Post-shock Layer Research Articles

Prospects of Fast Flavor Neutrino Conversion in Rotating Core-collapse Supernovae

Abstract There is mounting evidence that neutrinos undergo fast flavor conversion (FFC) in core-collapse supernova (CCSN). In this paper, we investigate the roles of stellar rotation on the occurrence of FFC by carrying out axisymmetric CCSN simulations with full Boltzmann neutrino transport. Our result suggests that electron neutrino lepton number (ELN) angular crossings, which are the necessary and sufficient condition to trigger FFC, preferably occur in the equatorial region for rotating CCSNe. By scrutinizing the neutrino–matter interaction and neutrino radiation field, we find some pieces of evidence that the stellar rotation facilitates the occurrence of FFC. The low-electron-fraction region in the post-shock layer expands by centrifugal force, enhancing the disparity of neutrino absorption between electron-type neutrinos (ν e) and their anti-particles ( ν ¯ e ). This has a significant impact on the angular distribution of neutrinos in momentum space, in which ν e tends to be more isotropic than ν ¯ e ; consequently, ELN crossings emerge. The ELN crossing found in this study is clearly associated with rotation, which motivates further investigation on how the subsequent FFC influences explosion dynamics, nucleosynthesis, and neutrino signals in rotating CCSNe.

Gravitational-wave signals from 3D supernova simulations with different neutrino-transport methods

ABSTRACT We compare gravitational-wave (GW) signals from eight 3D simulations of core-collapse supernovae, using two different progenitors with zero-age main-sequence masses of 9 and 20 solar masses (M⊙). The collapse of each progenitor was simulated four times, at two different grid resolutions and with two different neutrino transport methods, using the aenus-alcar code. The main goal of this study is to assess the validity of recent concerns that the so-called ‘Ray-by-Ray+’ (RbR+) approximation is problematic in core-collapse simulations and can adversely affect theoretical GW predictions. Therefore, signals from simulations using RbR+ are compared to signals from corresponding simulations using a fully multidimensional (FMD) transport scheme. The 9 M⊙ progenitor successfully explodes, whereas the 20 M⊙ model does not. Both the standing accretion shock instability and hot-bubble convection develop in the post-shock layer of the non-exploding models. In the exploding models, neutrino-driven convection in the post-shock flow is established around 100 ms after core bounce and lasts until the onset of shock revival. We can, therefore, judge the impact of the numerical resolution and neutrino transport under all conditions typically seen in non-rotating core-collapse simulations. We find excellent qualitative agreement in all GW features. We find minor quantitative differences between simulations, but find no systematic differences between simulations using different transport schemes. Resolution-dependent differences in the hydrodynamic behaviour of low-resolution and high-resolution models have a greater impact on the GW signals than consequences of the different transport methods. Furthermore, increasing the resolution decreases the discrepancies between models with different neutrino transport.

Self-gravitating filament formation from shocked flows: velocity gradients across filaments

ABSTRACT In typical environments of star-forming clouds, converging supersonic turbulence generates shock-compressed regions, and can create strongly magnetized sheet-like layers. Numerical magnetohydrodynamic simulations show that within these post-shock layers, dense filaments and embedded self-gravitating cores form via gathering material along the magnetic field lines. As a result of the preferred-direction mass collection, a velocity gradient perpendicular to the filament major axis is a common feature seen in simulations. We show that this prediction is in good agreement with recent observations from the CARMA Large Area Star Formation Survey (CLASSy), from which we identified several filaments with prominent velocity gradients perpendicular to their major axes. Highlighting a filament from the north-west part of Serpens South, we provide both qualitative and quantitative comparisons between simulation results and observational data. In particular, we show that the dimensionless ratio Cv ≡ Δvh2/(GM/L), where Δvh is half of the observed perpendicular velocity difference across a filament, and M/L is the filament’s mass per unit length, can distinguish between filaments formed purely due to turbulent compression and those formed due to gravity-induced accretion. We conclude that the perpendicular velocity gradient observed in the Serpens South north-west filament can be caused by gravity-induced anisotropic accretion of material from a flattened layer. Using synthetic observations of our simulated filaments, we also propose that a density-selection effect may explain observed subfilaments (one filament breaking into two components in velocity space) as reported in recent observations.

