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

A subgrid-scale model for deflagration-to-detonation transitions in Type la supernova explosion simulations Numerical implementation

Delayed detonations of Chandrasekhar-mass white dwarfs are a promising model for normal Type Ia supernova explosions. In these white dwarfs, 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 recently determined. The region of detonation initiation cannot be spatially resolved in multidimensional full-star simulations of the explosion

Type Ia supernova diversity: white dwarf central density as a secondary parameter in three-dimensional delayed detonation models

Delayed detonations of Chandrasekhar mass white dwarfs (WDs) have been very successful in explaining the spectra, light curves and the width–luminosity relation of spectroscopically normal Type Ia supernovae (SNe Ia). The ignition of the thermonuclear deflagration flame at the end of the convective carbon ‘simmering’ phase in the core of the WD is still not well understood, and much about the ignition kernel distribution remains unknown. Furthermore, the central density at the time of ignition depends on the still uncertain screened carbon fusion reaction rates, the accretion history and cooling time of the progenitor, and the composition. We present the results of 12 high-resolution three-dimensional delayed detonation SN Ia explosion simulations that employ a new criterion to trigger the deflagration to detonation transition (DDT). The simulations fall into three ignition categories: relatively bright SNe with five ignition kernels and a weak deflagration phase (three different central densities); relatively dim SNe with 1600 ignition kernels and a strong deflagration phase (three different central densities) and intermediate SNe with 200 ignition kernels (six different central densities). All simulations trigger our DDT criterion and the resulting delayed detonations unbind the star. We find a trend of increasing iron group element (IGE) production with increasing central density for all three categories. The total 56Ni yield, however, remains more or less constant, even though increased electron captures at high density result in a decreasing 56Ni mass fraction of the IGE material. We attribute this to an approximate balance of 56Ni producing and destroying effects. The deflagrations that were ignited at higher density initially have a faster growth rate of subgrid-scale turbulence. Hence, the effective flame speed increases faster, which triggers the DDT criterion earlier, at a time when the central density of the expanded star is higher. This leads to an overall increase of IGE production, which offsets the percental reduction of 56Ni due to neutronization

Turbulence in a 3D deflagration model for type Ia SNe: II. Intermittency and the deflagration-to-detonation transition probability

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.Comment: 33 pages, 10 figures, submitted to Ap

Three-dimensional simulations of gravitationally confined detonations compared to observations of SN 1991T

The gravitationally confined detonation (GCD) model has been proposed as a possible explosion mechanism for Type Ia supernovae in the single-degenerate evolution channel. Driven by buoyancy, a deflagration flame rises in a narrow cone towards the surface. For the most part, the flow of the expanding ashes remains radial, but upon reaching the outer, low-pressure layers of the white dwarf, an additional lateral component develops. This makes the deflagration ashes converge again at the opposite side, where the compression heats fuel and a detonation may be launched. To test the GCD explosion model, we perform a 3D simulation for a model with an ignition spot offset near the upper limit of what is still justifiable, 200 km. This simulation meets our deliberately optimistic detonation criteria and we initiate a detonation. The detonation burns through the white dwarf and leads to its complete disruption. We determine nucleosynthetic yields by post-processing 10^6 tracer particles with a 384 nuclide reaction network and we present multi-band light curves and time-dependent optical spectra. We find that our synthetic observables show a prominent viewing-angle sensitivity in UV and blue bands, which is in tension with observed SNe Ia. The strong dependence on viewing-angle is caused by the asymmetric distribution of the deflagration ashes in the outer ejecta layers. Finally, we perform a comparison of our model to SN 1991T. The overall flux-level of the model is slightly too low and the model predicts pre-maximum light spectral features due to Ca, S, and Si that are too strong. Furthermore, the model chemical abundance stratification qualitatively disagrees with recent abundance tomography results in two key areas: our model lacks low velocity stable Fe and instead has copious amounts of high-velocity 56Ni and stable Fe. We therefore do not find good agreement of the model with SN 1991T.Comment: 11 pages, accepted for publication in Astronomy & Astrophysic

Three-dimensional delayed-detonation models with nucleosynthesis for type ia supernovae

We present results for a suite of 14 three-dimensional, high-resolution hydrodynamical simulations of delayed-detonation models of Type Ia supernova (SN Ia) explosions. This model suite comprises the first set of three-dimensional SN Ia simulations with detailed isotopic yield information. As such, it may serve as a data base for Chandrasekhar-mass delayed-detonation model nucleosynthetic yields and for deriving synthetic observables such as spectra and light curves. We employ a physically motivated, stochastic model based on turbulent velocity fluctuations and fuel density to calculate in situ the deflagration-to-detonation transition probabilities. To obtain different strengths of the deflagration phase and thereby different degrees of pre-expansion, we have chosen a sequence of initial models with 1, 3, 5, 10, 20, 40, 100, 150, 200, 300 and 1600 (two different realizations) ignition kernels in a hydrostatic white dwarf with a central density of 2.9 × 109 g cm−3, as well as one high central density (5.5 × 109 g cm−3) and one low central density (1.0 × 109 g cm−3) rendition of the 100 ignition kernel configuration. For each simulation, we determined detailed nucleosynthetic yields by post-processing 106 tracer particles with a 384 nuclide reaction network. All delayed-detonation models result in explosions unbinding the white dwarf, producing a range of 56Ni masses from 0.32 to 1.11 M⊙. As a general trend, the models predict that the stable neutron-rich iron-group isotopes are not found at the lowest velocities, but rather at intermediate velocities (∼3000–10 000 km s−1) in a shell surrounding a 56Ni-rich core. The models further predict relatively low-velocity oxygen and carbon, with typical minimum velocities around 4000 and 10 000 km s−1, respectively

