Asymmetry and the Nucleosynthetic Signature of Nearly Edge-Lit Detonation in White Dwarf Cores

Most of the leading explosion scenarios for Type Ia supernovae involve the nuclear incineration of a white dwarf star through a detonation wave. Several scenarios have been proposed as to how this detonation may actually occur, but the exact mechanism and environment in which it takes place remain unknown. We explore the effects of an off-center initiated detonation on the spatial distribution of the nucleosynthetic yield products in a toy model -- a pre-expanded near Chandrasekhar-mass white dwarf. We find that a single-point near edge-lit detonation results in asymmetries in the density and thermal profiles, notably the expansion timescale, throughout the supernova ejecta. We demonstrate that this asymmetry of the thermodynamic trajectories should be common to off-center detonations where a small amount of the star is burned prior to detonation. The sensitivity of the yields on the expansion timescale results in an asymmetric distribution of the elements synthesized as reaction products. We tabulate the shift in the center of mass of the various elements produced in our model supernova and find an odd-even pattern for elements past silicon. Our calculations show that off-center single-point detonations in carbon-oxygen white dwarfs are marked by significant composition asymmetries in their remnants which bear potentially observable signatures in both velocity and coordinate space, including an elemental nickel mass fraction which varies by a factor of two to three from one side of the remnant to the other.Comment: 7 pages, 7 figures, accepted for publication in the Astrophysical Journa

Effects of magnetic fields on the propagation of nuclear flames in magnetic white dwarfs

We investigate effects of the magnetic field on the propagation of laminar flames of nuclear reactions taking place in white dwarfs (WDs) with the mass close to the Chandrasekhar limit. We calculate the velocities of laminar flames parallel and perpendicular to uniform magnetic fields as eigenvalues of steady solutions for magnetic hydrodynamical equations. As a result, we find that even when the magnetic pressure does not dominate the entire pressure it is possible for the magnetic field to suppress the flame propagation through the thermal conduction. Above the critical magnetic field, the flame velocity decreases with increasing magnetic field strength as $v \sim B^{-1}$. In media with densities of 10^{7}, 10^{8}, \,\mathrm{and}\,10^{9} \unit{g\,cm^{-3}}, the critical magnetic fields are orders of \sim 10^{10}, 10^{11}, \,\mathrm{and}\,10^{12} \unit{G}, respectively.Comment: 9 pages, 8 figures, 1 tables, to appear in Ap

Evaluating Systematic Dependencies of Type Ia Supernovae: The Influence of Deflagration to Detonation Density

We explore the effects of the deflagration to detonation transition (DDT) density on the production of Ni-56 in thermonuclear supernova explosions (type Ia supernovae). Within the DDT paradigm, the transition density sets the amount of expansion during the deflagration phase of the explosion and therefore the amount of nuclear statistical equilibrium (NSE) material produced. We employ a theoretical framework for a well-controlled statistical study of two-dimensional simulations of thermonuclear supernovae with randomized initial conditions that can, with a particular choice of transition density, produce a similar average and range of Ni-56 masses to those inferred from observations. Within this framework, we utilize a more realistic "simmered" white dwarf progenitor model with a flame model and energetics scheme to calculate the amount of Ni-56 and NSE material synthesized for a suite of simulated explosions in which the transition density is varied in the range 1-3x10^7 g/cc. We find a quadratic dependence of the NSE yield on the log of the transition density, which is determined by the competition between plume rise and stellar expansion. By considering the effect of metallicity on the transition density, we find the NSE yield decreases by 0.055 +/- 0.004 solar masses for a 1 solar metallicity increase evaluated about solar metallicity. For the same change in metallicity, this result translates to a 0.067 +/- 0.004 solar mass decrease in the Ni-56 yield, slightly stronger than that due to the variation in electron fraction from the initial composition. Observations testing the dependence of the yield on metallicity remain somewhat ambiguous, but the dependence we find is comparable to that inferred from some studies.Comment: 15 pages, 13 figures, accepted to ApJ on July 6, 201

On Silicon Group Elements Ejected by Supernovae Type Ia

There is compelling evidence that the peak brightness of a Type Ia supernova is affected by the electron fraction Ye at the time of the explosion. The electron fraction is set by the aboriginal composition of the white dwarf and the reactions that occur during the pre explosive convective burning. To date, determining the makeup of the white dwarf progenitor has relied on indirect proxies, such as the average metallicity of the host stellar population. In this paper, we present analytical calculations supporting the idea that the electron fraction of the progenitor systematically influences the nucleosynthesis of silicon group ejecta in Type Ia supernovae. In particular, we suggest the abundances generated in quasi nuclear statistical equilibrium are preserved during the subsequent freezeout. This allows one to potential recovery of Ye at explosion from the abundances recovered from an observed spectra. We show that measurement of 28Si, 32S, 40Ca, and 54Fe abundances can be used to construct Ye in the silicon rich regions of the supernovae. If these four abundances are determined exactly, they are sufficient to recover Ye to 6 percent. This is because these isotopes dominate the composition of silicon-rich material and iron rich material in quasi nuclear statistical equilibrium. Analytical analysis shows that the 28Si abundance is insensitive to Ye, the 32S abundance has a nearly linear trend with Ye, and the 40Ca abundance has a nearly quadratic trend with Ye. We verify these trends with post-processing of 1D models and show that these trends are reflected in model synthetic spectra.Comment: Submitted to the Ap

