ABSTRACT

We present a new formulation for numerically obtaining axisymmetric equilibrium structures of rotating stars in two spatial dimensions. With a view to apply it to the secular evolution of rotating stars, we base it on the Lagrangian description, i.e. we solve the force-balance equations to find the spatial positions of fluid elements endowed individually with a mass, specific entropy and angular momentum. The system of non-linear equations obtained by finite-differencing the basic equations is solved with the W4 method, which is a new multidimensional root-finding scheme of our own devising. We augment it with a remapping scheme to avoid distortions of the Lagrangian coordinates. In this first one of a series of papers, we will give a detailed description of these methods initially. We then present the results of some test calculations, which include the construction of both rapidly rotating barotropic and baroclinic equilibrium states. We gauge their accuracies quantitatively with some diagnostic quantities as well as via comparisons with the counterparts obtained with an Eulerian code. For a demonstrative purpose, we apply the code to a toy-model cooling calculation of a rotating white dwarf.

Abstract

It is known that muons are scarce just after the birth of a proto-neutron star via a supernova explosion, but get more abundant as the proto-neutron star cools via neutrino emissions on the Kelvin–Helmholtz timescale. We evaluate all the relevant rates of the neutrino interactions with muons at different times in the proto-neutron star cooling. We are particularly interested in the late phase ($t \gtrsim 10 \operatorname{s}$), which will be accessible in the next Galactic supernova but has not been studied well so far. We calculate both leptonic and semi-leptonic processes, for the latter of which we also pay attention to the form factors with their dependence on the transferred momentum as well as to the modification of the dispersion relations for nucleons on the mean field level. We find that the flavor-exchange reactions νe + μ− → νμ + e− and $\bar{\nu }_{\mu } + \mu ^- \rightarrow \bar{\nu }_e + e^-$ can be dominant, particularly at low energies, over the capture of νe on neutron and the scatterings of $\bar{\nu }_{\mu }$ on nucleons as the opacity sources for these species, and that the inverse muon decay $\bar{\nu }_e + \nu _{\mu } + e^- \leftrightarrows \mu ^-$ can overwhelm the scatterings of $\bar{\nu }_e$ and νμ on nucleons again at low energies. At high energies, on the other hand, the corrections in the semi-leptonic processes mentioned above are more important. We also show the non-trivial energy and angular dependencies of the flavor-exchange reactions and the inverse muon decay. In the study of the diffusion coefficients from these reactions, we find that $\bar{\nu }_{\mu }$ is most affected. These pieces of information are indispensable for numerical computations and the interpretation of their results for proto-neutron star cooling, particularly at the very late phase.

Abstract

Using full Boltzmann neutrino transport, we performed 2D core-collapse supernova simulations in axisymmetry for two progenitor models with 11.2 and 15.0 M_⊙, both rotational and nonrotational. We employed the results obtained in the early post-bounce phase (t ≲ 20 ms) to assess performance under rapid rotation of some closure relations commonly employed in the truncated moment method. We first made a comparison in 1D under spherical symmetry, though, of the Eddington factor p defined in the fluid rest frame (FR). We confirmed that the maximum entropy closure for the Fermionic distribution (MEFD) performs better than others near the proto–neutron star surface, where p < 1/3 occurs, but does not work well even in 1D when the phase-space occupancy satisfies e < 0.5 together with p < 1/3, the condition known to be not represented by MEFD. For the 2D models with the rapid rotation, we employed the principal-axis analysis of the Eddington tensor. We paid particular attention to the direction of the longest principal axis. We observed in FR that it is aligned neither with the radial direction nor with the neutrino flux in 2D, particularly so in convective and/or rapidly rotating regions, the fact not accommodated in the moment method. We repeated the same analysis in the laboratory frame and found again that the direction of the longest principal axis is not well reproduced by MEFD because the interpolation between the optically thick and thin limits is not very accurate in this frame.

