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Subsonic Burning Fronts (aka Flames)

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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.
Laminar Flame Speeds in Degenerate Oxygen-Neon Mixtures (Flames VI, 2020)
The collapse of degenerate oxygen-neon cores (i.e., electron-capture supernovae or accretion-induced collapse) proceeds through a phase in which a deflagration wave ("flame") forms at or near the center and propagates through the star. In models, the assumed speed of this flame influences whether this process leads to an explosion or to the formation of a neutron star.

In this article we calculate the laminar flame speeds in degenerate oxygen-neon mixtures with compositions motivated by detailed stellar evolution models. These mixtures include trace amounts of carbon and have a lower electron fraction than those considered in previous work. We find that trace carbon has little effect on the flame speeds, but that material with electron fraction Ye $\simeq$ 0.48-0.49 has laminar flame speeds that are 2 times faster than those at Ye=0.5. We provide tabulated flame speeds and a corresponding fitting function so that the impact of this difference can be assessed via full star hydrodynamical simulations of the collapse process.


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Turbulent Chemical Diffusion In Convectively Bounded Carbon Flames (Flames V, 2016)
It has been proposed that mixing induced by convective overshoot can disrupt the inward propagation of carbon deflagrations in super-asymptotic giant branch stars. To test this theory, in this article we study an idealized model of convectively bounded carbon flames with 3D hydrodynamic simulations of the Boussinesq equations using the pseudospectral code Dedalus.

Because the flame propagation timescale is is much longer than the convection timescale, we approximate the flame as fixed in space, and only consider its effects on the buoyancy of the fluid. By evolving a passive scalar field, we derive a turbulent chemical diffusivity produced by the convection as a function of height, $D_t(z)$. Convection can stall a flame if the chemical mixing timescale, set by the turbulent chemical diffusivity, $D_t$, is shorter than the flame propagation timescale, set by the thermal diffusivity, $\kappa$, i.e., when $D_t > \kappa$. However, we find $D_t < \kappa$ for most of the flame because convective plumes are not dense enough to penetrate into the flame. Extrapolating to realistic stellar conditions, this implies that convective mixing cannot stall a carbon flame and that ``hybrid carbon-oxygen-neon'' white dwarfs are not a typical product of stellar evolution.


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The Laminar Flame Speedup by 22Ne Enrichment in White Dwarf Supernovae (Flames IV, 2007)
Carbon-oxygen white dwarfs contain $^{22}$Ne formed from $\alpha$-captures onto 14N during core He burning in the progenitor star. In a white dwarf (Type Ia) supernova, the $^{22}$Ne abundance determines, in part, the neutron-to-proton ratio and hence the abundance of radioactive 56Ni that powers the light curve. The $^{22}$Ne abundance also changes the burning rate and hence the laminar flame speed. In this article we tabulate the flame speedup for different initial $^{12}$C and $^{22}$Ne abundances and for a range of densities. This increase in the laminar flame speed -- about 30% for a $^{22}$Ne mass fraction of 6% -- affects the deflagration just after ignition near the center of the white dwarf, where the laminar speed of the flame dominates over the buoyant rise, and in regions of lower density, $\simeq$ 10$^7$ g cm$^{-3}$ where a transition to distributed burning is conjectured to occur. The increase in flame speed will decrease the density of any transition to distributed burning.


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Physical Properties of Laminar Helium Deflagrations (Flames III, 2000)
The physical properties of laminar deflagrations propagating through helium-rich compositions are determined for a wide range of temperatures and densities in this article. The speeds, thermal widths, reactive widths, density contrasts, critical temperatures, and trigger masses are analyzed, along with their sensitivity to the input thermal transport coefficients, nuclear reaction rates, nuclear reaction network employed, and equation of state. A simple fitting formula of modest accuracy for the laminar flame speed is given, as well as detailed tables that list all of the physical properties. These physical properties may be incorporated into hydrodynamic programs as subgrid models for flame-tracking algorithms, and have applications toward models of X-ray bursts and the thin-shell helium flash of intermediate-mass stars.

I can't believe that I didn't publish the result that the final composition behind such flames is calcium, titanium, and chromium rich. Arrggh!


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The Conductive Propagation of Nuclear Flames. II. Convectively Bounded Flames in C+O and O+Ne+Mg Cores (Flames II, 1994)
In this article we determine the speeds, and many other physical properties, of flame fronts that propagate inward into degenerate and semidegenerate cores of carbon and oxygen (CO) and neon and oxygen (NeOMg) white dwarfs when such flames are bounded on their exterior by a convective region.

Combustion in such fronts, per se, is incomplete, with only a small part of the initial mass function burned. A condition of balanced power is set up in the star where the rate of energy emitted as neutrinos from the convective region equals the power available from the unburned fuel that crosses the burning front. The propagation of the burning front itself is in turn limited by the temperature at the base of the convective shell, while cannot greatly exceed the adiabatic value. Solving for consistency between these two conditions gives a unique speed for the flame. Typical values for CO white dwarfs are a few hundredths of a centimeter per second. Flames in NeOMg mixtures are slower. Tables are presented in a form that can easily be implemented in stellar evolution codes and yield the rate at which the convective shell advances into the interior. Combining these velocities with the local equations for stellar structure, we find a minimum density for each gravitational potential below with the local equations for stellar structure, we find a minimum density for each gravitational potential below which the flame cannot propagate, and must die.

Although detailed stellar models will have to be constructed to resolve some issues conclusively, our results that a CO white dwarf inginted at its edge will not burn carbon all the way to its center unless the mass of the white dwarf exceeds 0.8 M$_{\odot}$. On the other hand, it is difficult to ignite carbon burning by compression alone anywhere in a white dwarf whose mass does not exceed 1.0 M$_{\odot}$. Thus, compressionally ignited shell carbon burning in an accreting CO dwarf almost certainly propagates all the way to the center of the star. Implications for neutron star formation, and Type Ia supernova models, are briefly discussed. These are also applicable to massive stars in the about 10-12 M$_{\odot}$ range which ignite neon burning off center.


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The Conductive Propagation of Nuclear Flames. I. Degenerate C + O and O + NE + MG White Dwarfs (Flames I, 1992)
This article determines 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 for a grid of initial densities and compositions. 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 investigated. The occurrence of accretion-induced collapse of a white dwarf is found to be critically dependent on the velocity of the nuclear conductive burning front and the growth rate 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, it is found, for all reasonable values of the fractal dimension, that for initial C + O or O + Ne + Mg densities above about 9 $\times$ 10$^9$ c cm$^{-3}$ the white dwarf should collapse to a neutron star.


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