arXiv subjects

Ivo R. Seitenzahl

Publications and source records attributed to Ivo R. Seitenzahl.

71 records · Page 4Linked to original sources

arXiv2016

Neutrinos from type Ia supernovae: the deflagration-to-detonation transition scenario

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.

astro-ph.HE↗

arXiv2016

Do electron-capture supernovae make neutron stars? First multidimensional hydrodynamic simulations of the oxygen deflagration

In the classical picture, electron-capture supernovae and the accretion-induced collapse of oxygen-neon white dwarfs (ONeWDs) undergo an oxygen deflagration phase before gravitational collapse produces a neutron star (NS). These types of core collapse events are postulated to explain several astronomical phenomena. In this work, the deflagration phase is simulated for the first time using multidimensional hydrodynamics, with the aim of gaining new insight into the explosive deaths of $8-10~M_\odot$ stars and ONeWDs that accrete material from a binary companion star. The main aim is to determine whether these events are thermonuclear or core-collapse supernova explosions, and hence whether NSs are formed by such phenomena. The deflagration is simulated in ONe cores with three different central ignition densities. The intermediate density case is perhaps the most realistic, being based on recent nuclear physics calculations and 1D stellar models. The 3D hydrodynamic simulations presented in this work begin from a centrally confined flame structure using a level-set-based flame approach and are performed in $256^3$ and $512^3$ numerical resolutions. In the simulations with intermediate and low ignition density, the cores do not appear to collapse into NSs. Instead, almost a solar mass of material becomes unbound from the cores, leaving bound remnants. These simulations represent the case in which semiconvective mixing during the electron-capture phase preceding the deflagration is inefficient. The masses of the bound remnants double when Coulomb corrections are included in the EoS, however they still do not exceed the effective Chandrasekhar mass and, hence, would not collapse into NSs. The simulations with the highest ignition density ($\log_{10}ρ_{\rm c}=10.3$), representing the case where semiconvective mixing is very efficient, show clear signs that the core will collapse into a NS.

astro-ph.SR↗

arXiv2016

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.

astro-ph.SR↗

arXiv2016

Forbidden Iron Lines and Dust Destruction in Supernova Remnant Shocks: The Case of N49 in the Large Magellanic Cloud

We present results of a complete integral field survey of the bright SNR N49 in the LMC, obtained with the WiFeS instrument mounted on the ANU 2.3m telescope at Siding Spring Observatory. From theoretical shock modelling with the new MAPPINGS 5.1 code we have, for the first time, subjected the optical Fe emission line spectrum of a supernova remnant to a detailed abundance and dynamical analysis covering 8 separate stages of ionisation. This allows us to derive the dust depletion factors as a function of ionisation stage. We have shown that there is substantial (30% - 90%) destruction of Fe-bearing dust grains in these fast shocks ($v_s \sim 250$ km/s), and we have confirmed that the dominant dust destruction is through the non-thermal sputtering and grain-grain collision mechanisms developed in a number of theoretical works.

astro-ph.GA↗

arXiv2016

Late-Time Photometry of Type Ia Supernova SN 2012cg Reveals the Radioactive Decay of $^{57}$Co

Seitenzahl et al. (2009) have predicted that roughly three years after its explosion, the light we receive from a Type Ia supernova (SN Ia) will come mostly from reprocessing of electrons and X-rays emitted by the radioactive decay chain $^{57}{\rm Co}~\to~^{57}{\rm Fe}$, instead of positrons from the decay chain $^{56}{\rm Co}~\to~^{56}{\rm Fe}$ that dominates the SN light at earlier times. Using the {\it Hubble Space Telescope}, we followed the light curve of the SN Ia SN 2012cg out to $1055$ days after maximum light. Our measurements are consistent with the light curves predicted by the contribution of energy from the reprocessing of electrons and X-rays emitted by the decay of $^{57}$Co, offering evidence that $^{57}$Co is produced in SN Ia explosions. However, the data are also consistent with a light echo $\sim14$ mag fainter than SN 2012cg at peak. Assuming no light-echo contamination, the mass ratio of $^{57}$Ni and $^{56}$Ni produced by the explosion, a strong constraint on any SN Ia explosion model, is $0.043^{+0.012}_{-0.011}$, roughly twice Solar. In the context of current explosion models, this value favors a progenitor white dwarf with a mass near the Chandrasekhar limit.

astro-ph.HE↗

arXiv2016

Neutrino and gravitational wave signal of a delayed-detonation model of Type Ia supernovae

