Shoichi Yamada

Postbounce Evolution of Core-Collapse Supernovae: Long-Term Effects of the Equation of State

We study the evolution of a supernova core from the beginning of the gravitational collapse of a 15 M☉ star up to 1 s after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic ν-radiation hydrodynamics in the implicit time differencing. We aim to explore the evolution of shock waves in the long term and investigate the formation of proto-neutron stars together with supernova neutrino signatures. These studies are done to examine the influence of the equation of state (EOS) on the postbounce evolution of shock waves in the late phase and the resulting thermal evolution of proto-neutron stars. We compare two sets of EOSs, namely, those by Lattimer and Swesty (LS-EOS) and by Shen et al. (SH-EOS). We found that, for both EOSs, the core does not explode and the shock wave stalls similarly in the first 100 ms after bounce. A revival of the shock wave does not occur even after a long period in either case. However, the recession of the shock wave appears different beyond 200 ms after bounce, having different thermal evolution of the central core. A more compact proto-neutron star is found for LS-EOS than SH-EOS with a difference in the central density by a factor of ~2 and a difference of ~10 MeV in the peak temperature. The resulting spectra of supernova neutrinos are different to an extent that may be detectable by terrestrial neutrino detectors.

Numerical analysis of standing accretion shock instability with neutrino heating in supernova cores

We have numerically studied the instability of the spherically symmetric standing accretion shock wave against nonspherical perturbations. We have in mind the application to collapse-driven supernovae in the postbounce phase, where the prompt shock wave generated by core bounce is commonly stalled. We take an experimental standpoint in this paper. Using spherically symmetric, completely steady, shocked accretion flows as unperturbed states, we have clearly observed both the linear growth and the subsequent nonlinear saturation of the instability. In so doing, we have employed a realistic equation of state, together with heating and cooling via neutrino reactions with nucleons. We have performed a mode analysis based on the spherical harmonics decomposition and found that the modes with l = 1,2 are dominant not only in the linear regime but also after nonlinear couplings generate various modes and saturation occurs. By varying the neutrino luminosity, we have constructed unperturbed states both with and without a negative entropy gradient. We have found that in both cases the growth of the instability is similar, suggesting that convection does not play a dominant role, which also appears to be supported by the recent linear analysis of the convection in accretion flows by Foglizzo et al. The oscillation period of the unstable l = 1 mode is found to fit better with the advection time rather than with the sound crossing time. Whatever the cause may be, the instability favors a shock revival.

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.

Magnetorotational Effects on Anisotropic Neutrino Emission and Convection in Core-Collapse Supernovae

We perform a series of two-dimensional hydrodynamic simulations of the magnetorotational collapse of a supernova core. We employ a realistic equation of state and take into account electron capture and neutrino transport by the so-called leakage scheme. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than the poloidal ones at the presupernova stage. In this study we systematically investigate the effects of the toroidal magnetic fields on the anisotropic neutrino radiation and convection. Our results show that the shapes of the shock wave and the neutrino spheres generally become more oblate for the models whose profiles of rotation and the magnetic field are shell type and become, in contrast, more prolate for the models whose profiles of rotation and the magnetic field are cylindrical than for the corresponding models without the magnetic fields. Furthermore, we find that magnetorotational instability induced by nonaxisymmetric perturbations is expected to develop within the prompt-shock timescale. Combined with the anisotropic neutrino radiation, which heats matter near the rotational axis preferentially, the growth of the instability may enhance the heating near the axis. This might suggest that magnetar formation is accompanied by a jetlike explosion.

Explosive Nucleosynthesis in Axisymmetrically Deformed Type II Supernovae

Explosive nucleosynthesis under the axisymmetric explosion in Type II supernovae has been examined by means of two-dimensional hydrodynamic calculations. We have compared the results with the observations of SN 1987A. Our chief findings are as follows: (1)44Ti is synthesized in a sufficient amount to explain the tail of the bolometric light curve of SN 1987A. We think this is because the alpha-rich freezeout takes place more actively under the axisymmetric explosion. (2)57Ni and 58Ni tend to be overproduced compared with the observations. However, this tendency relies strongly on the model of the progenitor. We have also compared the abundance of each element in the mass number range A = 16-73 with the solar values. We have found three outstanding features. (1) For the nuclei in the range A = 16-40, their abundances are insensitive to the initial form of the shock wave. This insensitivity is favored since the spherical calculations thus far can explain the solar system abundances in this mass range. (2) There is an enhancement around A = 45 in the axisymmetric explosion that compares fairly well with that of the spherical explosion. In particular,44Ca, which is underproduced in the present spherical calculations, is enhanced significantly. (3) In addition, there is an enhancement around A = 65. This feature relies on the form not of the mass cut but of the initial shock wave. This enhancement may cause the problem of overproduction in this mass range, although this effect would be relatively small since Type I supernovae are chiefly responsible for this mass number range.