Resolution Study for Three-dimensional Supernova Simulations with the Prometheus-Vertex Code

Abstract We present a carefully designed, systematic study of the angular resolution dependence of simulations with the Prometheus-Vertex neutrino-hydrodynamics code. Employing a simplified neutrino heating–cooling scheme in the Prometheus hydrodynamics module allows us to sample the angular resolution between 4° and 0.°5. With a newly implemented static mesh refinement (SMR) technique on the Yin-Yang grid, the angular coordinates can be refined in concentric shells, compensating for the diverging structure of the spherical grid. In contrast to previous studies with Prometheus and other codes, we find that higher angular resolution and therefore lower numerical viscosity provides more favorable explosion conditions and faster shock expansion. We discuss the possible reasons for the discrepant results. The overall dynamics seem to converge at a resolution of about 1°. Applying the SMR setup to marginally exploding progenitors is disadvantageous for the shock expansion, however, because the kinetic energy of downflows is dissipated to internal energy at resolution interfaces, leading to a loss of turbulent pressure support and a steeper temperature gradient. We also present a way to estimate the numerical viscosity on grounds of the measured turbulent kinetic energy spectrum, leading to smaller values that are better compatible with the flow behavior witnessed in our simulations than results following calculations in previous literature. Interestingly, the numerical Reynolds numbers in the turbulent, neutrino-heated postshock layer (some 10 to several hundred) are in the ballpark of expected neutrino drag effects on the relevant length scales. We provide a formal derivation and quantitative assessment of the neutrino drag terms in an appendix.

Incident shock wave and supersonic turbulent boundarylayer interactions near an expansion corner

Direct numerical simulations of incident shock wave and supersonic turbulent boundary layer interactions near an expansion corner are performed at Mach number M∞ = 2.9 and Reynolds number Re∞ = 5581 to investigate the expansion effect on the characteristic features of this phenomenon. Four expansion angles, i.e. α = 00 (flat-plate), 20, 50 and 100 are considered. The nominal impingement point of the oblique shock wave with a flow deflection angle of 120 is fixed at the onset of the expansion corner, and flow conditions are kept the same for all cases. The numerical results are in good agreement with previous experimental and numerical data. Various flow phenomena, including the flow separation, the post-shock turbulent boundary layer and the flow unsteadiness in the interaction region, have been systematically studied. Analysis of the instantaneous and mean flow fields indicates that the main effect of the expansion corner is to significantly decrease the size and three-dimensionality of the separation bubble. A modified scaling analysis is proposed for the expansion effect on the interaction length scale, and a satisfactory result is obtained. Distributions of the mean velocity, the Reynolds shear stress and the turbulent kinetic energy show that the post-shock turbulent boundary layer in the downstream region experiences a faster recovery to the equilibrium state as the expansion angle is increased. The flow unsteadiness is studied using spectral analysis and dynamic mode decomposition, and dynamically relevant modes associated with flow structures originated from the incoming turbulent boundary layer are clearly identified. At large expansion angle (α=100), the unsteadiness of the separated shock is dominated by medium frequencies motions, and no low frequency unsteadiness is observed. The present study confirms that the driving mechanism of the low frequency unsteadiness is strongly related to the separated shock and the detached shear layer.

Features of Accretion-phase Gravitational-wave Emission from Two-dimensional Rotating Core-collapse Supernovae