The progenitor system(s) and the explosion mechanism(s) of Type Ia supernovae (SNe Ia) are still under debate. Non-electromagnetic observables, in particular gravitational waves and neutrino emission, of thermonuclear supernovae are a complementary window to light curves and spectra for studying these enigmatic objects. A leading model for SNe Ia is the thermonuclear incineration of a near-Chandrasekhar mass carbon-oxygen white dwarf star in a "delayed-detonation". We calculate a three-dimensional hydrodynamic explosion for the N100 delayed-detonation model extensively discussed in the literature, taking the dynamical effects of neutrino emission from all important contributing source terms into account. Although neutrinos carry away $2 \times 10^{49}$ erg of energy, we confirm the common view that neutrino energy losses are dynamically not very important, resulting in only a modest reduction of the final kinetic energy by two per cent. We then calculate the gravitational wave signal from the time evolution of the quadrupole moment. Our model radiates $7 \times 10^{39}$ erg in gravitational waves and the spectrum has a pronounced peak around 0.4 Hz. Depending on viewing angle and polarization, we find that the future space-based gravitational wave missions DECIGO and BBO would be able to detect our source to a distance of 1.3 Mpc. We predict a clear signature of the deflagration-to-detonation transition in the neutrino and the gravitational wave signals. If observed, such a feature would be a strong indicator of the realization of delayed-detonations in near-Chandrasekhar mass white dwarfs.

astro-ph.SR↗

arXiv2015

Type Ia supernovae from exploding oxygen-neon white dwarfs

The progenitor problem of Type Ia supernovae (SNe Ia) is still unsolved. Most of these events are thought to be explosions of carbon-oxygen (CO) white dwarfs (WDs), but for many of the explosion scenarios, particularly those involving the externally triggered detonation of a sub-Chandrasekhar mass WD (sub-M Ch WD), there is also a possibility of having an oxygen-neon (ONe) WD as progenitor. We simulate detonations of ONe WDs and calculate synthetic observables from these models. The results are compared with detonations in CO WDs of similar mass and observational data of SNe Ia. We perform hydrodynamic explosion simulations of detonations in initially hydrostatic ONe WDs for a range of masses below the Chandrasekhar mass (M Ch), followed by detailed nucleosynthetic postprocessing with a 384-isotope nuclear reaction network. The results are used to calculate synthetic spectra and light curves, which are then compared with observations of SNe Ia. We also perform binary evolution calculations to determine the number of SNe Ia involving ONe WDs relative to the number of other promising progenitor channels. The ejecta structures of our simulated detonations in sub-M Ch ONe WDs are similar to those from CO WDs. There are, however, small systematic deviations in the mass fractions and the ejecta velocities. These lead to spectral features that are systematically less blueshifted. Nevertheless, the synthetic observables of our ONe WD explosions are similar to those obtained from CO models. Our binary evolution calculations show that a significant fraction (3-10%) of potential progenitor systems should contain an ONe WD. The comparison of our ONe models with our CO models of comparable mass (1.2 Msun) shows that the less blueshifted spectral features fit the observations better, although they are too bright for normal SNe Ia.

astro-ph.SR↗

arXiv2014

The white dwarf's carbon fraction as a secondary parameter of Type Ia supernovae

Binary stellar evolution calculations predict that Chandrasekhar-mass carbon/oxygen white dwarfs (WDs) show a radially varying profile for the composition with a carbon depleted core. Many recent multi-dimensional simulations of Type Ia supernovae (SNe Ia), however, assume the progenitor WD has a homogeneous chemical composition. In this work, we explore the impact of different initial carbon profiles of the progenitor WD on the explosion phase and on synthetic observables in the Chandrasekhar-mass delayed detonation model. Spectra and light curves are compared to observations to judge the validity of the model. The explosion phase is simulated using the finite volume supernova code LEAFS, which is extended to treat different compositions of the progenitor WD. The synthetic observables are computed with the Monte Carlo radiative transfer code ARTIS. Differences in binding energies of carbon and oxygen lead to a lower nuclear energy release for carbon depleted material; thus, the burning fronts that develop are weaker and the total nuclear energy release is smaller. For otherwise identical conditions, carbon depleted models produce less Ni-56. Comparing different models with similar Ni-56 yields shows lower kinetic energies in the ejecta for carbon depleted models, but only small differences in velocity distributions and line velocities in spectra. The light curve width-luminosity relation (WLR) obtained for models with differing carbon depletion is roughly perpendicular to the observed WLR, hence the carbon mass fraction is probably only a secondary parameter in the family of SNe Ia.

