustic glitch to determine the Helium abundance in the envelopes of these stars.
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angular momentum transport within evolved low mass stars
The Astrophysical Journal, 2014Co-Authors: Matteo Cantiello, Lars Bildsten, Christopher Mankovich, J Christensendalsgaard, Bill PaxtonAbstract:Asteroseismology of 1.0-2.0 M {sub ☉} red giants by the Kepler satellite has enabled the first definitive measurements of interior rotation in both first ascent red giant branch (RGB) stars and those on the Helium Burning clump. The inferred rotation rates are 10-30 days for the ≈0.2 M {sub ☉} He degenerate cores on the RGB and 30-100 days for the He Burning core in a clump star. Using the Modules for Experiments in Stellar Evolution code, we calculate state-of-the-art stellar evolution models of low mass rotating stars from the zero-age main sequence to the cooling white dwarf (WD) stage. We include transport of angular momentum due to rotationally induced instabilities and circulations, as well as magnetic fields in radiative zones (generated by the Tayler-Spruit dynamo). We find that all models fail to predict core rotation as slow as observed on the RGB and during core He Burning, implying that an unmodeled angular momentum transport process must be operating on the early RGB of low mass stars. Later evolution of the star from the He Burning clump to the cooling WD phase appears to be at nearly constant core angular momentum. We also incorporate the adiabatic pulsation code, ADIPLS, tomore » explicitly highlight this shortfall when applied to a specific Kepler asteroseismic target, KIC8366239.« less
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angular momentum transport within evolved low mass stars
arXiv: Solar and Stellar Astrophysics, 2014Co-Authors: Matteo Cantiello, Lars Bildsten, Christopher Mankovich, J Christensendalsgaard, Bill PaxtonAbstract:Asteroseismology of 1.0-2.0 Msun red giants by the Kepler satellite has enabled the first definitive measurements of interior rotation in both first ascent red giant branch (RGB) stars and those on the Helium Burning clump. The inferred rotation rates are 10-30 days for the ~0.2Msun He degenerate cores on the RGB and 30-100 days for the He Burning core in a clump star. Using the MESA code we calculate state-of-the-art stellar evolution models of low mass rotating stars from the zero-age main sequence to the cooling white dwarf (WD) stage. We include transport of angular momentum due to rotationally induced instabilities and circulations, as well as magnetic fields in radiative zones (generated by the Tayler-Spruit dynamo). We find that all models fail to predict core rotation as slow as observed on the RGB and during core He Burning, implying that an unmodeled angular momentum transport process must be operating on the early RGB of low mass stars. Later evolution of the star from the He Burning clump to the cooling WD phase appears to be at nearly constant core angular momentum. We also incorporate the adiabatic pulsation code, ADIPLS, to explicitly highlight this shortfall when applied to a specific Kepler asteroseismic target, KIC8366239. The MESA inlist adopted to calculate the models in this paper can be found at \url{this https URL} (bottom of the document).
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gravity modes as a way to distinguish between hydrogen and Helium Burning red giant stars
Nature, 2011Co-Authors: T R Bedding, B Mosser, J Christensendalsgaard, Daniel Huber, J Montalban, P G Beck, Yvonne Elsworth, R A Garcia, A Miglio, Dennis StelloAbstract:Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell1, 2. Once a red giant is sufficiently evolved, the Helium in the core also undergoes fusion3. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before Helium ignition and the amount of internal mixing from rotation and other processes4. Progress is hampered by our inability to distinguish between red giants Burning Helium in the core and those still only Burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies5. Here we report observations of gravity-mode period spacings in red giants6 that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained by the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-Burning stars (period spacing mostly ~50 seconds) and those that are also Burning Helium (period spacing ~100 to 300 seconds).
L Stella - One of the best experts on this subject based on the ideXlab platform.
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the x ray spectrum of the bursting atoll source 4u 1728 34 observed with integral
Astronomy and Astrophysics, 2006Co-Authors: M Falanga, D Gotz, P Goldoni, R Farinelli, A Goldwurm, S Mereghetti, A Bazzano, L StellaAbstract:We present for the first time a study of the 3–200 keV broad band spectra of the bursting atoll source 4U 1728-34 (GX 354-0) along its hardness intensity diagram. The analysis was done using the INTEGRAL public and Galactic Center deep exposure data ranging from February 2003 to October 2004. The spectra are well described by a thermal Comptonization model with an electron temperature from 35 keV to 3 keV and Thomson optical depth, τT, from 0.5 to 5 in a slab geometry. The source undergoes a transition from an intermediate/hard to a soft state where the source luminosity increases from 2 to 12% of Eddington. We have also detected 36 type I X-ray bursts two of which show photospheric radius expansion. The energetic bursts with photospheric radius expansion occurred at an inferred low mass accretion rate per unit area of u m ∼ 1.7 × 10 3 gc m −2 s −1 , while the others at a higher one between 2.4 × 10 3 −9.4 × 10 3 gm −2 s −1 . For 4U 1728-34 the bursts’ total fluence, and the bursts’ peak flux are anti-correlated with the mass accretion rate. The type I X-ray bursts involve pure Helium Burning either during the hard state, or during the soft state of the source.
