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Aims: We present the first full-star three-dimensional explosion simulations of thermonuclear supernovae including parameterized deflagration-to-detonation transitions that occur once the flame enters the distributed burning regime. Methods: Treating the propagation of both the deflagration and the detonation waves in a common front-tracking approach, the detonation is prevented from crossing ash regions. Results: Our criterion triggers the detonation wave at the outer edge of the deflagration flame and consequently it has to sweep around the complex structure and to compete with expansion. Despite the impeded detonation propagation, the obtained explosions show reasonable agreement with global quantities of observed type Ia supernovae. By igniting the flame in different numbers of kernels around the center of the exploding white dwarf, we set up three different models shifting the emphasis from the deflagration phase to the detonation phase. The resulting explosion energies and iron group element productions cover a large part of the diversity of type Ia supernovae. Conclusions: Flame-driven deflagration-to-detonation transitions, if hypothetical, remain a possibility deserving further investigation., Comment: 4 pages, 1 figure

The onset of the thermonuclear runaway in a Chandrasekhar-mass white dwarf, leading to the explosion as a type Ia supernova, is studied with hydrodynamical simulations. We investigate the evolution of temperature fluctuations (``bubbles'') in the WD's convective core by means of 2D numerical simulations. We show how the occurrence of the thermonuclear runaway depends on various bubble parameters. The relevance of the progenitor's composition for the ignition process is also discussed., Comment: 4 pages, 2 figures, proceedings of the Catania Workshop on Nuclear and Neutrino Astrophysics (WNNA 2007)

A simulation of the thermonuclear explosion of a Chandrasekhar-mass C+O white dwarf, the most popular scenario of a type Ia supernova (SN Ia), is presented. The underlying modeling is pursued in a self-consistent way, treating the combustion wave as a turbulent deflagration using well tested methods developed for laboratory combustion and based on the concept of `large eddy simulations' (LES). Such consistency requires to capture the onset of the turbulent cascade on resolved scales. This is achieved by computing the dynamical evolution on a 1024$^3$ moving grid, which resulted in the best-resolved three-dimensional SN Ia simulation carried out thus far, reaching the limits of what can be done on present supercomputers. Consequently, the model has no free parameters other than the initial conditions at the onset of the explosion, and therefore it has considerable predictive power. Our main objective is to determine to which extent such a simulation can account for the observations of normal SNe Ia. Guided by previous simulations with less resolution and a less sophisticated flame model, initial conditions were chosen that yield a reasonably strong explosion and a sufficient amount of radioactive nickel for a bright display. We show that observables are indeed matched to a reasonable degree. In particular, good agreement is found with the light curves of normal SNe Ia. Moreover, the model reproduces the general features of the abundance stratification as inferred from the analysis of spectra. This indicates that it captures the main features of the explosion mechanism of SNe Ia. However, we also show that even a seemingly best-choice pure deflagration model has shortcomings that indicate the need for a different mode of nuclear burning at late times, perhaps the transition to a detonation at low density., Comment: 8 pages, 5 figures, accepted for publication in the ApJ

In the context of explosion models for Type Ia Supernovae, we present one- and two-dimensional simulations of fully resolved detonation fronts in degenerate C+O White Dwarf matter including clumps of previously burned material. The ability of detonations to survive the passage through sheets of nuclear ashes is tested as a function of the width and composition of the ash region. We show that detonation fronts are quenched by microscopically thin obstacles with little sensitivity to the exact ash composition. Front-tracking models for detonations in macroscopic explosion simulations need to include this effect in order to predict the amount of unburned material in delayed detonation scenarios., Comment: 6 pages, 9 figures, uses isotope.sty, accepted for publication in A&A

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.pdf

We present a one-equation subgrid scale model that evolves the turbulence energy corresponding to unresolved velocity fluctuations in large eddy simulations. The model is derived in the context of the Germano consistent decomposition of the hydrodynamical equations. The eddy-viscosity closure for the rate of energy transfer from resolved toward subgrid scales is localised by means of a dynamical procedure for the computation of the closure parameter. Therefore, the subgrid scale model applies to arbitrary flow geometry and evolution. For the treatment of microscopic viscous dissipation a semi-statistical approach is used, and the gradient-diffusion hypothesis is adopted for turbulent transport. A priori tests of the localised eddy-viscosity closure and the gradient-diffusion closure are made by analysing data from direct numerical simulations. As an a posteriori testing case, the large eddy simulation of thermonuclear combustion in forced isotropic turbulence is discussed. We intend the formulation of the subgrid scale model in this paper as a basis for more advanced applications in numerical simulations of complex astrophysical phenomena involving turbulence., Comment: 18 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_I_AA.pdf