Abstract We explore the influence of progenitor mass and rotation on the gravitational-wave (GW) emission from core-collapse supernovae, during the postbounce, preexplosion, accretion phase. We present the results from 15 two-dimensional (2D) neutrino radiation-hydrodynamic simulations from initial stellar collapse to ∼300 ms after core bounce. We examine the features of the GW signals for four zero-age main sequence (ZAMS) progenitor masses ranging from 12 M ⊙ to 60 M ⊙ and four core rotation rates from 0 to 3 rad s−1. We find that GW strain immediately around core bounce is fairly independent of ZAMS mass and—consistent with previous findings—that it is more heavily dependent on the core angular momentum. At later times, all nonrotating progenitors exhibit loud GW emission, which we attribute to vibrational g-modes of the protoneutron star (PNS) excited by convection in the postshock layer and the standing accretion shock instability (SASI). We find that increasing rotation rates results in muting of the accretion-phase GW signal due to centrifugal effects that inhibit convection in the postshock region, quench the SASI, and slow the rate at which the PNS peak vibrational frequency increases. Additionally, we verify the efficacy of our approximate general relativistic (GR) effective potential treatment of gravity by comparing our core bounce GW strains with the recent 2D GR results of other groups.

Gravitational waves from 3D core-collapse supernova models: The impact of moderate progenitor rotation

We present predictions for the gravitational-wave (GW) emission of three-dimensional supernova (SN) simulations performed for a 15 solar-mass progenitor with the Prometheus-Vertex code using energy-dependent, three-flavor neutrino transport. The progenitor adopted from stellar evolution calculations including magnetic fields had a fairly low specific angular momentum (j_Fe <~ 10^{15} cm^2/s) in the iron core (central angular velocity ~0.2 rad/s), which we compared to simulations without rotation and with artificially enhanced rotation (j_Fe <~ 2*10^{16} cm^2/s; central angular velocity ~0.5 rad/s). Our results confirm that the time-domain GW signals of SNe are stochastic, but possess deterministic components with characteristic patterns at low frequencies (<~200 Hz), caused by mass motions due to the standing accretion shock instability (SASI), and at high frequencies, associated with gravity-mode oscillations in the surface layer of the proto-neutron star (PNS). Non-radial mass motions in the post-shock layer as well as PNS convection are important triggers of GW emission, whose amplitude scales with the power of the hydrodynamic flows. There is no monotonic increase of the GW amplitude with rotation, but a clear correlation with the strength of SASI activity. Our slowly rotating model is a fainter GW emitter than the non-rotating model because of weaker SASI activity and damped convection in the post-shock layer and PNS. In contrast, the faster rotating model exhibits a powerful SASI spiral mode during its transition to explosion, producing the highest GW amplitudes with a distinctive drift of the low-frequency emission peak from ~80-100 Hz to ~40-50 Hz. This migration signifies shock expansion, whereas non-exploding models are discriminated by the opposite trend.

The Early Stage of Molecular Cloud Formation by Compression of Two-phase Atomic Gases

Abstract We investigate the formation of molecular clouds from atomic gas by using three-dimensional magnetohydrodynamic simulations, including non-equilibrium chemical reactions and heating/cooling processes. We consider super-Alfvénic head-on colliding flows of atomic gas possessing the two-phase structure that consists of H i clouds and surrounding warm diffuse gas. We examine how the formation of molecular clouds depends on the angle θ between the upstream flow and the mean magnetic field. We find that there is a critical angle θ cr above which the shock-amplified magnetic field controls the post-shock gas dynamics. If the atomic gas is compressed almost along the mean magnetic field (θ ≪ θ cr), super-Alfvénic anisotropic turbulence is maintained by the accretion of the highly inhomogeneous upstream atomic gas. As a result, a greatly extended turbulence-dominated post-shock layer is generated. Around θ ∼ θ cr, the shock-amplified magnetic field weakens the post-shock turbulence, leading to a dense post-shock layer. For θ ≫ θ cr, the strong magnetic pressure suppresses the formation of cold dense clouds. Efficient molecular cloud formation is expected if θ is less than a few times θ cr. Developing an analytic model and performing a parameter survey, we obtain an analytic formula for the critical angle as a function of the mean density, collision speed, and field strength of the upstream atomic gas. The critical angle is found to be less than ∼15° as long as the field strength is larger than 1 μG, indicating that the probability of occurrence of compression with θ &lt; θ cr is limited if shock waves come from various directions.