Abstract

We trained deep neural networks (DNNs) as a function of the neutrino energy density, flux, and the fluid velocity to reproduce the Eddington tensor for neutrinos obtained in our first-principles core-collapse supernova simulation. Although the moment method, which is one of the most popular approximations for neutrino transport, requires a closure relation, none of the analytical closure relations commonly employed in the literature capture all aspects of the neutrino angular distribution in momentum space. In this paper, we develop a closure relation by using DNNs that take the neutrino energy density, flux, and the fluid velocity as the inputs and the Eddington tensor as the output. We consider two kinds of DNNs: a conventional DNN, named a component-wise neural network (CWNN), and a tensor-basis neural network (TBNN). We find that the diagonal component of the Eddington tensor is better reproduced by the DNNs than the M1 closure relation, especially for low to intermediate energies. For the off-diagonal component, the DNNs agree better with the Boltzmann solver than the M1 closure relation at large radii. In the comparison between the two DNNs, the TBNN displays slightly better performance than the CWNN. With these new closure relations at hand, based on DNNs that well reproduce the Eddington tensor at much lower costs, we have opened up a new possibility for the moment method.

Recent progress of neutrino detectors makes it possible to detect pre-SN neutrinos, which are emitted from the core of massive stars before supernova explosions. Pre-SN neutrino observations will become an alarm for supernovae. We hence calculate the number luminosity and energy spectra of pre-SN neutrinos from the 15 M o progenitor based on the state-of-the-art calculations of massive stars. We find that the number luminosity of ve 's is before core collapse and core bounce, respectively, whereas that of. We then estimate the number of neutrino events at neutrino detectors taking neutrino oscillations into the obtained luminosities and spectra. We find that an alarm is issued a few days before the explosion by detecting 's at liquid-scintilation type detectors if the progenitor is located at 200 pc. Finally, we perform a systematic study of pre-SN neutrino emission for 7 progenitor models with different initial masses. We find that the difference of the number luminosities is ∼ 1 order and the dependence of the initial mass have to be taken into the theoretical predictions of pre-SN neutrino observations.

<title>Abstract</title>
We calculate new equations of state (EOSs) for astrophysical simulations in the framework of the extended nuclear statistical equilibrium, in which we minimize the free energy density for the full ensemble of nuclei in a hot and dense stellar environment. To evaluate bulk and surface energies of heavy nuclei and free energies of uniformly distributed nucleons, we use fitting formulae for the interaction energies and single-nucleon potentials at zero temperature of a Dirac–Brückner Hartree–Fock (DBHF) theory, one of the modern approaches to describe homogeneous nuclear matter. We find that the DBHF EOS exhibits larger mass fractions for medium-mass nuclei and smaller mass fractions for the other nuclei than the EOS obtained using the variational method (VM), another modern model for homogeneous nuclear matter. This effect is due to the more deeply bound energy for symmetric nuclear matter and the larger symmetry energy encoded in the DBHF EOS. At supra-nuclear densities, the DBHF EOS exhibits characteristics of a larger free energy, a higher pressure, and a larger neutron chemical potential of neutron-rich matter, which lead to a larger radius of cold neutron stars than that obtained by the VM EOS.

© 2019. The American Astronomical Society.. In this Letter we present the result of an axisymmetric core-collapse supernovae simulation conducted with appropriate treatments of neutrino transport and proper motions of proto-neutron stars (PNSs), in which a remarkable PNS acceleration is observed in association with asymmetric neutrino emissions 300 ms after bounce. We find that these asymmetric neutrino emissions play important roles in the acceleration of PNSs in this phase. The correlation between the PNS proper motion and the asymmetric ejecta is similar to that in a neutron star (NS) kick of hydrodynamic origin. Both electron-type neutrinos (ν e) and their anti-particles () have a ∼10% level of asymmetry between the northern and southern hemispheres, while other heavy-leptonic neutrinos (ν x) have much a smaller asymmetry of ∼1%. The emissions of and ν x are higher in the hemisphere of stronger shock expansion, whereas the ν e emission is enhanced in the opposite hemisphere: in total, the neutrinos carry some linear momentum to the hemisphere of the stronger shock expansion. This asymmetry is attributed to the non-spherical distribution of electron-fraction (Y e) in the envelope of PNS. Although it is similar to lepton-emission self-sustained asymmetry, the Y e asymmetry seems to be associated with the PNS motion: the latter triggers lateral circular motions in the envelope of PNS by breaking the symmetry of the matter distribution there, which is then sustained by a combination of convection, lateral neutrino diffusion, and matter-pressure gradient. Our findings may have an influence on the current theories on the NS kick mechanism, although long-term simulations are required to assess their impact on later evolution.