astro-ph.SR↗

arXiv2014

The effect of helium accretion efficiency on rates of Type Ia supernovae: double-detonations in accreting binaries

The double-detonation explosion scenario of Type Ia supernovae has gained increased support from the SN Ia community as a viable progenitor model, making it a promising candidate alongside the well-known single degenerate and double degenerate scenarios. We present delay times of double-detonation SNe, in which a sub-Chandrasekhar mass carbon-oxygen white dwarf accretes non-dynamically from a helium-rich companion. One of the main uncertainties in quantifying SN rates from double-detonations is the (assumed) retention efficiency of He-rich matter. Therefore, we implement a new prescription for the treatment of accretion/accumulation of He-rich matter on white dwarfs. In addition, we test how the results change depending on which criteria are assumed to lead to a detonation in the helium shell. In comparing the results to our standard case (Ruiter et al. 2011), we find that regardless of the adopted He accretion prescription, the SN rates are reduced by only 25% if low-mass He shells (< 0.05 Msun) are sufficient to trigger the detonations. If more massive (0.1 Msun) shells are needed, the rates decrease by 85% and the delay time distribution is significantly changed in the new accretion model - only SNe with prompt (< 500 Myr) delay times are produced. Since theoretical arguments favour low-mass He shells for normal double-detonation SNe, we conclude that the rates from double-detonations are likely to be high, and should not critically depend on the adopted prescription for accretion of He.

astro-ph.SR↗

arXiv2013

Solar abundance of manganese: a case for the existence of near Chandrasekhar-mass Type Ia supernova progenitors

Context: Manganese is predominantly synthesised in Type Ia supernova (SN Ia) explosions. Owing to the entropy dependence of the Mn yield in explosive thermonuclear burning, SNe Ia involving near Chandrasekhar-mass white dwarfs (WDs) are predicted to produce Mn to Fe ratios significantly exceeding those of SN Ia explosions involving sub-Chandrasekhar mass primary WDs. Of all current supernova explosion models, only SN Ia models involving near-Chandrasekhar mass WDs produce [Mn/Fe] > 0.0. Aims: Using the specific yields for competing SN Ia scenarios, we aim to constrain the relative fractions of exploding near-Chandrasekhar mass to sub-Chandrasekhar mass primary WDs in the Galaxy. Methods: We extract the Mn yields from three-dimensional thermonuclear supernova simulations referring to different initial setups and progenitor channels. We then compute the chemical evolution of Mn in the Solar neighborhood, assuming SNe Ia are made up of different relative fractions of the considered explosion models. Results: We find that due to the entropy dependence of freeze-out yields from nuclear statistical equilibrium, [Mn/Fe] strongly depends on the mass of the exploding WD, with near-Chandraskher mass WDs producing substantially higher [Mn/Fe] than sub-Chandrasekhar mass WDs. Of all nucleosynthetic sources potentially influencing the chemical evolution of Mn, only explosion models involving the thermonuclear incineration of near-Chandrasekhar mass WDs predict solar or super-solar [Mn/Fe]. Consequently, we find in our chemical evolution calculations that the observed [Mn/Fe] in the Solar neighborhood at [Fe/H] > 0.0 cannot be reproduced without near-Chandrasekhar mass SN Ia primaries. Assuming that 50 per cent of all SNe Ia stem from explosive thermonuclear burning in near-Chandrasekhar mass WDs results in a good match to data.

astro-ph.SR↗

arXiv2013

The Effects of Variations in Nuclear Interactions on Nucleosynthesis in Thermonuclear Supernovae

The impact of nuclear physics uncertainties on nucleosynthesis in thermonuclear supernovae has not been fully explored using comprehensive and systematic studies with multiple models. To better constrain predictions of yields from these phenomena, we have performed a sensitivity study by post-processing thermodynamic histories from two different hydrodynamic, Chandrasekhar-mass explosion models. We have individually varied all input reaction and, for the first time, weak interaction rates by a factor of ten and compared the yields in each case to yields using standard rates. Of the 2305 nuclear reactions in our network, we find that the rates of only 53 reactions affect the yield of any species with an abundance of at least 10^-8 M_sun by at least a factor of two, in either model. The rates of the 12C(a,g), 12C+12C, 20Ne(a,p), 20Ne(a,g) and 30Si(p,g) reactions are among those that modify the most yields when varied by a factor of ten. From the individual variation of 658 weak interaction rates in our network by a factor of ten, only the stellar 28Si(b+)28Al, 32S(b+)32P and 36Ar(b+)36Cl rates significantly affect the yields of species in a model. Additional tests reveal that reaction rate changes over temperatures T > 1.5 GK have the greatest impact, and that ratios of radionuclides that may be used as explosion diagnostics change by a factor of less than two from the variation of individual rates by a factor of 10. Nucleosynthesis in the two adopted models is relatively robust to variations in individual nuclear reaction and weak interaction rates. Laboratory measurements of a limited number of reactions would help to further constrain predictions. As well, we confirm the need for a consistent treatment for relevant stellar weak interaction rates since simultaneous variation of these rates (as opposed to individual variation) has a significant effect on yields in our models.