Dynamics and Neutrino Signal of Black Hole Formation in Nonrotating Failed Supernovae. I. Equation of State Dependence

We study black hole formation and the neutrino signal from the gravitational collapse of a nonrotating massive star of 40 M☉. Adopting two different sets of realistic equations of state (EOSs) for dense matter, we perform numerical simulations of general relativistic ν-radiation hydrodynamics under spherical symmetry. We make comparisons of core bounce, shock propagation, evolution of nascent proto-neutron stars, and the resulting recollapse to a black hole to reveal the influence of EOSs. We also explore the influence of EOSs on neutrino emission during the evolution toward black hole formation. We find that the speed of contraction of the nascent proto-neutron star, whose mass increases quickly due to the intense accretion, is different depending on the EOS and that the resulting profiles of density and temperature differ significantly. The black hole formation occurs at 0.6-1.3 s after bounce, when the proto-neutron star exceeds its maximum mass, which is crucially determined by the EOS. We find that the average energies of neutrinos increase after bounce because of rapid temperature increase, but at different speeds depending on the EOS. The duration of neutrino emission up to black hole formation is found to be different according to different recollapse timing. These characteristics of neutrino signatures are distinguishable from those for ordinary proto-neutron stars in successful core-collapse supernovae. We discuss the idea that a future detection of neutrinos from a black hole-forming collapse will contribute to revealing the black hole formation and to constraining the EOS at high density and temperature.

Anisotropic Neutrino Radiation in Rotational Core Collapse

We have done a series of two-dimensional hydrodynamic simulations of the rotational collapse of a supernova core and estimated the anisotropy of neutrino radiation from nonspherical neutrino spheres. We have employed a realistic equation of state and approximated electron captures and neutrino transport by the so-called leakage scheme. We have calculated heating rates outside the neutrino sphere, assuming that neutrinos are emitted isotropically from each point on the neutrino sphere. We have found that neutrinos heat matter near the rotational axis more strongly than those near the equatorial plane. This might induce a globally anisotropic explosion.

Numerical Study on the Rotational Collapse of Strongly Magnetized Cores of Massive Stars

Hydrodynamics of the rotational collapse of strongly magnetized massive stellar cores has been studied numerically. Employing simplified microphysics and a two-dimensional nonrelativistic MHD code, we have performed a parametric research with respect to the strength of magnetic field and rotation, paying particular attention to the systematics of dynamics. We assume initially that the rotation is almost uniform and the magnetic field is constant in space and parallel to the rotation axis. The initial angular velocity and magnetic field strength span 1.7-6.8 rad s-1 and × 1012 G, respectively. We have found that the combination of rotation and magnetic field can lead to a jetlike prompt explosion in the direction of the rotational axis, which would not be produced by either of them alone. The range of the maximum angular velocity and field strength is 2.3 × 10-3 to 5.8 × 10-4 rad s-1 and 2.3 × 1015 to 5.6 × 1016 G, respectively, at the end of computations. Although the results appear to be consistent with those by LeBlanc & Wilson and Symbalisty, the magnetic fields behind the shock wave, not in the inner core, are the main driving factor of the jet in our models. The fields are amplified by the strong differential rotations in the region between the shock wave and the boundary of the inner and outer cores, enhanced further by the lateral matter motions induced either by an oblique shock wave (for a strong shock case) or possibly by the MRI (magnetorotational instability)-like instability (for a weak shock case). We have also calculated the gravitational wave forms in the quadrupole approximation. Although the wave form from a nonrotating magnetic core is qualitatively different from those from rotating cores, the amplitude is about an order of magnitude smaller. Otherwise, we have found no substantial difference in the first burst of gravitational waves among the magnetized and nonmagnetized models, since the bounce is mainly driven by the combination of the matter pressure and the centrifugal force.

Jet propagations, breakouts, and photospheric emissions in collapsing massive progenitors of long-duration gamma-ray bursts

We investigate the following by two-dimensional axisymmetric relativistic hydrodynamical simulations: (1) jet propagations through an envelope of a rapidly rotating and collapsing massive star, which is supposed to be a progenitor of long-duration gamma-ray bursts (GRBs); (2) breakouts and subsequent expansions into stellar winds; and (3) the accompanying photospheric emissions. We find that if the envelope rotates uniformly almost at the mass shedding limit, its outer part eventually stops contracting when the centrifugal force becomes large enough. Then another shock wave is formed, propagates outward, and breaks out of the envelope into the stellar wind. Whether the jet or the centrifugal bounce-induced shock breaks out earlier depends on the timing of jet injection. If the shock breakout occurs earlier, owing to a later injection, the jet propagation and subsequent photospheric emissions are affected substantially. We pay particular attention to observational consequences of the difference in the timing of jet injection. We calculate optical depths to find the location of photospheres, extracting densities, and temperatures at appropriate retarded times from the hydrodynamical data. We show that the luminosity and observed temperature of the photospheric emissions are both much lower than those reported in previous studies. Although luminosities are still high enough for GRBs, the observed temperatures are lower than the energy at the spectral peak expected by the Yonetoku relation. This may imply that energy exchanges between photons and matter are terminated deeper inside or that some non-thermal processes are operating to boost photon energies.

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.