Neutrinos are densely populated deep inside the core of massive stars after their gravitational collapse to produce supernova explosions and form compact stars such as neutron stars and black holes. It has been considered that they may change their flavor identities through so-called fast-pairwise conversions induced by mutual forward scatterings. If that is really the case, the dynamics of supernova explosion will be influenced, since the conversion may occur near the neutrino sphere, from which neutrinos are effectively emitted. In this paper, we conduct a pilot study of such possibilities based on the results of fully self-consistent, realistic simulations of a core-collapse supernova explosion in two spatial dimensions under axisymmetry. As we solved the Boltzmann equations for neutrino transfer in the simulation not as a postprocess but in real time, the angular distributions of neutrinos in momentum space for all points in the core at all times are available, a distinct feature of our simulations. We employ some of these distributions extracted at a few selected points and times from the numerical data and apply linear analysis to assess the possibility of the conversion. We focus on the vicinity of the neutrino sphere, where different species of neutrinos move in different directions and have different angular distributions as a result. This is a pilot study for a more thorough survey that will follow soon. We find no positive sign of conversion unfortunately at least for the spatial points and times we studied in this particular model. We hence investigate rather in detail the condition for the conversion by modifying the neutrino distributions rather arbitrarily by hand.

This paper is a sequel to Takahashi et al., in which the authors investigated the influences of fluctuations in preshock accreting matter on the linear stability of the standing accretion shock in core-collapse supernovae (CCSNe). If one understands that this was concerning the effect of the outer boundary condition for the postshock accretion flows, the present paper should be regarded as an investigation of the possible influences of the inner boundary conditions. More specifically, we impose a time-dependent, oscillating condition at the inner boundary, having in mind the injection of acoustic power by an oscillating proto-neutron star. We also consider possible correlations between the inner and outer boundary conditions as invoked in the argument for Lepton-number Emission Self-sustained Asymmetry (LESA). In this paper, we conduct the linear stability analysis of the standing accretion shock commonly encountered in CCSNe on the basis of Laplace transform. We find that the acoustic power enhances the standing accretion shock instability (SASI), especially when the luminosity is low. On the other hand, the correlation between the fluctuations of neutrino luminosity at the neutrino sphere has little influence on the instability, changing the amplitudes of eigenmodes only slightly. We further investigate steady solution of perturbation equations, being motivated by LESA, and conclude that not the difference but the sum of the fluxes of ν e and is the key ingredient to production of the self-sustained steady perturbed configuration.

With the Boltzmann-radiation-hydrodynamics code, which we have developed to<br />
solve numerically the Boltzmann equations for neutrino transfer, the Newtonian<br />
hydrodynamics equations, and the Newtonian self-gravity simultaneously and<br />
consistently, we simulate the collapse of a rotating core of the progenitor<br />
with a zero-age-main-sequence mass of $11.2\,M_\odot$ and a shelluler rotation<br />
of $1\,{\rm rad\,s^{-1 } }$ at the center. We pay particular attention in this<br />
paper to the neutrino distribution in phase space, which is affected by the<br />
rotation. By solving the Boltzmann equations directly, we can assess the<br />
rotation-induced distortion of the angular distribution in momentum space,<br />
which gives rise to the rotational component of the neutrino flux. We compare<br />
the Eddington tensors calculated both from the raw data and from the M1-closure<br />
approximation. We demonstrate that the Eddington tensor is determined by<br />
complicated interplays of the fluid velocity and the neutrino interactions, and<br />
that the M1-closure, which assumes that the Eddington factor is determined by<br />
the flux factor, fails to fully capture this aspect especially in the vicinity<br />
of the shock. We find that the error in the Eddington factor reaches $\sim<br />
20\%$ in our simulation. This is due to not the resolution but different<br />
dependence of the Eddington and flux factors on the angular profile of the<br />
neutrino distribution function and hence modification to the closure relation<br />
is needed.

We propose a new class of method for solving nonlinear systems of equations,<br />
which, among other things,has four nice features: (i) it is inspired by the<br />
mathematical property of damped oscillators, (ii) it can be regarded as a<br />
simple extention to the Newton-Raphson(NR) method, (iii) it has the same local<br />
convergence as the NR method does, (iv) it has a significantly wider<br />
convergence region or the global convergence than that of the NR method. In<br />
this article, we present the evidence of these properties, applying our new<br />
method to some examples and comparing it with the NR method.

