We present results of new three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. These simulations are the first of their kind and include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae are fundamentally different from what was anticipated on the basis of previous simulations in axisymmetry (2D). A strong bipolar jet that develops in a simulation constrained to 2D is crippled by a spiral instability and fizzles in full 3D. While multiple (magneto-)hydrodynamic instabilities may be present, our analysis suggests that the jet is disrupted by an m = 1 kink instability of the ultra-strong toroidal field near the rotation axis. Instead of an axially symmetric jet, a completely new, previously unreported flow structure develops. Highly magnetized spiral plasma funnels expelled from the core push out the shock in polar regions, creating wide secularly expanding lobes. We observe no runaway explosion by the end of the full 3D simulation at 185 ms after bounce. At this time, the lobes have reached maximum radii of ∼900 km.

We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M progenitor was studied in 2D by Müller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low--mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.

We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D general-relativistic hydrodynamic simulations of a 27-M progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), (3) SASI dominated evolution. This confirms previous 3D results of Hanke et al. (2013), ApJ 770:66 and Couch & Connor (2014), ApJ 785:123. We carry out simulations with resolutions differing by up to a factor of ∼4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case, since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum E( ) develops in the heating layer. Like other 3D studies, we find E( ) ∝ −1 in the "inertial range," while theory and local simulations argue for E( ) ∝ −5/3 . We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy containing scale, creating a "bottleneck" that prevents an efficient turbulent cascade.

Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them potentially interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the implicit Monte Carlo photon transport scheme of Fleck & Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.

The late collapse, core bounce, and the early postbounce phase of rotating core collapse leads to a characteristic gravitational wave (GW) signal. The precise shape of the signal is governed by the interplay of gravity, rotation, nuclear equation of state (EOS), and electron capture during collapse. We explore the detailed dependence of the signal on total angular momentum and its distribution in the progenitor core by means of a large set of axisymmetric general-relativistic hydrodynamics core collapse simulations, in which we systematically vary the initial angular momentum distribution in the core. Our simulations include a microphysical finite-temperature EOS, an approximate electron capture treatment during collapse, and a neutrino leakage scheme for the postbounce evolution. Our results show that the total angular momentum of the inner core at bounce and the inner core's ratio of rotational kinetic energy to gravitational energy T /|W | are both robust parameters characterizing the GW signal. We find that the precise distribution of angular momentum is relevant only for very rapidly rotating cores with T /|W | 8% at bounce. We construct a numerical template bank from our baseline set of simulations, and carry out additional simulations to generate trial waveforms for injection into simulated Advanced LIGO noise at a fiducial galactic distance of 10 kpc. Using matched filtering, we show that for an optimally-oriented source and Gaussian noise, Advanced LIGO could measure the total angular momentum to within ±20%, for rapidly rotating cores. For most waveforms, the nearest known degree of precollapse differential rotation is correctly inferred by both our matched filtering analysis and an alternative Bayesian model selection approach. We test our results for robustness against systematic uncertainties by injecting waveforms from simulations utilizing a different EOS and and variations in the electron fraction in the inner core. The results of these tests show that these uncertainties significantly reduce the accuracy with which the total angular momentum and its precollapse distribution can be inferred from observations.

