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Register a new userA Subgrid-scale Model for Deflagration-to-Detonation Transitions in Type Ia Supernova Explosion Simulations - Numerical implementation
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Friedrich Konrad Roepke
Publication date
2013
fields
Physics
and research's language is
English
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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.
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The delayed detonation model describes the observational properties of the majority of type Ia supernovae very well. Using numerical data from a three-dimensional deflagration model for type Ia supernovae, the intermittency of the turbulent velocity field and its implications on the probability of a deflagration-to-detonation (DDT) transition are investigated. From structure functions of the turbulent velocity fluctuations, we determine intermittency parameters based on the log-normal and the log-Poisson models. On the other hand, the analysis of the turbulent velocity fluctuations in the vicinity of the flame front by Roepke suggests a much higher probability of large velocity fluctuations on the grid scale in comparison to the log-normal intermittency model. Following Pan et al., we computed probability density functions for a DDT for the different distributions. Assuming that a DDT can occur in the stirred flame regime, as proposed by Woosley et al., the log-normal model would imply a delayed detonation between 0.7 and 0.8 seconds after the beginning of the deflagration phase for the multi-spot ignition scenario used in the simulation. However, the probability drops to virtually zero if a DDT is further constrained by the requirement that the turbulent velocity fluctuations reach about 500 km/s. Under this condition, delayed detonations are only possible if the distribution of the velocity fluctuations is not log-normal. From our calculations follows that the distribution obtained by Roepke allow for multiple DDTs around 0.8 seconds after ignition at a transition density close to 1x10^7 g/cm^3.
It has long been recognized that the neutrinos detected from the next core-collapse supernova in the Galaxy have the potential to reveal important information about the dynamics of the explosion and the nucleosynthesis conditions as well as allowing us to probe the properties of the neutrino itself. The neutrinos emitted from thermonuclear - type Ia - supernovae also possess the same potential, although these supernovae are dimmer neutrino sources. For the first time, we calculate the time, energy, line of sight, and neutrino-flavor-dependent features of the neutrino signal expected from a three-dimensional delayed-detonation explosion simulation, where a deflagration-to-detonation transition triggers the complete disruption of a near-Chandrasekhar mass carbon-oxygen white dwarf. We also calculate the neutrino flavor evolution along eight lines of sight through the simulation as a function of time and energy using an exact three-flavor transformation code. We identify a characteristic spectral peak at $sim 10$ MeV as a signature of electron captures on copper. This peak is a potentially distinguishing feature of explosion models since it reflects the nucleosynthesis conditions early in the explosion. We simulate the event rates in the Super-K, Hyper-K, JUNO, and DUNE neutrino detectors with the SNOwGLoBES event rate calculation software and also compute the IceCube signal. Hyper-K will be able to detect neutrinos from our model out to a distance of $sim 10$ kpc. At 1 kpc, JUNO, Super-K, and DUNE would register a few events while IceCube and Hyper-K would register several tens of events.
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.
We explore the evolution of thermonuclear supernova explosions when the progenitor white dwarf star ignites asymmetrically off-center. Several numerical simulations are carried out in two and three dimensions to test the consequences of different initial flame configurations such as spherical bubbles displaced from the center, more complex deformed configurations, and teardrop-shaped ignitions. The burning bubbles float towards the surface while releasing energy due to the nuclear reactions. If the energy release is too small to gravitationally unbind the star, the ash sweeps around it, once the burning bubble approaches the surface. Collisions in the fuel on the opposite side increase its temperature and density and may -- in some cases -- initiate a detonation wave which will then propagate inward burning the core of the star and leading to a strong explosion. However, for initial setups in two dimensions that seem realistic from pre-ignition evolution, as well as for all three-dimensional simulations the collimation of the surface material is found to be too weak to trigger a detonation.
We analyze the statistical properties of the turbulent velocity field in the deflagration model for Type Ia supernovae. In particular, we consider the question of whether turbulence is isotropic and consistent with the Kolmogorov theory at small length scales. Using numerical data from a high-resolution simulation of a thermonuclear supernova explosion, spectra of the turbulence energy and velocity structure functions are computed. We show that the turbulent velocity field is isotropic at small length scales and follows a scaling law that is consistent with the Kolmogorov theory until most of the nuclear fuel is burned. At length scales greater than a certain characteristic scale, turbulence becomes anisotropic. Here, the radial velocity fluctuations follow the scaling law of the Rayleigh-Taylor instability, whereas the angular component still obeys Kolmogorov scaling. In the late phase of the explosion, this characteristic scale drops below the numerical resolution of the simulation. The analysis confirms that a subgrid-scale model for the unresolved turbulence energy is required for the consistent calculation of the flame speed in deflagration models of Type Ia supernovae, and that the assumption of isotropy on these scales is appropriate.
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