We present the first results of our spatially axisymmetric core-collapse supernova simulations with full Boltzmann neutrino transport, which amount to a time-dependent five-dimensional (two in space and three in momentum space) problem. Special relativistic effects are fully taken into account with a two-energy-grid technique. We performed two simulations for a progenitor of 11.2 M⊙, employing different nuclear equations of state (EOSs): Lattimer and Swesty's EOS with the incompressibility of K =220 MeV (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 ∼700 km at 300 ms after bounce and is still expanding, whereas in the FS EOS it stalled at ∼200 km 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 postbounce 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 nonaxisymmetric 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 semitransparent region. These data will be useful to further test and possibly improve the prescriptions used in the approximate methods.

In this paper, we systematically calculate the polarization in soft X-rays emitted from magnetized neutron stars, which are expected to be observed by next-generation X-ray satellites. Magnetars are one of the targets for these observations. This is because thermal radiation is normally observed in the soft X-ray band, and it is thought to be linearly polarized because of different opacities for two polarization modes of photons in the magnetized atmosphere of neutron stars and the dielectric properties of the vacuum in strong magnetic fields. In their study, Taverna et al. illustrated how strong magnetic fields influence the behavior of the polarization observables for radiation propagating in vacuo without addressing a precise, physical emission model. In this paper, we pay attention to the conversion of photon polarization modes that can occur in the presence of an atmospheric layer above the neutron star surface, computing the polarization angle and fraction and systematically changing the magnetic field strength, radii of the emission region, temperature, mass, and radii of the neutron stars. We confirmed that if plasma is present, the effects of mode conversion cannot be neglected when the magnetic field is relatively weak, B ∼ 1013 G. Our results indicate that strongly magnetized (B ≳ 1014 G) neutron stars are suitable to detect polarizations, but not-so-strongly magnetized (B ∼ 1013 G) neutron stars will be the ones to confirm the mode conversion.

This paper is a sequel to our 2015 paper, Kato et al., which calculated the luminosities and spectra of electron-type anti-neutrinos ((v) over bar (e)) from the progenitors of core-collapse supernovae. Expecting that the capability to detect electron-type neutrinos (ne) will increase dramatically with the emergence of liquid-argon detectors such as DUNE, we broaden the scope in this study to include all flavors of neutrinos emitted from the pre-bounce phase. We pick up three progenitor models of electron capture supernovae (ECSNe) and iron-core collapse supernovae (FeCCSNe). We find that the number luminosities reach similar to 10(57) s(-1). and similar to 10(53) s(-1) at maximum for v(e) and (v) over bar (e), respectively. We also estimate the numbers of detection events at terrestrial neutrino detectors including DUNE, taking flavor oscillations into account and assuming the distance to the progenitors to be 200 pc. It is demonstrated that (v) over bar (e) from the ECSN progenitor will be undetected at almost all detectors, whereas we will be able to observe greater than or similar to 15,900 v(e) at DUNE for the inverted mass hierarchy. From the FeCCSN progenitors, the number of (v) over bar (e) events will be largest for JUNO, 200-900 v(e), depending on the mass hierarchy, whereas the number of ne events at DUNE is greater than or similar to 2100 for the inverted mass hierarchy. These results imply that the detection of (v) over bar (e) is useful to distinguish progenitors of FeCCSNe from those of ECSNe, while ne will provide us with detailed information on the collapse phase regardless of the type and mass of the progenitor.

The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. We carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to both methods. The DO method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are subdominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and we find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic MC random walk approximation.