astro-ph.SR↗

arXiv2013

Spectral modelling of the "Super-Chandra" Type Ia SN 2009dc - testing a 2 M_sun white dwarf explosion model and alternatives

Extremely luminous, super-Chandrasekhar (SC) Type Ia Supernovae (SNe Ia) are as yet an unexplained phenomenon. We analyse a well-observed SN of this class, SN 2009dc, by modelling its photospheric spectra with a spectral synthesis code, using the technique of 'Abundance Tomography'. We present spectral models based on different density profiles, corresponding to different explosion scenarios, and discuss their consistency. First, we use a density structure of a simulated explosion of a 2 M_sun rotating C-O white dwarf (WD), which is often proposed as a possibility to explain SC SNe Ia. Then, we test a density profile empirically inferred from the evolution of line velocities (blueshifts). This model may be interpreted as a core-collapse SN with an ejecta mass ~ 3 M_sun. Finally, we calculate spectra assuming an interaction scenario. In such a scenario, SN 2009dc would be a standard WD explosion with a normal intrinsic luminosity, and this luminosity would be augmented by interaction of the ejecta with a H-/He-poor circumstellar medium. We find that no model tested easily explains SN 2009dc. With the 2 M_sun WD model, our abundance analysis predicts small amounts of burning products in the intermediate-/high-velocity ejecta (v > 9000 km/s). However, in the original explosion simulations, where the nuclear energy release per unit mass is large, burned material is present at high v. This contradiction can only be resolved if asymmetries strongly affect the radiative transfer or if C-O WDs with masses significantly above 2 M_sun exist. In a core-collapse scenario, low velocities of Fe-group elements are expected, but the abundance stratification in SN 2009dc seems 'SN Ia-like'. The interaction-based model looks promising, and we have some speculations on possible progenitor configurations. However, radiation-hydro simulations will be needed to judge whether this scenario is realistic at all.

astro-ph.SR↗

arXiv2012

Three-dimensional delayed-detonation models with nucleosynthesis for Type Ia supernovae

We present results for a suite of fourteen three-dimensional, high resolution hydrodynamical simulations of delayed-detonation modelsof 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 database 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 (DDT) 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 central density of 2.9 x 10^9 gcc, plus in addition one high central density (5.5 x 10^9 gcc), and one low central density (1.0 x 10^9 gcc) rendition of the 100 ignition kernel configuration. For each simulation we determined detailed nucleosynthetic yields by post-processing 10^6 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 solar masses. 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 (~3,000 - 10,000 km/s) in a shell surrounding a 56Ni-rich core. The models further predict relatively low velocity oxygen and carbon, with typical minimum velocities around 4,000 and 10,000 km/s, respectively.

astro-ph.SR↗

arXiv2012

The First Maximum-Light Ultraviolet through Near-Infrared Spectrum of a Type Ia Supernova

We present the first maximum-light ultraviolet (UV) through near-infrared (NIR) Type Ia supernova (SN Ia) spectrum. This spectrum of SN 2011iv was obtained nearly simultaneously by the Hubble Space Telescope at UV/optical wavelengths and the Magellan Baade telescope at NIR wavelengths. These data provide the opportunity to examine the entire maximum-light SN Ia spectral-energy distribution. Since the UV region of a SN Ia spectrum is extremely sensitive to the composition of the outer layers of the explosion, which are transparent at longer wavelengths, this unprecedented spectrum can provide strong constraints on the composition of the SN ejecta, and similarly the SN explosion and progenitor system. SN 2011iv is spectroscopically normal, but has a relatively fast decline (Delta m_15 (B) = 1.69 +/- 0.05 mag). We compare SN 2011iv to other SNe Ia with UV spectra near maximum light and examine trends between UV spectral properties, light-curve shape, and ejecta velocity. We tentatively find that SNe with similar light-curve shapes but different ejecta velocities have similar UV spectra, while those with similar ejecta velocities but different light-curve shapes have very different UV spectra. Through a comparison with explosion models, we find that both a solar-metallicity W7 and a zero-metallicity delayed-detonation model provide a reasonable fit to the spectrum of SN 2011iv from the UV to the NIR.