Evolution of the surface magnetic field of rotating proto-neutron stars

We study the evolution of the field on the surface of proto-neutron stars in the immediate aftermath of stellar core collapse by analyzing the results of self-consistent, axisymmetric simulations of the cores of rapidly rotating high-mass stars. To this end, we compare the field topology and the angular spectra of the poloidal and toroidal field components over a time of about one seconds for cores. Both components are characterized by a complex geometry with high power at intermediate angular scales. The structure is mostly the result of the accretion of magnetic flux embedded in the matter falling through the turbulent post-shock layer onto the PNS. Our results may help to guide further studies of the long-term magneto-thermal evolution of proto-neutron stars. We find that the accretion of stellar progenitor layers endowed with low or null magnetization bury the magnetic field on the PNS surface very effectively.

Numerical and experimental analysis of spallation phenomena

The spallation phenomenon was studied through numerical analysis using a coupled Lagrangian particle tracking code and a hypersonic aerothermodynamics computational fluid dynamics solver. The results show that carbon emission from spalled particles results in a significant modification of the gas composition of the post-shock layer. Results from a test campaign at the NASA Langley HYMETS facility are presented. Using an automated image processing of short exposure images, two-dimensional velocity vectors of the spalled particles were calculated. In a 30-s test at 100 W/cm2 of cold-wall heat flux, more than 722 particles were detected, with an average velocity of 110 m/s.

PRESTELLAR CORE FORMATION, EVOLUTION, AND ACCRETION FROM GRAVITATIONAL FRAGMENTATION IN TURBULENT CONVERGING FLOWS

We investigate prestellar core formation and accretion based on three-dimensional hydrodynamic simulations. Our simulations represent local $\sim 1$pc regions within giant molecular clouds where a supersonic turbulent flow converges, triggering star formation in the post-shock layer. We include turbulence and self-gravity, applying sink particle techniques, and explore a range of inflow Mach number ${\cal M}=2-16$. Two sets of cores are identified and compared: $t_1$-cores are identified of a time snapshot in each simulation, representing dense structures in a single cloud map; $t_\mathrm{coll}$-cores are identified at their individual time of collapse, representing the initial mass reservoir for accretion. We find that cores and filaments form and evolve at the same time. At the stage of core collapse, there is a well-defined, converged characteristic mass for isothermal fragmentation that is comparable to the critical Bonner-Ebert mass at the post-shock pressure. The core mass functions (CMFs) of $t_\mathrm{coll}$-cores show a deficit of high-mass cores ($\gtrsim 7M_\odot$) compared to the observed stellar initial mass function (IMF). However, the CMFs of $t_1$-cores are similar to the observed CMFs and include many low-mass cores that are gravitationally stable. The difference between $t_1$-cores and $t_\mathrm{coll}$-cores suggests that the full sample from observed CMFs may not evolve into protostars. Individual sink particles accrete at a roughly constant rate throughout the simulations, gaining one $t_\mathrm{coll}$-core mass per free-fall time even after the initial mass reservoir is accreted. High-mass sinks gain proportionally more mass at late times than low-mass sinks. There are outbursts in accretion rates, resulting from clumpy density structures falling into the sinks.

Magnetic field amplification and magnetically supported explosions of collapsing, non-rotating stellar cores

We study the amplification of magnetic fields in the collapse and the post-bounce evolution of the core of a non-rotating star of 15 solar masses in axisymmetry. To this end, we solve the coupled equations of magnetohydrodynamics and neutrino transport in the two-moment approximation. The pre-collapse magnetic field is strongly amplified by compression in the infall. Initial fields of the order of 1010 G translate into proto-neutron star fields similar to the ones observed in pulsars, while stronger initial fields yield magnetar-like final field strengths. After core bounce, the field is advected through the hydrodynamically unstable neutrino-heating layer, where non-radial flows due to convection and the standing accretion shock instability amplify the field further. Consequently, the resulting amplification factor of order five is the result of the number of small-eddy turnovers taking place within the time scale of advection through the post-shock layer. Due to this limit, most of our models do not reach equipartition between kinetic and magnetic energy and, consequently, evolve similarly to the non-magnetic case, exploding after about 800 ms when a single or few high-entropy bubbles persist over several dynamical time scales. In the model with the strongest initial field we studied, \$10^{12}\$ G, for which equipartition between flow and field is achieved, the magnetic tension favours a much earlier development of such long-lived high-entropy bubbles and enforces a fairly ordered large-scale flow pattern. Consequently, this model, after exhibiting very regular shock oscillations, explodes much earlier than non-magnetic ones.

