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.

Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by magneto-rotational instability (MRI). Using them to predict accurately quantities such as stress, accretion rate, and surface brightness profile requires that purely numerical effects, arising from both resolution and algorithm, be understood and controlled. We use the flux-conservative Athena code to conduct a series of experiments on disks having a variety of magnetic topologies to determine what constitutes adequate resolution. We develop and apply several resolution metrics: Q z and Q φ , the ratio of the grid zone size to the characteristic MRI wavelength, α mag , the ratio of the Maxwell stress to the magnetic pressure, and B 2 R / B 2 φ , the ratio of radial to toroidal magnetic field energy. For the initial conditions considered here, adequate resolution is characterized by Q z ≥ 15, Q φ ≥ 20, α mag ≈ 0.45, and B 2 R / B 2 φ ≈ 0.2. These values are associated with ≥ 35 zones per scaleheight H, a result consistent with shearing box simulations. Numerical algorithm is also important. Use of the HLLE flux solver or second-order interpolation can significantly degrade the effective resolution compared to the HLLD flux solver and third-order interpolation. Resolution at this standard can be achieved only with

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.