Abstract:
We study the dependence of the delayed neutrino-heating mechanism for core-collapse supernovae on the equation of state. Using a simplified treatment of the neutrino physics with a parameterized neutrino luminosity, we explore the relationship between explosion time, mass accretion rate, and neutrino luminosity for a 15 Msun progenitor in 1D and 2D. We test three different equations of state commonly used in core-collapse simulations: the models of Lattimer & Swesty (1991) with incompressibility of 180 MeV and 220 MeV, and the model of Shen et al. (1998), in order of increasing stiffness. We find that for a given neutrino luminosity the time after bounce until explosion increases with the stiffness of the equation of state: the Lattimer & Swesty EOS explode more easily than that of Shen et al. We find this holds in both 1D and 2D, while for all models explosions are obtained more easily in 2D than in 1D. We also discuss the relevance of approximate instability criteria to realistic simulations.

Abstract:
We present 1D, 2D, and 3D hydrodynamical simulations of core-collapse supernovae including a parameterized neutrino heating and cooling scheme in order to investigate the critical core neutrino luminosity (L_crit) required for explosion. In contrast to some previous works, we find that 3D simulations explode later than 2D simulations, and that L_crit at fixed mass accretion rate is somewhat higher in 3D than in 2D. We find, however, that in 2D L_crit increases as the numerical resolution of the simulation increases. In contrast to some previous works, we argue that the average entropy of the gain region is in fact not a good indicator of explosion but is rather a reflection of the greater mass in the gain region in 2D. We compare our simulations to semi-analytic explosion criteria and examine the nature of the convective motions in 2D and 3D. We discuss the balance between neutrino-driven-buoyancy and drag forces. In particular, we show that the drag force will be proportional to a buoyant plume's surface area while the buoyant force is proportional to a plume's volume and, therefore, plumes with greater volume-to-surface area ratios will rise more quickly. We show that buoyant plumes in 2D are inherently larger, with greater volume-to-surface area ratios, than plumes in 3D. In the scenario that the supernova shock expansion is dominated by neutrino-driven buoyancy, this balance between buoyancy and drag forces may explain why 3D simulations explode later than 2D simulations and why L_crit increases with resolution. Finally, we provide a comparison of our results with other calculations in the literature.

Abstract:
Three-dimensional simulations of core-collapse supernovae are granting new insight into the as-yet uncertain mechanism that drives successful explosions. While there is still debate about whether explosions are obtained more easily in 3D than in 2D, it is undeniable that there exist qualitative and quantitative differences between the results of 3D and 2D simulations. We present an extensive set of high-resolution one-, two-, and three-dimensional core-collapse supernova simulations with multispecies neutrino leakage carried out in two different progenitors. Our simulations confirm the results of Couch (2013) indicating that 2D explodes more readily than 3D. We argue that this is due to the inadequacies of 2D to accurately capture important aspects of the three-dimensional dynamics. We find that without artificially enhancing the neutrino heating rate we do not obtain explosions in 3D. We examine the development of neutrino-driven convection and the standing accretion shock instability and find that, in separate regimes, either instability can dominate. We find evidence for growth of the standing accretion shock instability for both 15-$M_\odot$ and 27-$M_\odot$ progenitors, however, it is weaker in 3D exploding models. The growth rate of both instabilities is artificially enhanced along the symmetry axis in 2D as compared with our axis-free 3D Cartesian simulations. Our work highlights the growing consensus that core-collapse supernovae must be studied in 3D if we hope to solve the mystery of how the explosions are powered.

Abstract:
Multi-dimensional simulations of advanced nuclear burning stages of massive stars suggest that the Si/O layers of presupernova stars harbor large deviations from the spherical symmetry typically assumed for presupernova stellar structure. We carry out three-dimensional core-collapse supernova simulations with and without aspherical velocity perturbations to assess their potential impact on the supernova hydrodynamics in the stalled shock phase. Our results show that realistic perturbations can qualitatively alter the postbounce evolution, triggering an explosion in a model that fails to explode without them. This finding underlines the need for a multi-dimensional treatment of the presupernova stage of stellar evolution.