SASI ACTIVITY IN THREE-DIMENSIONAL NEUTRINO-HYDRODYNAMICS SIMULATIONS OF SUPERNOVA CORES

ABSTRACT The relevance of the standing accretion shock instability (SASI) compared to neutrino-driven convection in three-dimensional (3D) supernova-core environments is still highly controversial. Studying a 27 M ☉ progenitor, we demonstrate, for the first time, that violent SASI activity can develop in 3D simulations with detailed neutrino transport despite the presence of convection. This result was obtained with the Prometheus-Vertex code with the same sophisticated neutrino treatment so far used only in one-dimensional and two-dimensional (2D) models. While buoyant plumes initially determine the nonradial mass motions in the postshock layer, bipolar shock sloshing with growing amplitude sets in during a phase of shock retraction and turns into a violent spiral mode whose growth is only quenched when the infall of the Si/SiO interface leads to strong shock expansion in response to a dramatic decrease of the mass accretion rate. In the phase of large-amplitude SASI sloshing and spiral motions, the postshock layer exhibits nonradial deformation dominated by the lowest-order spherical harmonics (ℓ = 1, m = 0, ±1) in distinct contrast to the higher multipole structures associated with neutrino-driven convection. We find that the SASI amplitudes, shock asymmetry, and nonradial kinetic energy in three dimensions can exceed those of the corresponding 2D case during extended periods of the evolution. We also perform parameterized 3D simulations of a 25 M ☉ progenitor, using a simplified, gray neutrino transport scheme, an axis-free Yin-Yang grid, and different amplitudes of random seed perturbations. They confirm the importance of the SASI for another progenitor, its independence of the choice of spherical grid, and its preferred growth for fast accretion flows connected to small shock radii and compact proto-neutron stars as previously found in 2D setups.

Supermassive black hole formation by cold accretion shocks in the first galaxies

We propose a new scenario for supermassive star (SMS;>10^5Msun) formation in shocked regions of colliding cold accretion flows near the centers of first galaxies. Recent numerical simulations indicate that assembly of a typical first galaxy with virial temperature (~10^4K) proceeds via cold and dense flows penetrating deep to the center, where the supersonic streams collide each other to develop a hot and dense (~10^4K, ~10^3/cc) shocked gas. The post-shock layer first cools by efficient Ly alpha emission and contracts isobarically until 8000K. Whether the layer continues the isobaric contraction depends on the density at this moment: if the density is high enough for collisionally exciting H2 rovibrational levels (>10^4/cc), enhanced H2 collisional dissociation suppresses the gas to cool further. In this case, the layer fragments into massive (>10^5Msun) clouds, which collapse isothermally (~8000K) by the Ly alpha cooling without subsequent fragmentation. As an outcome, SMSs are expected to form and evolve eventually to seeds of supermassive black holes (SMBH). By calculating thermal evolution of the post-shock gas, we delimit the range of post-shock conditions for the SMS formation, which can be expressed as: T>6000K/(n/10^4/cc) for n<10^4/cc and T>5000-6000K for n>10^4/cc, depending somewhat on initial ionization degree. We found that metal enrichment does not affect the above condition for metallicity below 10^-3Zsun if metals are in the gas phase, while condensation of several percent of metals into dust decreases this critical value of metallicity by an order of magnitude. Unlike the previously proposed scenario for SMS formation, which postulates extremely strong ultraviolet radiation to quench H2 cooling, our scenario naturally explains the SMBH seed formation in the assembly process of the first galaxies, even without such a strong radiation.