astro-ph.CO↗

arXiv2011

Asymmetry and the Nucleosynthetic Signature of Nearly Edge-Lit Detonation in White Dwarf Cores

Most of the leading explosion scenarios for Type Ia supernovae involve the nuclear incineration of a white dwarf star through a detonation wave. Several scenarios have been proposed as to how this detonation may actually occur, but the exact mechanism and environment in which it takes place remain unknown. We explore the effects of an off-center initiated detonation on the spatial distribution of the nucleosynthetic yield products in a toy model -- a pre-expanded near Chandrasekhar-mass white dwarf. We find that a single-point near edge-lit detonation results in asymmetries in the density and thermal profiles, notably the expansion timescale, throughout the supernova ejecta. We demonstrate that this asymmetry of the thermodynamic trajectories should be common to off-center detonations where a small amount of the star is burned prior to detonation. The sensitivity of the yields on the expansion timescale results in an asymmetric distribution of the elements synthesized as reaction products. We tabulate the shift in the center of mass of the various elements produced in our model supernova and find an odd-even pattern for elements past silicon. Our calculations show that off-center single-point detonations in carbon-oxygen white dwarfs are marked by significant composition asymmetries in their remnants which bear potentially observable signatures in both velocity and coordinate space, including an elemental nickel mass fraction which varies by a factor of two to three from one side of the remnant to the other.

astro-ph.SR↗

arXiv2009

Initiation of the detonation in the gravitationally confined detonation model of Type Ia supernovae

We study the initiation of the detonation in the gravitationally confined detonation (GCD) model of Type Ia supernovae (SNe Ia). Initiation of the detonation occurs spontaneously in a region where the length scale of the temperature gradient extending from a flow (in which carbon burning is already occurring) into unburned fuel is commensurate to the range of critical length scales which have been derived from 1D simulations that resolve the initiation of a detonation. By increasing the maximum resolution in a truncated cone that encompasses this region, beginning somewhat before initiation of the detonation occurs, we successfully simulate in situ the first gradient-initiated detonation in a whole-star simulation. The detonation emerges when a compression wave overruns a pocket of fuel situated in a Kelvin-Helmholtz cusp at the leading edge of the inwardly directed jet of burning carbon. The compression wave pre-conditions the temperature in the fuel in such a way that the Zel'dovich gradient mechanism can operate and a detonation ensues. We explore the dependence of the length scale of the temperature gradient on spatial resolution and discuss the implications for the robustness of this detonation mechanism. We find that the time and the location at which initiation of the detonation occurs varies with resolution. In particular, initiation of a detonation had not yet occurred in our highest resolution simulation by the time we ended the simulation because of the computational demand it required. We suggest that the turbulent shear layer surrounding the inwardly directed jet provides the most favorable physical conditions, and therefore the most likely location, for initiation of a detonation in the GCD model.

astro-ph.SR↗

arXiv2009

Spontaneous Initiation of Detonations in White Dwarf Environments: Determination of Critical Sizes

Some explosion models for Type Ia supernovae (SN Ia), such as the gravitationally confined detonation (GCD) or the double detonation sub-Chandrasekhar (DDSC) models, rely on the spontaneous initiation of a detonation in the degenerate C/O material of a white dwarf. The length scales pertinent to the initiation of the detonation are notoriously unresolved in multi-dimensional stellar simulations, prompting the use of results of 1D simulations at higher resolution, such as the ones performed for this work, as guidelines for deciding whether or not conditions reached in the higher dimensional full star simulations successfully would lead to the onset of a detonation. Spontaneous initiation relies on the existence of a suitable gradient in self-ignition (induction) times of the fuel, which we set up with a spatially localized non-uniformity of temperature -- a hot spot. We determine the critical (smallest) sizes of such hot spots that still marginally result in a detonation in white dwarf matter by integrating the reactive Euler equations with the hydrodynamics code FLASH. We quantify the dependences of the critical sizes of such hot spots on composition, background temperature, peak temperature, geometry, and functional form of the temperature disturbance, many of which were hitherto largely unexplored in the literature. We discuss the implications of our results in the context of modeling of SNe Ia.

astro-ph.SR↗