Abstract:
We apply the mathematical formalism of vector spherical harmonics decomposition to convective stellar velocity fields from multi-dimensional hydrodynamics simulations, and show that the resulting power spectra furnish a robust and stable statistical description of stellar convective turbulence. Analysis of the power spectra help identify key physical parameters of the convective process such as the dominant scale of the turbulent motions that influence the structure of massive evolved pre-supernova stars. We introduce the numerical method that can be used to calculate vector spherical harmonics power spectra from 2D and 3D convective shell simulation data. Using this method we study the properties of oxygen shell burning and convection for a 15 Msun star simulated by the hydrodynamics code FLASH in 2D and 3D. We discuss the importance of realistic initial conditions to achieving successful core-collapse supernova explosions in multi-dimensional simulations. We show that the calculated power spectra can be used to generate realizations of the velocity fields of pre-supernova convective shells. We find that the slope of the solenoidal mode power spectrum remains mostly constant throughout the evolution of convection in the oxygen shell in both 2D and 3D simulations. We also find that the characteristic radial scales of the convective elements are smaller in 3D than in 2D while the angular scales are larger in 3D.

Abstract:
The neutrino-heated "gain layer" immediately behind the stalled shock in a core-collapse supernova is unstable to high-Reynolds-number turbulent convection. We carry out and analyze a new set of 19 high-resolution three-dimensional (3D) simulations with a three-species neutrino leakage/heating scheme and compare with spherically-symmetric (1D) and axisymmetric (2D) simulations carried out with the same methods. We study the postbounce supernova evolution in a $15$-$M_\odot$ progenitor star and vary the local neutrino heating rate, the magnitude and spatial dependence of asphericity from convective burning in the Si/O shell, and spatial resolution. Our simulations suggest that there is a direct correlation between the strength of turbulence in the gain layer and the susceptability to explosion. 2D and 3D simulations explode at much lower neutrino heating rates than 1D simulations. This is commonly explained by the fact that nonradial dynamics allows accreting material to stay longer in the gain layer. We show that this explanation is incomplete. Our results indicate that the effective turbulent ram pressure exerted on the shock plays a crucial role by allowing multi-D models to explode at a lower postshock thermal pressure and thus with less neutrino heating than 1D models. We connect the turbulent ram pressure with turbulent energy at large scales and in this way explain why 2D simulations are erroneously exploding more easily than 3D simulations.

Abstract:
Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated. The standard formulation of multipole self-gravity suffers from two significant sources of error, which we correct in the formulation presented in this article. The first source of error is due to the numerical approximation that effectively places grid cell mass at the central point of the cell, then computes the gravitational potential at that point, resulting in a convergence failure of the multipole expansion. We describe a new scheme that avoids this problem by computing gravitational potential at cell faces. The second source of error is due to sub-optimal choice of location for the expansion center, which results in angular power at high multipole $l$ values in the gravitational field, requiring a high --- and expensive --- value of multipole cutoff \lmax. By introducing a global measure of angular power in the gravitational field, we show that the optimal coordinate for the expansion is the square-density-weighted mean location. We subject our new multipole self-gravity algorithm to two rigorous test problems: MacLaurin spheroids for which exact analytic solutions are known, and core-collapse supernovae. We show that key observables of the core-collapse simulations, particularly shock expansion, proto-neutron star motion, and momentum conservation, are extremely sensitive to the accuracy of the multipole gravity, and the accuracy of their computation is greatly improved by our reformulated solver.