DENSE CORE FORMATION IN SUPERSONIC TURBULENT CONVERGING FLOWS

We use numerical hydrodynamic simulations to investigate prestellar core formation in the dynamic environment of giant molecular clouds, focusing on planar post-shock layers produced by colliding turbulent flows. A key goal is to test how core evolution and properties depend on the velocity dispersion in the parent cloud; our simulation suite consists of 180 models with inflow Mach numbers Ma=v/c_s=1.1-9. At all Mach numbers, our models show that turbulence and self-gravity collect gas within post-shock regions into filaments at the same time as overdense areas within these filaments condense into cores. This morphology, together with the subsonic velocities we find inside cores, is similar to observations. We extend previous results showing that core collapse develops in an ``outside-in'' manner, with density and velocity approaching the Larson-Penston asymptotic solution. The time for the first core to collapse varies as 1/sqrt(v), consistent with analytic estimates. Core building takes 10 times as long as core collapse, consistent with observed prestellar core lifetimes. Core shapes change from oblate to prolate as they evolve. To define cores, we use isosurfaces of the gravitational potential. We compare to cores defined using the potential computed from projected surface density, finding good agreement for core masses and sizes; this offers a new way to identify cores in observed maps. Cores with masses varying by three orders of magnitude (0.05 - 50 M_sun) are identified in our simulations. Stability analysis of post-shock layers predicts that the first core to collapse will have mass M \propto v^-1/2, and that the minimum mass for cores formed at late times will have M\propto v^-1. From our simulations, the median mass lies between these two relations.

Statistical inference in the presence of an inclination effect in laboratory radiative shock experiments

A laser-driven experiment produces images of dense shocked material by x-ray transmission. The post-shock material is sufficiently dense that no significant signal passes through the dense layer, and therefore the shock compression cannot be directly measured by comparing transmitted intensities. One could try to determine the shock compression ratio by observing the ratio of the total distance travelled by the shock to the dense post-shock layer width, but small deviations of the angle of the shock with respect to the angle of imaging create large asymmetric errors in observation. A statistical approach to recovering shock compression by appropriately combining data from several experiments is developed, using fits to a simple model for the shock and shock tube geometry.

Near-Ultraviolet Emission Spectroscopy During an Airborne Observation of the Stardust Reentry

Thermal radiation of the heatshield and the emission of the postshock layer around the Stardust capsule, during its reentry, were detected by a NASA-led observation campaign aboard NASA’s DC-8 airborne observatory involving teams from several nations. The German SLIT experiment used a conventional spectrometer, in a Czerny–Turner configuration (300 mm focal length and a 600 lines=mm grating), fed by fiber optics, to cover a wavelength range from 324 to 456 nm with a pixel resolution of 0.08 nm. The reentering spacecraft was tracked manually using a camerawith a viewangle of 20 deg, and light from the capsulewas collected using a smallmirror telescopewith a view angle of only 0.45 deg. Data were gathered with a measurement frequency of 5 Hz in a 30-s time interval around the point of maximum heating until the capsule left the field of view. The emission of carbon nitride (as a major ablation product), N 2 and different atoms were monitored successfully during that time. Because of the nature of the experimental setup, spatial resolution of the radiation field was not possible. Therefore, all measured values represent an integration of radiation from the visible part of the glowing heatshield, and from the plasma in the postshock region. Further, due to challenges in tracking, not every spectrum gathered contained data. Themeasured spectra can be split up into two parts: 1) continuum spectra, which represent a superposition of the heatshield radiation and the continuum radiation of particles due to microspallation in the plasma, and 2) line spectra from the plasma in the shock layer. Planck temperatures (interpreted as the surface temperatures of the Stardust heatshield) were determined assuming either a constant surface temperature, or a temperature distribution deduced from numerical simulation. The constant surface temperatures are in good agreement with numerical simulations, but the peak values at the stagnation point are significantly lower than those in the numerical simulation if a temperature distribution over the surface is assumed. Emission bands of carbon nitride and N 2 were tracked along the visible trajectory and compared with a spectral simulation with satisfying agreement. Values for the integrated radiation of the transitions of interest for these species were extracted from this comparison.

