Wakana Iwakami

Three-dimensional simulations of standing accretion shock instability in core-collapse supernovae

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 proto-neutron 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 Ylm, just as expected for a spherically symmetric background; (2) nonlinear mode couplings produce only m = 0 modes for axisymmetric perturbations, whereas m≠ 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.

EFFECTS OF ROTATION ON STANDING ACCRETION SHOCK INSTABILITY IN NONLINEAR PHASE FOR CORE-COLLAPSE SUPERNOVAE

We study 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 prepare a spherically symmetric and steady accretion flow through a standing shock wave onto a proto-neutron star (PNS). When the SASI enters the nonlinear phase, we impose uniform rotation on the flow advecting from the outer boundary of the iron core, whose specific angular momentum is assumed to agree with recent stellar evolution models. Using spherical harmonics in space and Fourier decompositions in time, we perform mode analysis of the nonspherical deformed shock wave to observe rotational effects on the SASI in the nonlinear phase. We find that rotation imposed on the axisymmetric flow does not make any spiral modes and hardly affects sloshing modes, except for steady l = 2, m = 0 modes. In contrast, rotation imposed on the nonaxisymmetric flow increases the amplitude of spiral modes so that some spiral flows accreting on the PNS are more clearly formed inside the shock wave than without rotation. The amplitudes of spiral modes increase significantly with rotation in the progressive direction.

Stochastic nature of gravitational waves from supernova explosions with standing accretion shock instability

We study the properties of gravitational waves (GWs) based on three-dimensional (3D) simulations, which demonstrate neutrino-driven explosions aided by 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 SASI which develops chaotically in all directions. Our results show that the GW spectrum has its peak near ~100 Hz, reflecting 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.

Critical surface for explosions of rotational core-collapse supernovae

The effect of rotation on the explosion of core-collapse supernovae is investigated systematically in three-dimensional simulations. In order to obtain the critical conditions for explosion as a function of mass accretion rate, neutrino luminosity, and specific angular momentum, rigidly rotating matter was injected from the outer boundary with an angular momentum, which is increased every 500 ms. It is found that there is a critical value of the specific angular momentum, above which the standing shock wave revives, for a given combination of mass accretion rate and neutrino luminosity, i.e., an explosion can occur by rotation even if the neutrino luminosity is lower than the critical value for a given mass accretion rate in non-rotational models. The coupling of rotation and hydrodynamical instabilities plays an important role in characterizing the dynamics of shock revival for the range of specific angular momentum that are supposed to be realistic. Contrary to expectations from past studies, the most rapidly expanding direction of the shock wave is not aligned with the rotation axis. Being perpendicular to the rotation axis on average, it can be oriented in various directions. Its dispersion is small when the spiral mode of the standing accretion shock instability (SASI) governs the dynamics, while it is large when neutrino-driven convection is dominant. As a result of the comparison between two-dimensional and three-dimensional rotational models, it is found that m ≠ 0 modes of neutrino-driven convection or SASI are important for shock revival around the critical surface.

PARAMETRIC STUDY OF FLOW PATTERNS BEHIND THE STANDING ACCRETION SHOCK WAVE FOR CORE-COLLAPSE SUPERNOVAE

In this study, we conduct three-dimensional hydrodynamic simulations systematically to investigate the flow patterns behind the accretion shock waves that are commonly formed in the post-bounce phase of core-collapse supernovae. Adding small perturbations to spherically symmetric, steady, shocked accretion flows, we compute the subsequent evolutions to find what flow pattern emerges as a consequence of hydrodynamical instabilities such as convection and standing accretion shock instability for different neutrino luminosities and mass accretion rates. Depending on these two controlling parameters, various flow patterns are indeed realized. We classify them into three basic patterns and two intermediate ones; the former includes sloshing motion (SL), spiral motion (SP), and multiple buoyant bubble formation (BB); the latter consists of spiral motion with buoyant-bubble formation (SPB) and spiral motion with pulsationally changing rotational velocities (SPP). Although the post-shock flow is highly chaotic, there is a clear trend in the pattern realization. The sloshing and spiral motions tend to be dominant for high accretion rates and low neutrino luminosities, and multiple buoyant bubbles prevail for low accretion rates and high neutrino luminosities. It is interesting that the dominant pattern is not always identical between the semi-nonlinear and nonlinear phases near the critical luminosity; the intermediate cases are realized in the latter case. Running several simulations with different random perturbations, we confirm that the realization of flow pattern is robust in most cases.

Simulations of Core-collapse Supernovae in Spatial Axisymmetry with Full Boltzmann Neutrino Transport

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 (EOSs): Lattimer and Swestys EOS with the incompressibility of K = 220MeV (LS EOS) and Furusawas 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 r {\theta}-component reaches ~10% of the dominant rr-component and, more importantly, it dictates the evolution of lateral neutrino fluxes, dominating over the {\theta}{\theta}-component, in the semi-transparent region. These data will be useful to further test and possibly improve the prescriptions used in the approximate methods.

Three-dimensional Boltzmann-Hydro code for core-collapse in massive stars II. The Implementation of moving-mesh for neutron star kicks

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.

LINKS between the SHOCK INSTABILITY in CORE-COLLAPSE SUPERNOVAE and ASYMMETRIC ACCRETIONS of ENVELOPES

The explosion mechanism of core-collapse supernovae has not been fully understood yet but multi-dimensional fluid instabilities such as standing accretion shock instability (SASI) and convection are now believed to be crucial for shock revival. Another multi-dimensional effect that has been recently argued is the asymmetric structures in progenitors, which are induced by violent convections in silicon/oxygen layers that occur before the onset of collapse, as revealed by recent numerical simulations of the last stage of massive star evolutions. Furthermore, it has been also demonstrated numerically that accretions of such non-spherical envelopes could facilitate shock revival. These two multi-dimensional may hence hold a key to successful explosions. In this paper, we performed a linear stability analysis of the standing accretion shock in core-collapse supernovae, taking into account non-spherical, unsteady accretion flows onto the shock to clarify the possible links between the two effects. We found that such pre-shock perturbations can excite the fluid instabilities efficiently and hence help the shock revive in core-collapse supernovae.

A new approach for error reduction in the volume penalizationmethod

A new approach for reducing error of the volume penalization method is proposed. The mask function is modified by shifting the interface between solid and fluid by toward the fluid region, where v and η are the viscosity and the permeability, respectively. The shift length is derived from the analytical solution of the one-dimensional diffusion equation with a penalization term. The effect of the error reduction is verified numerically for the one-dimensional diffusion equation, Burgers’ equation, and the two-dimensional Navier-Stokes equations. The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy, while it converges to a non-zero constant value as the number of grid points increases for the original mask function. However, the new approach is effectivewhen the grid resolution is sufficiently high so that the boundary layer,whose width is proportional to , is resolved. Hence, the approach should be used when an appropriate combination of ν and η is chosen with a given numerical grid.

Standing accretion shock instability: numerical simulations of core-collapse supernova

Standing accretion shock instability (SASI) is one of the candidates to solve the mystery of why we cannot reproduce the explosion with the present core-collapse supernova models. We have studied this phenomenon with including neutrino heating and realistic EOS and found that SASI may enhance neutrino heating. Although g-mode of proto-neutron star may enhance the SASI growth, the simulations just including the pressure perturbation as a mimic of g-mode induced sound wave reveal no significant effect on the shock dynamics. Moreover, we discuss the required conditions toward the possible laboratory experiment of SASI.