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the x ray spectrum of the bursting atoll source 4u 1728 34 observed with integral
arXiv: Astrophysics, 2006Co-Authors: M Falanga, D Gotz, P Goldoni, R Farinelli, A Goldwurm, S Mereghetti, A Bazzano, L StellaAbstract:We present for the first time a study of the 3-200 keV broad band spectra of the bursting atoll source 4U 1728-34 (GX 354-0) along its hardness intensity diagram. The analysis was done using the INTEGRAL public and Galactic Center deep exposure data ranging from February 2003 to October 2004. The spectra are well described by a thermal Comptonization model with an electron temperature from 35 keV to 3 keV and Thomson optical depth, tau_T, from 0.5 to 5 in a slab geometry. The source undergoes a transition from an intermediate/hard to a soft state where the source luminosity increases from 2 to 12% of Eddington. We have also detected 36 type I X-ray bursts two of which show photospheric radius expansion. The energetic bursts with photospheric radius expansion occurred at an inferred low mass accretion rate per unit area of \dot m ~ 1.7x10E3 g/cm2/s, while the others at a higher one between 2.4x10E3 - 9.4x10E3 g/cm2/s. For 4U1728-34 the bursts' total fluence, and the bursts' peak flux are anti-correlated with the mass accretion rate. The type I X-ray bursts involve pure Helium Burning either during the hard state, or during the soft state of the source.
Claudio Ritossa - One of the best experts on this subject based on the ideXlab platform.
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on the evolution of stars that form electron degenerate cores processed by carbon Burning v shell convection sustained by Helium Burning transient neon Burning dredge out urca cooling and other properties of an 11 m population i model star
The Astrophysical Journal, 1999Co-Authors: Claudio Ritossa, E Garciaberro, Icko IbenAbstract:A stellar model of mass 11 M☉ and Population I composition is evolved from the hydrogen-Burning main sequence through the core carbon-Burning phase. In contrast with 9, 10, and 10.5 M☉ models studied in earlier papers of this series, carbon Burning is ignited at the center of the 11 M☉ model. Like the 10.5 M☉ model, the 11 M☉ model experiences a dredge-out episode at the end of the carbon-Burning phase. At the beginning of this episode, a semiconvective zone forms at the base of the hydrogen-rich envelope and carries hydrogen inward in mass toward the outer edge of a fully convective zone that is sustained by Helium Burning at its base. Hydrogen diffuses into the Helium-rich convective zone untila hydrogen shell flash occurs. Helium Burning dies out and the outer edge of the convective layer,sustained by fluxes due to hydrogen Burning, extends outward in mass through hydrogen-rich material, mixing freshly synthesized nuclei outward. Then, hydrogen Burning dies out and the outer edge of the convective shell, now sustained primarily by fluxes due to the release of gravothermal energy, moves outward until it reaches the inner edge of the convective envelope. Freshly synthesized material is then convected to the surface. Mixing during the final phase of homogenization in the convective envelope is maintained by fluxes due to the release of gravothermal energy. At the end of the dredge-out phase, the surface nitrogen abundance has decreased and the C/N ratio has changed from less than unity to larger than unity, showing that mixing has extended into regions where Helium Burning has manufactured substantial quantities of 12C and destroyed 14N. Prior to the dredge-out phase, neon Burning is narrowly averted, and, after the dredge-out phase, neutrino losses due to electron capture and decay reactions between A=25 and A=23 isotopes in and above convective Urca shells cool the inner portions of the electron-degenerate oxygen-neon (ONe) core. Ultimately, the model becomes a thermally pulsing super-asymptotic giant branch (TPSAGB) star with an ONe core of mass ~1.368 M☉. Hydrogen and Helium Burning over a period of ~1.4×104 yr of TPSAGB evolution add a carbon-oxygen layer of mass ~0.014 M☉ to the electron-degenerate core. Then, electron captures on products of carbon Burning lead to the collapse of the core into a neutron star and expulsion of the envelope in a weak Type II supernova explosion. The ratio of Helium to hydrogen in the ejecta is approximately twice solar.
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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
The Astrophysical Journal, 1997Co-Authors: E Garciaberro, Claudio Ritossa, Icko IbenAbstract: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.