Thermonuclear supernova simulations with stochastic ignition

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.pd

Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence

The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in these simulations is of purely numerical origin. For the dimensionless mean rate of dissipation, we find values in agreement with known results from mostly incompressible turbulence simulations. The calculation of a Smagorinsky length corresponding to the rate of numerical dissipation supports the notion of the PPM supplying an implicit subgrid scale model. In the turbulence energy spectra of various flow realisations, we find the so-called bottleneck phenomenon, i.e., a flattening of the spectrum function near the wavenumber of maximal dissipation. The shape of the bottleneck peak in the compensated spectrum functions is comparable to what is found in turbulence simulations with hyperviscosity. Although the bottleneck effect reduces the range of nearly inertial length scales considerably, we are able to estimate the value of the Kolmogorov constant. For steady turbulence with a balance between energy injection and dissipation, it appears that $C\approx 1.7$. However, a smaller value is found in the case of transonic turbulence with a large fraction of compressive components in the driving force. Moreover, we discuss length scales related to the dissipation, in particular, an effective numerical length scale $\Delta_{\mathrm{eff}}$, which can be regarded as the characteristic smoothing length of the implicit filter associated with the PPM.Comment: 23 pages, 7 figures. Revised version accepted by Comp. Fluids. Not all figures included due to size restriction. Complete PDF available at http://www.astro.uni-wuerzburg.de/%7Eschmidt/Paper/NumDiss_CF.pd

Type Ia Supernova Explosion Models: Homogeneity versus Diversity

Type Ia supernovae (SN Ia) are generally believed to be the result of the thermonuclear disruption of Chandrasekhar-mass carbon-oxygen white dwarfs, mainly because such thermonuclear explosions can account for the right amount of Ni-56, which is needed to explain the light curves and the late-time spectra, and the abundances of intermediate-mass nuclei which dominate the spectra near maximum light. Because of their enormous brightness and apparent homogeneity SN Ia have become an important tool to measure cosmological parameters. In this article the present understanding of the physics of thermonuclear explosions is reviewed. In particular, we focus our attention on subsonic (``deflagration'') fronts, i.e. we investigate fronts propagating by heat diffusion and convection rather than by compression. Models based upon this mode of nuclear burning have been applied very successfully to the SN Ia problem, and are able to reproduce many of their observed features remarkably well. However, the models also indicate that SN Ia may differ considerably from each other, which is of importance if they are to be used as standard candles.Comment: 11 pages, 4 figures. To appear in Proc. 10th Ann. Astrophys. Conf. "Cosmic Explosions", Univ. of Maryland 1999, eds. S.S. Holt and W.W. Zhan

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

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&