The Laminar Flame Speedup by Neon-22 Enrichment in White Dwarf Supernovae

Carbon-oxygen white dwarfs contain neon-22 formed from alpha-captures onto nitrogen during core He burning in the progenitor star. In a white dwarf (type Ia) supernova, the neon-22 abundance determines, in part, the neutron-to-proton ratio and hence the abundance of radioactive nickel-56 that powers the lightcurve. The neon-22 abundance also changes the burning rate and hence the laminar flame speed. We tabulate the flame speedup for different initial carbon and neon-22 abundances and for a range of densities. This increase in the laminar flame speed--about 30% for a neon-22 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 ~ 10^7 g/cm3 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.Comment: 5 pages, 2 figures, to be published in ApJ Letters. Table 2 is avalible from http://www.pa.msu.edu/~ebrown/Research/typeIa

MAESTRO: An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows

Many astrophysical phenomena are highly subsonic, requiring specialized numerical methods suitable for long-time integration. In a series of earlier papers we described the development of MAESTRO, a low Mach number stellar hydrodynamics code that can be used to simulate long-time, low-speed flows that would be prohibitively expensive to model using traditional compressible codes. MAESTRO is based on an equation set derived using low Mach number asymptotics; this equation set does not explicitly track acoustic waves and thus allows a significant increase in the time step. MAESTRO is suitable for two- and three-dimensional local atmospheric flows as well as three-dimensional full-star flows. Here, we continue the development of MAESTRO by incorporating adaptive mesh refinement (AMR). The primary difference between MAESTRO and other structured grid AMR approaches for incompressible and low Mach number flows is the presence of the time-dependent base state, whose evolution is coupled to the evolution of the full solution. We also describe how to incorporate the expansion of the base state for full-star flows, which involves a novel mapping technique between the one-dimensional base state and the Cartesian grid, as well as a number of overall improvements to the algorithm. We examine the efficiency and accuracy of our adaptive code, and demonstrate that it is suitable for further study of our initial scientific application, the convective phase of Type Ia supernovae.Comment: Accepted to Astrophysical Journal Suppliment (http://iop.org). 56 pages, 15 figures

The Reduction of the Electron Abundance during the Pre-explosion Simmering in White Dwarf Supernovae

Prior to the explosion of a carbon-oxygen white dwarf in a Type Ia supernova there is a long "simmering," during which the 12C + 12C reaction gradually heats the white dwarf on a long (~ 1000 yr) timescale. Piro & Bildsten showed that weak reactions during this simmering set a maximum electron abundance Ye at the time of the explosion. We investigate the nuclear reactions during this simmering with a series of self-heating, at constant pressure, reaction network calculations. Unlike in AGB stars, proton captures onto 22Ne and heavier trace nuclei do not play a significant role. The 12C abundance is sufficiently high that the neutrons preferentially capture onto 12C, rather than iron group nuclei. As an aid to hydrodynamical simulations of the simmering phase, we present fits to the rates of heating, electron capture, change in mean atomic mass, and consumption of 12C in terms of the screened thermally averaged cross section for 12C + 12C. Our evaluation of the net heating rate includes contributions from electron captures into the 3.68 MeV excited state of 13C. This results in a slightly larger energy release, per 12C consumed, than that found by Piro & Bildsten, but less than that released for a burn to only 20Ne and 23Na. We compare our one-zone results to more accurate integrations over the white dwarf structure to estimate the amount of 12C that must be consumed to raise the white dwarf temperature, and hence to determine the net reduction of Ye during simmering.Comment: Accepted for publication in The Astrophysical Journal, 9 pages, 6 figure

Study of the Detonation Phase in the Gravitationally Confined Detonation Model of Type Ia Supernovae

We study the gravitationally confined detonation (GCD) model of Type Ia supernovae through the detonation phase and into homologous expansion. In the GCD model, a detonation is triggered by the surface flow due to single point, off-center flame ignition in carbon-oxygen white dwarfs. The simulations are unique in terms of the degree to which non-idealized physics is used to treat the reactive flow, including weak reaction rates and a time dependent treatment of material in nuclear statistical equilibrium (NSE). Careful attention is paid to accurately calculating the final composition of material which is burned to NSE and frozen out in the rapid expansion following the passage of a detonation wave over the high density core of the white dwarf; and an efficient method for nucleosynthesis post-processing is developed which obviates the need for costly network calculations along tracer particle thermodynamic trajectories. Observational diagnostics are presented for the explosion models, including abundance stratifications and integrated yields. We find that for all of the ignition conditions studied here, a self regulating process comprised of neutronization and stellar expansion results in final \iso{Ni}{56} masses of $\sim$1.1\msun. But, more energetic models result in larger total NSE and stable Fe peak yields. The total yield of intermediate mass elements is $\sim0.1$\msun and the explosion energies are all around 1.5$\times10^{51}$ ergs. The explosion models are briefly compared to the inferred properties of recent Type Ia supernova observations. The potential for surface detonation models to produce lower luminosity (lower \iso{Ni}{56} mass) supernovae is discussed.Comment: 43 pages, 4 tables, 20 figures -- submitted to Ap