We have constructed a nuclear equation of state (EOS) that includes a full nuclear ensemble for use in core-collapse supernova simulations. It is based on the EOS for uniform nuclear matter that two of the authors derived recently, applying a variational method to realistic two- and three-body nuclear forces. We have extended the liquid drop model of heavy nuclei, utilizing the mass formula that accounts for the dependences of bulk, surface, Coulomb and shell energies on density and/or temperature. As for light nuclei, we employ a quantum-theoretical mass evaluation, which incorporates the Pauli- and self-energy shifts. In addition to realistic nuclear forces, the inclusion of in-medium effects on the full ensemble of nuclei makes the new EOS one of the most realistic EOSs, which covers a wide range of density, temperature and proton fraction that supernova simulations normally encounter. We make comparisons with the FYSS EOS, which is based on the same formulation for the nuclear ensemble but adopts the relativistic mean field theory with the TM1 parameter set for uniform nuclear matter. The new EOS is softer than the FYSS EOS around and above nuclear saturation densities. We find that neutron-rich nuclei with small mass numbers are more abundant in the new EOS than in the FYSS EOS because of the larger saturation densities and smaller symmetry energy of nuclei in the former. We apply the two EOSs to 1D supernova simulations and find that the new EOS gives lower electron fractions and higher temperatures in the collapse phase owing to the smaller symmetry energy. As a result, the inner core has smaller masses for the new EOS. It is more compact, on the other hand, due to the softness of the new EOS and bounces at higher densities. It turns out that the shock wave generated by core bounce is a bit stronger initially in the simulation with the new EOS. The ensuing outward propagations of the shock wave in the outer core are very similar in the two simulations, which may be an artifact, though, caused by the use of the same tabulated electron capture rates for heavy nuclei ignoring differences in the nuclear composition between the two EOSs in these computations.

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 investigate the criterion for the acoustic mechanism to work successfully in core-collapse supernovae. The acoustic mechanism is an alternative to the neutrino-heating mechanism. It was proposed by Burrows et al., who. claimed. that acoustic waves emitted by g-mode oscillations in proto-neutron stars (PNS) energize a stalled shock wave and eventually. induce an explosion. Previous works mainly studied. to which. extent the g-modes are excited in the PNS. In this paper, on the other hand, we investigate. how strong the acoustic wave needs to. be if it were to revive a stalled shock wave. By adding the acoustic power as a new axis, we draw a critical surface, which is an extension of the critical curve commonly employed in the context of neutrino heating. We perform both 1D and 2D parametrized simulations, in which we inject acoustic waves from the inner boundary. In order to quantify the power of acoustic waves, we use. the extended Myers. theory to take neutrino reactions into proper account. We find for the 1D simulations that rather large acoustic powers are required to relaunch the shock wave, since the additional heating provided by the secondary shocks developed from acoustic waves is partially canceled by the neutrino cooling that is also enhanced. In 2D, the required acoustic powers are consistent with those of Burrows et al. Our results seem to imply, however, that it is the sum of neutrino heating and acoustic powers that matters for shock revival.

We carried out high resolution simulations of weakly-magnetized core-collapse supernovae in two-dimensional axisymmetry in order to see the influence of the magnetic field and rotation on the explosion. We found that the magnetic field amplified by magnetorotational instability (MRI) has a great positive impact on the explosion by enhancing the neutrino heating, provided that the progenitor has large angular momentum close to the highest value found in stellar evolution calculations. We also found that even for progenitors neither involving strong magnetic flux nor large angular momentum, the magnetic field is greatly amplified by the convection aand rotation, and this leads to the boost of the explosion again by enhancing the neutrino heating.

We investigate the influences of the nuclear composition on the weak interaction rates of heavy nuclei during the core collapse of massive stars. The nuclear abundances in nuclear statistical equilibrium (NSE) are calculated by some equation of state (EOS) models including in-medium effects on nuclear masses. We systematically examine the sensitivities of electron capture and neutrino-nucleus scattering on heavy nuclei to the nuclear shell effects and the single-nucleus approximation. We find that the washout of the shell effect at high temperatures brings significant change to weak rates by smoothing the nuclear abundance distribution: the electron capture rate decreases by similar to 20% in the early phase and increases by similar to 40% in the late phase at most, while the cross section for neutrino-nucleus scattering is reduced by similar to 15%. This is because the open-shell nuclei become abundant instead of those with closed neutron shells as the shell effects disappear. We also find that the single-nucleus description based on the average values leads to underestimations of weak rates. Electron captures and neutrino coherent scattering on heavy nuclei are reduced by similar to 80% in the early phase and by similar to 5% in the late phase, respectively. These results indicate that NSE like EOS accounting for shell washout is indispensable for the reliable estimation of weak interaction rates in simulations of core-collapse supernovae.