We present results from a new set of 3D general-relativistic hydrodynamic simulations of rotating iron core collapse. We assume octant symmetry and focus on axisymmetric collapse, bounce, the early postbounce evolution, and the associated gravitational wave (GW) and neutrino signals. We employ a finite-temperature nuclear equation of state, parameterized electron capture in the collapse phase, and a multi-species neutrino leakage scheme after bounce. The latter captures the important effects of deleptonization, neutrino cooling and heating and enables approximate predictions for the neutrino luminosities in the early evolution after core bounce. We consider 12-M and 40-M presupernova models and systematically study the effects of (i) rotation, (ii) progenitor structure, and (iii) postbounce neutrino leakage on dynamics, GW, and, neutrino signals. We demonstrate, that the GW signal of rapidly rotating core collapse is practically independent of progenitor mass and precollapse structure. Moreover, we show that the effects of neutrino leakage on the GW signal are strong only in nonrotating or slowly rotating models in which GW emission is not dominated by inner core dynamics. In rapidly rotating cores, core bounce of the centrifugally-deformed inner core excites the fundamental quadrupole pulsation mode of the nascent protoneutron star. The ensuing global oscillations (f ∼ 700 − 800 Hz) lead to pronounced oscillations in the GW signal and correlated strong variations in the rising luminosities of antineutrino and heavy-lepton neutrinos. We find these features in cores that collapse to protoneutron stars with spin periods 2.5 ms and rotational energies sufficient to drive hyper-energetic core-collapse supernova explosions. Hence, GW or neutrino observations of a core collapse event could deliver strong evidence for or against rapid core rotation. Joint GW + neutrino observations would allow to make statements with high confidence. Our estimates suggest that the GW signal should be detectable throughout the Milky Way by advanced laser-interferometer GW observatories, but a water-Cherenkov neutrino detector would have to be of near-megaton size to observe the variations in the early neutrino luminosities from a core collapse event at 1 kpc.

We present results from high-resolution semi-global simulations of neutrino-driven convection in core-collapse supernovae. We employ an idealized setup with parametrized neutrino heating/cooling and nuclear dissociation at the shock front. We study the internal dynamics of neutrino-driven convection and its role in re-distributing energy and momentum through the gain region. We find that even if buoyant plumes are able to locally transfer heat up to the shock, convection is not able to create a net positive energy flux and overcome the downwards transport of energy from the accretion flow. Turbulent convection does, however, provide a significant effective pressure support to the accretion flow as it favors the accumulation of energy, mass and momentum in the gain region. We derive an approximate equation that is able to explain and predict the shock evolution in terms of integrals of quantities such as the turbulent pressure in the gain region or the effects of non-radial motion of the fluid. We use this relation as a way to quantify the role of turbulence in the dynamics of the accretion shock. Finally, we investigate the effects of grid resolution, which we change by a factor 20 between the lowest and highest resolution. Our results show that the shallow slopes of the turbulent kinetic energy spectra reported in previous studies are a numerical artefact. Kolmogorov scaling is progressively recovered as the resolution is increased.

Gravitational waves (GWs) generated by axisymmetric rotating collapse, bounce, and early postbounce phases of a galactic core-collapse supernova are detectable by current-generation gravitational wave observatories. Since these GWs are emitted from the quadrupole-deformed nuclear-density core, they may encode information on the uncertain nuclear equation of state (EOS). We examine the effects of the nuclear EOS on GWs from rotating core collapse and carry out 1824 axisymmetric general-relativistic hydrodynamic simulations that cover a parameter space of 98 different rotation profiles and 18 different EOS. We show that the bounce GW signal is largely independent of the EOS and sensitive primarily to the ratio of rotational to gravitational energy, T=jWj, and at high rotation rates, to the degree of differential rotation. The GW frequency (f peak ∼ 600-1000 Hz) of postbounce core oscillations shows stronger EOS dependence that can be parametrized by the core's EOS-dependent dynamical frequency ffiffiffiffiffiffiffiffi Gρ c p . We find that the ratio of the peak frequency to the dynamical frequency f peak = ffiffiffiffiffiffiffiffi Gρ c p follows a universal trend that is obeyed by all EOS and rotation profiles and that indicates that the nature of the core oscillations changes when the rotation rate exceeds the dynamical frequency. We find that differences in the treatments of lowdensity nonuniform nuclear matter, of the transition from nonuniform to uniform nuclear matter, and in the description of nuclear matter up to around twice saturation density can mildly affect the GW signal. More exotic, higher-density physics is not probed by GWs from rotating core collapse. We furthermore test the sensitivity of the GW signal to variations in the treatment of nuclear electron capture during collapse. We find that approximations and uncertainties in electron capture rates can lead to variations in the GW signal that are of comparable magnitude to those due to different nuclear EOS. This emphasizes the need for reliable experimental and/or theoretical nuclear electron capture rates and for self-consistent multidimensional neutrino radiation-hydrodynamic simulations of rotating core collapse.