Gamma-ray diagnostics of Type Ia supernovae: Predictions of observables from three-dimensional modeling

Besides the fact that the gamma-ray emission due to radioactive decays is responsible for powering the light curves of Type Ia supernovae (SNe Ia), gamma rays themselves are of particular interest as a diagnostic tool because they provide a direct way to obtain deeper insights into the nucleosynthesis and the kinematics of these explosion events. Focusing on two of the most broadly discussed SN Ia progenitor scenarios - a delayed detonation in a Chandrasekhar-mass white dwarf (WD) and a violent merger of two WDs - we use three-dimensional explosion models and perform radiative transfer simulations to obtain synthetic gamma-ray spectra. Both chosen models produce the same mass of 56Ni and have similar optical properties that are in reasonable agreement with the recently observed supernova SN 2011fe. In contrast to the optical regime, the gamma-ray emission of our two chosen models proves to be rather different. The almost direct connection of the emission of gamma rays to fundamental physical processes occuring in SNe Ia permits additional constraints concerning several explosion model properties that are not easily accessible within other wavelength ranges. Proposed future MeV missions such as GRIPS will resolve all spectral details only for nearby SNe Ia, but hardness ratio and light curve measurements still allow for a distinction of the two different models at 10 and 16 Mpc for an exposure time of 10^6 s, respectively. The possibility to detect the strongest line features up to the Virgo distance will offer the opportunity to build up a first sample of SN Ia detections in the gamma-ray energy range and underlines the importance of future space observatories for MeV gamma rays.Comment: 10 pages, 8 figures, accepted for publication by A&

Turbulence in a three-dimensional deflagration model for Type Ia supernovae: I. Scaling properties

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.Comment: 7 pages with 16 figures, submitted to Ap

Predicting polarization signatures for double-detonation and delayed-detonation models of Type Ia supernovae

Calculations of synthetic spectropolarimetry are one means to test multidimensional explosion models for Type Ia supernovae. In a recent paper, we demonstrated that the violent merger of a 1.1 and 0.9 M⊙ white dwarf binary system is too asymmetric to explain the low polarization levels commonly observed in normal Type Ia supernovae. Here, we present polarization simulations for two alternative scenarios: the sub-Chandrasekhar mass double-detonation and the Chandrasekhar mass delayed-detonation model. Specifically, we study a 2D double-detonation model and a 3D delayed-detonation model, and calculate polarization spectra for multiple observer orientations in both cases. We find modest polarization levels (<1 per cent) for both explosion models. Polarization in the continuum peaks at ˜0.1-0.3 per cent and decreases after maximum light, in excellent agreement with spectropolarimetric data of normal Type Ia supernovae. Higher degrees of polarization are found across individual spectral lines. In particular, the synthetic Si II λ6355 profiles are polarized at levels that match remarkably well the values observed in normal Type Ia supernovae, while the low degrees of polarization predicted across the O I λ7774 region are consistent with the non-detection of this feature in current data. We conclude that our models can reproduce many of the characteristics of both flux and polarization spectra for well-studied Type Ia supernovae, such as SN 2001el and SN 2012fr. However, the two models considered here cannot account for the unusually high level of polarization observed in extreme cases such as SN 2004dt

Type Ia supernova diversity: white dwarf central density as a secondary parameter in three-dimensional delayed detonation models

Delayed detonations of Chandrasekhar-mass white dwarfs (WDs) have been very successful in explaining the spectra, light curves, and the width-luminosity relation of spectroscopically normal Type Ia supernovae (SNe Ia). The ignition of the thermonuclear deflagration flame at the end of the convective carbon "simmering" phase in the core of the WD is still not well understood and much about the ignition kernel distribution remains unknown. Furthermore, the central density at the time of ignition depends on the still uncertain screened carbon fusion reaction rates, the accretion history and cooling time of the progenitor, and the composition. We present the results of twelve high-resolution three-dimensional delayed detonation SN Ia explosion simulations that employ a new criterion to trigger the deflagration to detonation transition (DDT). All simulations trigger our DDT criterion and the resulting delayed detonations unbind the star. We find a trend of increasing iron group element (IGE) production with increasing central density for bright, faint, and intermediate SNe. The total 56Ni yield, however, remains more or less constant, even though increased electron captures at high density result in a decreasing 56Ni mass fraction of the IGE material. We attribute this to an approximate balance of 56Ni producing and destroying effects. The deflagrations that were ignited at higher density initially have a faster growth rate of subgrid-scale turbulence. Hence, the effective flame speed increases faster, which triggers the DDT criterion earlier, at a time when the central density of the expanded star is higher. This leads to an overall increase of IGE production, which off-sets the percental reduction of 56Ni due to neutronization.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in MNRAS. v2 now includes correct Fig. 6, which was missing from v