We investigated r-process nucleosynthesis in magneto-rotational supernovae, based on a new explosion mechanism induced by the magneto-rotational instability (MRI). A series of axisymmetric magneto-hydrodynamical simulations with detailed microphysics including neutrino heating is performed, numerically resolving the MRI. Neutrino-heating dominated explosions, enhanced by magnetic fields, showed mildly neutronrich ejecta producing nuclei up to A similar to 130 (i. e., the weak r-process), while explosion models with stronger magnetic fields reproduce a solar-like r-process pattern. More commonly seen abundance patterns in our models are in between the weak and regular r-process, producing lighter and intermediate-mass nuclei. These intermediate r-processes exhibit a variety of abundance distributions, compatible with several abundance patterns in r-process-enhanced metal-poor stars. The amount of Eu ejecta similar to 10(-5) M circle dot in magnetically driven jets agrees with predicted values in the chemical evolution of early galaxies. In contrast, neutrino-heating dominated explosions have a significant amount of Fe (Ni-56) and Zn, comparable to regular supernovae and hypernovae, respectively. These results indicate magneto-rotational supernovae can produce a wide range of heavy nuclei from iron-group to r-process elements, depending on the explosion dynamics.

A new method for multi-dimensional stellar structures is proposed in this study. As for stellar evolution calculations, the Heney method is the defacto standard now, but basically assumed to be spherical symmetric. It is one of the difficulties for deformed stellar-evolution calculations to trace the potentially complex movements of each fluid element. On the other hand, our new method is very suitable to follow such movements, since it is based on the Lagrange coordinate. This scheme is also based on the variational principle, which is adopted to the studies for the pasta structures inside of neutron stars. Our scheme could be a major break through for evolution calculations of any types of deformed stars: proto-planets, proto-stars, and proto-neutron stars, etc.

We construct new equations of state for baryons at sub-nuclear densities for the use in core-collapse supernova simulations. The abundance of various nuclei is obtained together with thermodynamic quantities. The formulation is an extension of the previous model, in which we adopted the relativistic mean field theory with the TM1 parameter set for nucleons, the quantum approach for d, t, h and alpha as well as the liquid drop model for the other nuclei under the nuclear statistical equilibrium. We reformulate the model of the light nuclei other than d, t, h and alpha based on the quasi-particle description. Furthermore, we modify the model so that the temperature dependences of surface and shell energies of heavy nuclei could be taken into account. The pasta phases for heavy nuclei and the Pauli- and self-energy shifts for d, t, h and alpha are taken into account in the same way as in the previous model. We find that nuclear composition is considerably affected by the modifications in this work, whereas thermodynamical quantities are not changed much. In particular, the washout of shell effect has a great impact on the mass distribution above T similar to 1 MeV. This improvement may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. (C) 2016 Elsevier B.V. All rights reserved.

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.

The explosion mechanism of core-collapse supernovae (CCSNe) has not been fully understood yet, but multidimensional fluid instabilities such as standing accretion shock instability and convection are now believed to be crucial for shock revival. Another multidimensional 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 nonspherical envelopes could facilitate shock revival. These two multidimensional effects may hence hold a key to successful explosions. In this paper, we performed a linear stability analysis of the standing accretion shock in CCSNe, taking into account nonspherical, unsteady accretion flows onto the shock to clarify the possible links between the two effects. We found that such preshock perturbations can excite the fluid instabilities efficiently and hence help the shock revive in CCSNe.

We propose to employ the circular polarization of gravitational waves emitted by core-collapse supernovae as an unequivocal indication of rapid rotation deep in their cores just prior to collapse. It has been demonstrated by three dimensional simulations that nonaxisymmetric accretion flows may develop spontaneously via hydrodynamical instabilities in the postbounce cores. It is not surprising, then, that the gravitational waves emitted by such fluid motions are circularly polarized. We show, in this Letter, that a network of the second generation detectors of gravitational waves worldwide may be able to detect such polarizations up to the opposite side of the Galaxy as long as the rotation period of the core is shorter than a few seconds prior to collapse.