HYDRODYNAMICAL NEUTRON STAR KICKS IN THREE DIMENSIONS

Using three-dimensional (3D) simulations of neutrino-powered supernova explosions we show that the hydrodynamical kick scenario proposed by Scheck et al. on the basis of two-dimensional (2D) models can yield large neutron star (NS) recoil velocities also in 3D. Although the shock stays relatively spherical, standing accretion-shock and convective instabilities lead to a globally asymmetric mass and energy distribution in the postshock layer. An anisotropic momentum distribution of the ejecta is built up only after the explosion sets in. Total momentum conservation implies the acceleration of the NS on a timescale of 1-3 seconds, mediated mainly by long-lasting, asymmetric accretion downdrafts and the anisotropic gravitational pull of large inhomogeneities in the ejecta. In a limited set of 15 solar-mass models with an explosion energy of about 10^51 erg this stochastic mechanism is found to produce kicks from <100 km/s to >500 km/s, and >1000 km/s seem possible. Strong rotational flows around the accreting NS do not develop in our collapsing, non-rotating progenitors. The NS spins therefore remain low with estimated periods of about 500-1000 ms and no alignment with the kicks.

Non-spherical core collapse supernovae

(abridged) We study the hydrodynamic evolution of a non-spherical core-collapse supernova in two spatial dimensions. We find that our model displays a strong tendency to expand toward the pole. We demonstrate that this expansion is a physical property of the low-mode, SASI instability. The SASI leaves behind a large lateral velocity gradient in the post shock layer which affects the evolution for minutes and hours later. This results in a prolate deformation of the ejecta and a fast advection of Ni-rich material from moderate latitudes to the polar regions. This effect might actually be responsible for the global asymmetry of the nickel lines in SN 1987A. The simulations demonstrate that significant radial and lateral motions in the post-shock region, produced by convective overturn and the SASI during the early explosion phase, contribute to the evolution for minutes and hours after shock revival. They lead to both later clump formation, and a significant prolate deformation of the ejecta which are observed even as late as one week after the explosion. As pointed out recently by Kjaer et al., such an ejecta morphology is in good agreement with the observational data of SN 1987A. Systematic future studies are needed to investigate how the SASI-induced late-time lateral expansion depends on the dominant mode of the SASI, and to which extent it is affected by the dimensionality of the simulations. The impact on and importance of the SASI for the distribution of iron group nuclei and the morphology of the young SNR argues for future three-dimensional explosion and post-explosion studies on singularity-free grids that cover the entire sphere. Given the results of our 2D resolution study, present 3D simulations must be regarded as underresolved, and their conclusions must be verified by a proper numerical convergence analysis in three dimensions.

THREE-DIMENSIONAL SIMULATIONS OF MIXING INSTABILITIES IN SUPERNOVA EXPLOSIONS

We present the first three-dimensional (3D) simulations of the large-scale mixing that takes place in the shock-heated stellar layers ejected in the explosion of a 15.5 solar-mass blue supergiant star. The outgoing supernova shock is followed from its launch by neutrino heating until it breaks out from the stellar surface more than two hours after the core collapse. Violent convective overturn in the post-shock layer causes the explosion to start with significant asphericity, which triggers the growth of Rayleigh-Taylor (RT) instabilities at the composition interfaces of the exploding star. Deep inward mixing of hydrogen (H) is found as well as fast-moving, metal-rich clumps penetrating with high velocities far into the H-envelope of the star as observed, e.g., in the case of SN 1987A. Also individual clumps containing a sizeable fraction of the ejected iron-group elements (up to several 0.001 solar masses) are obtained in some models. The metal core of the progenitor is partially turned over with Ni-dominated fingers overtaking oxygen-rich bullets and both Ni and O moving well ahead of the material from the carbon layer. Comparing with corresponding 2D (axially symmetric) calculations, we determine the growth of the RT fingers to be faster, the deceleration of the dense metal-carrying clumps in the He and H layers to be reduced, the asymptotic clump velocities in the H-shell to be higher (up to ~4500 km/s for the considered progenitor and an explosion energy of 10^{51} ergs, instead of <2000 km/s in 2D), and the outward radial mixing of heavy elements and inward mixing of hydrogen to be more efficient in 3D than in 2D. We present a simple argument that explains these results as a consequence of the different action of drag forces on moving objects in the two geometries. (abridged)