In the framework of the Chandrasekhar-mass deflagration model for Type Ia supernovae (SNe Ia), a persisting free parameter is the initial morphology of the flame front, which is linked to the ignition process in the progenitor white dwarf. Previous analytical models indicate that the thermal runaway is driven by temperature perturbations (''bubbles'') that develop in the white dwarf's convective core. In order to probe the conditions at ignition (diameters, temperatures and evolutionary timescales), we have performed hydrodynamical 2D simulations of buoyant bubbles in white dwarf interiors. Our results show that fragmentation occurring during the bubble rise affects the outcome of the bubble evolution. Possible implications for the ignition process of SNe Ia are discussed., Comment: 12 pages, 11 figures, submitted to A&A

We present a systematic survey of the capabilities of type Ia supernova explosion models starting from a number of flame seeds distributed around the center of the white dwarf star. To this end we greatly improved the resolution of the numerical simulations in the initial stages. This novel numerical approach facilitates a detailed study of multi-spot ignition scenarios with up to hundreds of ignition sparks. Two-dimensional simulations are shown to be inappropriate to study the effects of initial flame configurations. Based on a set of three-dimensional models, we conclude that multi-spot ignition scenarios may improve type Ia supernova models towards better agreement with observations. The achievable effect reaches a maximum at a limited number of flame ignition kernels as shown by the numerical models and corroborated by a simple dimensional analysis., Comment: 14 pages, 12 figures with reduced resolution to meet astro-ph file size restriction, full-resolution version available from http://www.mpa-garching.mpg.de/~fritz/publications/astro-ph/multispot.pdf submitted to A&A

We apply an ad hoc model for dynamical ignition in three-dimensional numerical simulations of thermonuclear supernovae assuming pure deflagrations. The model makes use of the statistical description of temperature fluctuations in the pre-supernova core proposed by Wunsch & Woosley (2004). Randomness in time is implemented by means of a Poisson process. We are able to vary the explosion energy and nucleosynthesis depending on the free parameter of the model which controls the rapidity of the ignition process. However, beyond a certain threshold, the strength of the explosion saturates and the outcome appears to be robust with respect to number of ignitions. In the most energetic explosions, we find about 0.75 solar masses of iron group elements. Other than in simulations with simultaneous multi-spot ignition, the amount of unburned carbon and oxygen at radial velocities of a few 1000 km/s tends to be reduced for an ever increasing number of ignition events and, accordingly, more pronounced layering results., Comment: 7 pages, 6 figures, accepted for publication in Astron. Astrophys.; PDF version with full resolution figures available from http://www.astro.uni-wuerzburg.de/~schmidt/Paper/StochIgnt_AA.pdf

We study the dynamics of thermonuclear flames propagating in fuel stirred by stochastic forcing. The fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the Chandrasekhar limit. The level set method is applied to represent the flame fronts numerically. The computational domain for the numerical simulations is cubic, and periodic boundary conditions are imposed. The goal is the development of a suitable flame speed model for the small-scale dynamics of turbulent deflagration in thermonuclear supernovae. Because the burning process in a supernova explosion is transient and spatially inhomogeneous, the localised determination of subgrid scale closure parameters is essential. We formulate a semi-localised model based on the dynamical equation for the subgrid scale turbulence energy $k_{\mathrm{sgs}}$. The turbulent flame speed $s_{\mathrm{t}}$ is of the order $\sqrt{2k_{\mathrm{sgs}}}$. In particular, the subgrid scale model features a dynamic procedure for the calculation of the turbulent energy transfer from resolved toward subgrid scales, which has been successfully applied to combustion problems in engineering. The options of either including or suppressing inverse energy transfer in the turbulence production term are compared. In combination with the piece-wise parabolic method for the hydrodynamics, our results favour the latter option. Moreover, different choices for the constant of proportionality in the asymptotic flame speed relation, $s_{\mathrm{t}}\propto\sqrt{2k_{\mathrm{sgs}}}$, are investigated., Comment: 36 pages, 11 figures (separately in PNG format), accepted for publication in Combust. Theory Modelling; PDF version with figures included can be downloaded from http://www.astro.uni-wuerzburg.de/~schmidt/Paper/TurbDefl_CTM.pdf

We show that a flame tracking/capturing scheme originally developed for deflagration fronts can be used to model thermonuclear detonations in multidimensional explosion simulations of type Ia supernovae. After testing the accuracy of the front model, we present a set of two-dimensional simulations of delayed detonations with a physically motivated off-center deflagration-detonation-transition point. Furthermore, we demonstrate the ability of the front model to reproduce the full range of possible interactions of the detonation with clumps of burned material. This feature is crucial for assessing the viability of the delayed detonation scenario., Comment: 7 pages, accepted by A&A