Multi-dimensional numerical simulations of type Ia supernova explosions

The major role type Ia supernovae play in many fields of astrophysics and in particular in cosmological distance determinations calls for self-consistent models of these events. Since their mechanism is believed to crucially depend on phenomena that are inherently three-dimensional, self-consistent numerical models of type Ia supernovae must be multi-dimensional. This field has recently seen a rapid development, which is reviewed in this article. The different modeling approaches are discussed and as an illustration a particular explosion model -- the deflagration model -- in a specific numerical implementation is presented in greater detail. On this exemplary case, the procedure of validating the model on the basis of comparison with observations is discussed as well as its application to study questions arising from type Ia supernova cosmology.Comment: 30 pages, 7 figures (Fig. 6 with reduced resolution

Flame-driven deflagration-to-detonation transitions in Type Ia supernovae?

Although delayed detonation models of thermonuclear explosions of white dwarfs seem promising for reproducing Type Ia supernovae, the transition of the flame propagation mode from subsonic deflagration to supersonic detonation remains hypothetical. A potential instant for this transition to occur is the onset of the distributed burning regime, i.e. the moment when turbulence first affects the internal flame structure. Some studies of the burning microphysics indicate that a deflagration-to-detonation transition may be possible here, provided the turbulent intensities are strong enough. Consequently, the magnitude of turbulent velocity fluctuations generated by the deflagration flame is analyzed at the onset of the distributed burning regime in several three-dimensional simulations of deflagrations in thermonuclear supernovae. It is shown that the corresponding probability density functions fall off towards high turbulent velocity fluctuations much more slowly than a Gaussian distribution. Thus, values claimed to be necessary for triggering a detonation are likely to be found in sufficiently large patches of the flame. Although the microphysical evolution of the burning is not followed and a successful deflagration-to-detonation transition cannot be guaranteed from simulations presented here, the results still indicate that such events may be possible in Type Ia supernova explosions.Comment: 6 pages, 2 figures, to appear in ApJ 668, 1103 (2007

Numerical simulations of multi-scale astrophysical problems: The example of Type Ia supernovae

Vastly different time and length scales are a common problem in numerical simulations of astrophysical phenomena. Here, we present an approach to numerical modeling of such objects on the example of Type Ia supernova simulations. The evolution towards the explosion proceeds on much longer time scales than the explosion process itself. The physical length scales relevant in the explosion process cover 11 orders of magnitude and turbulent effects dominate the physical mechanism. Despite these challenges, three-dimensional simulations of Type Ia supernova explosions have recently become possible and pave the way to a better understanding of these important astrophysical objects.Comment: 10 pages, 1 figure; in "Modelling and Simulation in Science", Proceedings of the 6th International Workshop on Data Analysis in Astronomy "Livio Scarsi", Erice, Italy 15 - 22 April 2007 (World Scientific, 2008

New numerical solver for flows at various Mach numbers

Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.Comment: 16 pages, 8 figures, accepted for publication by A&

A Subgrid-scale Model for Deflagration-to-Detonation Transitions in Type Ia Supernova Explosion Simulations - Numerical implementation

A promising model for normal Type Ia supernova (SN Ia) explosions are delayed detonations of Chandrasekhar-mass white dwarfs, in which the burning starts out as a subsonic deflagration and turns at a later phase of the explosion into a supersonic detonation. The mechanism of the underlying deflagration-to-detonation transition (DDT) is unknown in detail, but necessary conditions have been determined recently. The region of detonation initiation cannot be spatially resolved in multi-dimensional full-star simulations of the explosion. We develop a subgrid-scale (SGS) model for DDTs in thermonuclear supernova simulations that is consistent with the currently known constraints. The probability for a DDT to occur is calculated from the distribution of turbulent velocities measured on the grid scale in the vicinity of the flame and the fractal flame surface area that satisfies further physical constraints, such as fuel fraction and fuel density. The implementation of our DDT criterion provides a solid basis for simulations of thermonuclear supernova explosions in the delayed detonation scenario. It accounts for the currently known necessary conditions for the transition and avoids the inclusion of resolution-dependent quantities in the model. The functionality of our DDT criterion is demonstrated on the example of one three-dimensional thermonuclear supernova explosion simulation.Comment: accepted for publication in Astronomy and Astrophysic

Off-center ignition in type Ia supernova: I. Initial evolution and implications for delayed detonation

The explosion of a carbon-oxygen white dwarf as a Type Ia supernova is known to be sensitive to the manner in which the burning is ignited. Studies of the pre-supernova evolution suggest asymmetric, off-center ignition, and here we explore its consequences in two- and three-dimensional simulations. Compared with centrally ignited models, one-sided ignitions initially burn less and release less energy. For the distributions of ignition points studied, ignition within two hemispheres typically leads to the unbinding of the white dwarf, while ignition within a small fraction of one hemisphere does not. We also examine the spreading of the blast over the surface of the white dwarf that occurs as the first plumes of burning erupt from the star. In particular, our studies test whether the collision of strong compressional waves can trigger a detonation on the far side of the star as has been suggested by Plewa et al. (2004). The maximum temperature reached in these collisions is sensitive to how much burning and expansion has already gone on, and to the dimensionality of the calculation. Though detonations are sometimes observed in 2D models, none ever happens in the corresponding 3D calculations. Collisions between the expansion fronts of multiple bubbles also seem, in the usual case, unable to ignite a detonation. "Gravitationally confined detonation" is therefore not a robust mechanism for the explosion. Detonation may still be possible in these models however, either following a pulsation or by spontaneous detonation if the turbulent energy is high enough.Comment: 13 pages, 10 figures (resolution of some figures reduced to comply with astro-ph file size restriction); submitted to the Astrophysical Journal on 8/3/200

Thermonuclear Supernovae

The application of Type Ia supernovae (SNe Ia) as distance indicators in cosmology calls for a sound understanding of these objects. Recent years have seen a brisk development of astrophysical models which explain SNe Ia as thermonuclear explosions of white dwarf stars. While the evolution of the progenitor is still uncertain, the explosion mechanism certainly involves the propagation of a thermonuclear flame through the white dwarf star. Three-dimensional hydrodynamical simulations allowed to study a wide variety of possibilities involving subsonic flame propagation (deflagrations), flames accelerated by turbulence, and supersonic detonations. These possibilities lead to a variety of scenarios. I review the currently discussed approaches and present some recent results from simulations of the turbulent deflagration model and the delayed detonation model.Comment: 25 pages, 7 figures (some with reduced resolution), invited review at "Supernovae: lights in the darkness", October 3-5, 2007, Mao (Menorca), to appear in Proceedings of Scienc

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&