We have studied nonaxisymmetric standing accretion shock instabilities, or SASI, using three-dimensional (3D) hydrodynamical simulations. This is an extension of our previous study of axisymmetric SASI. We have prepared a spherically symmetric and steady accretion flow through a standing shock wave onto a protoYneutron star, taking into account a realistic equation of state and neutrino heating and cooling. This unperturbed model is meant to represent approximately the typical postbounce phase of core-collapse supernovae. We then added a small perturbation ($1%) to the radial velocity and computed the ensuing evolutions. Both axisymmetric and nonaxisymmetric perturbations have been imposed. We have applied mode analysis to the nonspherical deformation of the shock surface, using spherical harmonics. We have found that (1) the growth rates of SASI are degenerate with respect to the azimuthal index m of the spherical harmonics Y m l , just as expected for a spherically symmetric background; (2) nonlinear mode couplings produce only m ¼ 0 modes for axisymmetric perturbations, whereas m 6 ¼ 0 modes are also generated in the nonaxisymmetric cases, according to the selection rule for quadratic couplings; (3) the nonlinear saturation level of each mode is lower in general for 3D than for 2D, because a larger number of modes contribute to turbulence in 3D; (4) low-l modes are dominant in the nonlinear phase; (5) equipartition is nearly established among different m modes in the nonlinear phase; (6) spectra with respect to l obey power laws with a slope slightly steeper for 3D; and (7) although these features are common to the models with and without a shock revival at the end of the simulation, the dominance of low-l modes is more remarkable in the models with a shock revival.

We present the first results of our spatially axisymmetric core-collapse supernova simulations with full Boltzmann neutrino transport, which amount to a time-dependent 5-dimensional (2 in space and 3 in momentum space) problem in fact. Special relativistic effects are fully taken into account with a two-energy-grid technique. We performed two simulations for a progenitor of 11.2M ⊙ , employing different nuclear equations-of-state (EOS's): Lattimer and Swesty's EOS with the incompressibility of K = 220MeV (LS EOS) and Furusawa's EOS based on the relativistic mean field theory with the TM1 parameter set (FS EOS). In the LS EOS the shock wave reaches ∼ 700km at 300ms after bounce and is still expanding whereas in the FS EOS it stalled at ∼ 200km and has started to recede by the same time. This seems to be due to more vigorous turbulent motions in the former during the entire post-bounce phase, which leads to higher neutrino-heating efficiency in the neutrino-driven convection. We also look into the neutrino distributions in momentum space, which is the advantage of the Boltzmann transport over other approximate methods. We find non-axisymmetric angular distributions with respect to the local radial direction, which also generate off-diagonal components of the Eddington tensor. We find that the rθ-component reaches ∼ 10% of the dominant rr-component and, more importantly, it dictates the evolution of lateral neutrino fluxes, dominating over the θθ-component, in the semi-transparent region. These data will be useful to further test and possibly improve the prescriptions used in the approximate methods.

We study properties of gravitational waves based on the three-dimensional simulations, which demonstrate the neutrino-driven explosions aided by the standing accretion shock instability (SASI). Pushed by evidence supporting slow rotation prior to core-collapse, we focus on the asphericities in neutrino emissions and matter motions outside the protoneutron star. By performing a ray-tracing calculation in 3D, we estimate accurately the gravitational waveforms from anisotropic neutrino emissions. In contrast to the previous work assuming axisymmetry, we find that the gravitational waveforms vary much more stochastically because the explosion anisotropies depend sensitively on the growth of the SASI which develops chaotically in all directions. Our results show that the gravitational-wave spectrum has its peak near ∼ 100 Hz, reflecting the SASI-induced matter overturns of ∼ O(10) ms. We point out that the detection of such signals, possibly visible to the LIGO-class detectors for a Galactic supernova, could be an important probe into the long-veiled explosion mechanism.

We present a newly developed moving-mesh technique for the multi-dimensional Boltzmann-Hydro code for the simulation of core-collapse supernovae (CCSNe). What makes this technique different from others is the fact that it treats not only hydrodynamics but also neutrino transfer in the language of the 3+1 formalism of general relativity (GR), making use of the shift vector to specify the time evolution of the coordinate system. This means that the transport part of our code is essentially general relativistic, although in this paper it is applied only to the moving curvilinear coordinates in the flat Minknowski spacetime, since the gravity part is still Newtonian. The numerical aspect of the implementation is also described in detail. Employing the axisymmetric two-dimensional version of the code, we conduct two test computations: oscillations and runaways of proto-neutron star (PNS). We show that our new method works fine, tracking the motions of PNS correctly. We believe that this is a major advancement toward the realistic simulation of CCSNe.

We propose a ray-tracing method to estimate gravitational waves (GWs) generated by anisotropic neutrino emission in supernova cores. To calculate the gravitational waveforms, we derive analytic formulae in a useful form, which are applicable also for three-dimensional computations. Pushed by evidence of slow rotation prior to core-collapse, we focus on asphericities in neutrino emission and matter motions outside the protoneutron star. Based on the two-dimensional (2D) models, which mimic SASI-aided neutrino heating explosions, we compute the neutrino anisotropies via the ray-tracing method in a post-processing manner and calculate the resulting waveforms. For simplicity, neutrino absorption and emission by free nucleons, dominant processes outside the PNSs, are only taken into account, while the neutrino scattering and the velocity-dependent terms in the transport equations are neglected. With these computations, it is found that the waveforms exhibit more variety in contrast to the ones previously estimated by the ray-by-ray analysis (e.g., Kotake et al. (2007)). In addition to a positively growing feature, which was predicted to determine the total wave amplitudes predominantly, the waveforms are shown to exhibit large negative growth for some epochs during the growth of SASI. These features are found to stem from the excess of neutrino emission in lateral directions, which can be precisely captured by the ray-tracing calculation. Reflecting the nature of SASI

Core-collapse supernovae are dramatic explosions marking the catastrophic end of massive stars. The only means to get direct information about the supernova engine is from observations of neutrinos emitted by the forming neutron star, and through gravitational waves which are produced when the hydrodynamic flow or the neutrino flux is not perfectly spherically symmetric. The multidimensionality of the supernova engine, which breaks the sphericity of the central core such as convection, rotation, magnetic fields, and hydrodynamic instabilities of the supernova shock, is attracting great attention as the most important ingredient to understand the long-veiled explosion mechanism. Based on our recent work, weCCSNe are now about to start even another astronomy, Gravitational-Wave Astronomy.

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We studied the effects of rotation on standing accretion shock instability (SASI) by performing three-dimensional hydrodynamics simulations. Taking into account a realistic equation of state and neutrino heating/cooling, we prepared a spherically symmmetric and steady accretion flow through a standing shock wave onto a proto-neutron star (PNS). When the SASI entered the nonlinear phase, we imposed uniform rotation on the flow advecting from the outer boundary of the iron core, whose specific angular momentum was assumed to agree with recent stellar evolution models. Using spherical harmonics in space and Fourier decompositions in time, we performed mode analysis of the nonspherical deformed shock wave to observe rotational effects on the SASI in the nonlinear phase. We found that rotation imposed on the axisymmetric SASI did not make any spiral modes and hardly affected sloshing modes, except for steady l = 2, m = 0 modes. In contrast, rotation imposed on the non-axisymmetric flow increased the amplitude of spiral modes so that some spiral flows accreting on the PNS were more clearly formed inside the shock wave than without rotation. The amplitudes of spiral modes increased significantly with rotation in the progressive direction.