The Cellular Burning Regime in Type Ia Supernova Explosions - I. Flame Propagation into Quiescent Fuel

We present a numerical investigation of the cellular burning regime in Type Ia supernova explosions. This regime holds at small scales (i.e. below the Gibson scale), which are unresolved in large-scale Type Ia supernova simulations. The fundamental effects that dominate the flame evolution here are the Landau-Darrieus instability and its nonlinear stabilization, leading to a stabilization of the flame in a cellular shape. The flame propagation into quiescent fuel is investigated addressing the dependence of the simulation results on the specific parameters of the numerical setup. Furthermore, we investigate the flame stability at a range of fuel densities. This is directly connected to the questions of active turbulent combustion (a mechanism of flame destabilization and subsequent self-turbulization) and a deflagration-to-detonation transition of the flame. In our simulations we find no substantial destabilization of the flame when propagating into quiescent fuels of densities down to ~10^7 g/cm^3, corroborating fundamental assumptions of large-scale SN Ia explosion models. For these models, however, we suggest an increased lower cutoff for the flame propagation velocity to take the cellular burning regime into account.Comment: 12 pages, 2 tables, 10 figures, resolution of figures degraded due to archive file size restrictions, submitted to A&

A localised subgrid scale model for fluid dynamical simulations in astrophysics II: Application to type Ia supernovae

The dynamics of the explosive burning process is highly sensitive to the flame speed model in numerical simulations of type Ia supernovae. Based upon the hypothesis that the effective flame speed is determined by the unresolved turbulent velocity fluctuations, we employ a new subgrid scale model which includes a localised treatment of the energy transfer through the turbulence cascade in combination with semi-statistical closures for the dissipation and non-local transport of turbulence energy. In addition, subgrid scale buoyancy effects are included. In the limit of negligible energy transfer and transport, the dynamical model reduces to the Sharp-Wheeler relation. According to our findings, the Sharp-Wheeler relation is insuffcient to account for the complicated turbulent dynamics of flames in thermonuclear supernovae. The application of a co-moving grid technique enables us to achieve very high spatial resolution in the burning region. Turbulence is produced mostly at the flame surface and in the interior ash regions. Consequently, there is a pronounced anisotropy in the vicinity of the flame fronts. The localised subgrid scale model predicts significantly enhanced energy generation and less unburnt carbon and oxygen at low velocities compared to earlier simulations.Comment: 13 pages, 10 figures, accepted for publication in Astron. Astrophys.; 3D visualisations not included; complete PDF version can be downloaded from http://www.astro.uni-wuerzburg.de/%7Eschmidt/Paper/SGSModel_II_AA.pd

Following multi-dimensional Type Ia supernova explosion models to homologous expansion

The last years have witnessed a rapid development of three-dimensional models of Type Ia supernova explosions. Consequently, the next step is to evaluate these models under variation of the initial parameters and to compare them with observations. To calculate synthetic lightcurves and spectra from numerical models, it is mandatory to follow the evolution up to homologous expansion. We report on methods to achieve this in our current implementation of multi-dimensional Type Ia supernova explosion models. The novel scheme is thoroughly tested in two dimensions and a simple example of a three-dimensional simulation is presented. We discuss to what degree the assumption of homologous expansion is justified in these models.Comment: 15 pages, 16 figures, resolution of some figures reduced to meet astro-ph file size restriction, submitted to A&

Full-star Type Ia supernova explosion models

We present full-star simulations of Type Ia supernova explosions on the basis of the standard Chandrasekhar-mass deflagration model. Most simulations so far considered only one spatial octant and assumed mirror symmetry to the other octants. Two full-star models are evolved to homologous expansion and compared with previous single-octant simulations. Therefrom we analyze the effect of abolishing the artificial symmetry constraint on the evolution of the flame surface. It turns out that the development of asymmetries depends on the chosen initial flame configuration. Such asymmetries of the explosion process could possibly contribute to the observed polarization of some Type Ia supernova spectra.Comment: 11 pages, 10 figures, resolution of some figures reduced to meet astro-ph file size restriction, submitted to A&

On the Stability of Thermonuclear Burning Fronts in Type Ia Supernovae

The propagation of cellularly stabilized thermonuclear flames is investigated by means of numerical simulations. In Type Ia supernova explosions the corresponding burning regime establishes at scales below the Gibson length. The cellular flame stabilization - which is a result of an interplay between the Landau-Darrieus instability and a nonlinear stabilization mechanism - is studied for the case of propagation into quiescent fuel as well as interaction with vortical fuel flows. Our simulations indicate that in thermonuclear supernova explosions stable cellular flames develop around the Gibson scale and that deflagration-to-detonation transition is unlikely to be triggered from flame evolution effects here.Comment: 6 pages, 2 figures, to appear in the proceedings of the IAU Colloquium 192, "Supernovae (10 years of SN1993J)", 22-26 April 2003, Valencia, Spain, Eds. J.M. Marcaide and K.W. Weiler, Springer Verla