Abstract:
(Abridged) In the implicit large eddy simulation (ILES) paradigm, the dissipative nature of high-resolution shock-capturing schemes is exploited to provide an implicit model of turbulence. Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear. Especially considering that the accuracy of ILES for the regime of interest in CCSN, weakly compressible and strongly anisotropic, has not been systematically assessed before. In this paper we assess the accuracy of ILES using numerical methods most commonly employed in computational astrophysics by means of a number of local simulations of driven, weakly compressible, anisotropic turbulence. We report a detailed analysis of the way in which the turbulent cascade is influenced by the numerics. Our results suggest that anisotropy and compressibility in CCSN turbulence have little effect on the turbulent kinetic energy spectrum and a Kolmogorov $k^{-5/3}$ scaling is obtained in the inertial range. We find that, on the one hand, the kinetic energy dissipation rate at large scales is correctly captured even at relatively low resolutions, suggesting that very high effective Reynolds number can be achieved at the largest scales of the simulation. On the other hand, the dynamics at intermediate scales appears to be completely dominated by the so-called bottleneck effect, \ie the pile up of kinetic energy close to the dissipation range due to the partial suppression of the energy cascade by numerical viscosity. An inertial range is not recovered until the point where relatively high resolution $\sim 512^3$, which would be difficult to realize in global simulations, is reached. We discuss the consequences for CCSN simulations.

Abstract:
Shock breakout is the earliest, readily-observable emission from a core-collapse supernova explosion. Observing supernova shock breakout may yield information about the nature of the supernova shock prior to exiting the progenitor and, in turn, about the core-collapse supernova mechanism itself. X-ray Outburst 080109, later associated with SN 2008D, is a very well-observed example of shock breakout from a core-collapse supernova. Despite excellent observational coverage and detailed modeling, fundamental information about the shock breakout, such as the radius of breakout and driver of the light curve time scale, is still uncertain. The models constructed for explaining the shock breakout emission from SN 2008D all assume spherical symmetry. We present a study of the observational characteristics of {\it aspherical} shock breakout from stripped-envelope core-collapse supernovae. We conduct two-dimensional, jet-driven supernova simulations from stripped-envelope progenitors and calculate the resulting shock breakout X-ray spectra and light curves. The X-ray spectra evolve significantly in time as the shocks expand outward and are not well-fit by single-temperature and radius black bodies. The time scale of the X-ray burst light curve of the shock breakout is related to the shock crossing time of the progenitor, not the much shorter light crossing time that sets the light curve time scale in spherical breakouts. This could explain the long shock breakout light curve time scale observed for XRO 080109/SN 2008D.

Abstract:
We present axisymmetric hydrodynamical simulations of the long-term accretion of a rotating GRB progenitor star, a "collapsar," onto the central compact object. The simulations were carried out with the adaptive mesh refinement code FLASH in two spatial dimensions and with an explicit shear viscosity. The evolution of the central accretion rate exhibits phases reminiscent of the long GRB gamma-ray and X-ray light curve, which lends support to the proposal that the luminosity is modulated by the central accretion rate. After a few tens of seconds, an accretion shock sweeps outward through the star. The formation and outward expansion of the accretion shock is accompanied with a sudden and rapid power-law decline in the central accretion rate Mdot ~ t^{-2.8}, which resembles the L_X ~ t^{-3} decline observed in the X-ray light curves. The collapsed, shock-heated stellar envelope settles into a thick, low-mass equatorial disk embedded within a massive, pressure-supported atmosphere. After a few hundred seconds, the inflow of low-angular-momentum material in the axial funnel reverses into an outflow from the surface of the thick disk. Meanwhile, the rapid decline of the accretion rate slows down, or even settles a in steady state with Mdot ~ 5x10^{-5} Msun/s, which resembles the "plateau" phase in the X-ray light curve. While the duration of the "prompt" phase depends on the resolution in our simulations, we provide an analytical model taking into account neutrino losses that estimates the duration to be ~20 s. The model suggests that the steep decline in GRB X-ray light curves is triggered by the circularization of the infalling stellar envelope at radii where the virial temperature is below ~10^{10} K, such that neutrino cooling shuts off and an outward expansion of the accretion shock becomes imminent.