We carried out two-dimensional axisymmetric MHD. simulations of core-collapse supernovae for rapidly rotating magnetized progenitors. By changing both the strength of the magnetic field and the spatial resolution, the evolution of the magnetorotational instability (MRI) and its impacts upon the dynamics are investigated. We found that the MRI greatly amplifies the seed magnetic fields in the regime where. the buoyant mode, not the Alfven mode,. plays a primary role in the exponential growth phase. The MRI indeed has a powerful impact on the supernova dynamics. It makes the shock expansion faster and the explosion more energetic, with some models being accompanied by the collimated jet formations. These effects, however, are not made by the magnetic pressure except for the collimated jet formations. The angular momentum transfer induced by the MRI causes the expansion of the heating region, by which the accreting matter gain. additional time to be heated by neutrinos. The MRI also drifts low-Y-p matter from deep inside of the core to the heating region, which makes the net neutrino heating rate larger by the reduction of the cooling due to the electron capture. These two effects enhance the efficiency of the neutrino heating, which is found to be the key to boosting the explosion. Indeed, we found that our models explode far more weakly when the net neutrino heating is switched off. The contribution of the neutrino heating to the explosion energy could reach 60% even in the case of strongest magnetic field in the current simulations.

We study transitions of hadronic matter (HM) to three-flavor quark matter (3QM) locally, regarding the conversion processes as combustion and describing them hydrodynamically. Not only the jump condition on both sides of the conversion front but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions as well as equations of state (EOSs) in the mixed phase. Under the assumption that HM is metastable with their free energies being larger than those of 3QM but smaller than those of two-flavor quark matter (2QM), we consider the transition via 2QM triggered by a rapid density rise in a shock wave. Based on the results, we discuss which combustion modes (strong/weak detonation) may be realized. HM is described by an EOS based on the relativistic mean field theory, and 2QMs and 3QMs are approximated by the MIT bag model. We demonstrate for a wide range of the bag constant and strong coupling constant in this combination of EOSs that the combustion may occur in the so-called endothermic regime, in which the Hugoniot curve for combustion runs below the one for the shock wave in the p-V plane and which has no terrestrial counterpart. Elucidating the essential features in this scenario first by a toy model, we then analyze more realistic models. We find that strong detonation always occurs. Depending on the EOS of quark matter as well as the density of HM and the Mach number of the detonation front, deconfinement from HM to 2QM is either completed or not completed in the shock wave. In the latter case, which is more likely if the EOS of quark matter ensures that deconfinement occurs above the nuclear saturation density and that the maximum mass of cold quark stars is larger than 2M circle dot, the conversion continues further via the mixing state of HM and 3QM on the time scale of weak interactions.

We study transitions of hadronic matter (HM) to three-flavor quark matter (3QM), regarding the conversion processes as combustion and describing them hydrodynamically. Under the assumption that HM is metastable with their free energies being larger than those of 3QM but smaller than those of two-flavor quark matter, we consider in this paper the conversion induced by diffusions of the seed 3QM. This is a sequel to our previous paper, in which the shock-induced conversion was studied in the same framework. We not only pay attention to the jump condition on both sides of the conversion front, but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions. We employ for HM Shen's equation of state (EOS), which is based on the relativistic mean field theory, and the bag model-based EOS for quark matter just as in the previous paper. We demonstrated in that paper that in this combination of EOSs, the combustion will occur for a wide range of the bag constant and strong coupling constant in the so-called endothermic regime, in which the Hugoniot curve for combustion runs below the initial state. Elucidating the essential features of the diffusion-induced conversion both in the exothermic and endothermic regimes first by a toy model, we then analyze more realistic models. We find that weak deflagration nearly always occurs and that weak detonation is possible only when the diffusion constant is (unrealistically) large and the critical strange fraction is small. The velocities of the conversion front are similar to 10(3)-10(7) cm/s depending on the initial temperature and density as well as the parameters in the quark matter EOS and become particularly small when the final state is in the mixed phase. Finally we study linear stability of the laminar weak-deflagration front and find that it is unstable in the exothermic regime (Darrius-Landau instability) but stable in the endothermic regime, which is quite contrary to the ordinary combustions.

We conducted one-pdimensional. and two-pdimensional. hydrodynamic simulations of post-pshock. revival evolutions in core-pcollapse supernovae, employing the simple neutrino light. bulb approximation to produce explosions rather easily. In order to estimate the explosion energy, we took into proper account nuclear recombinations and fusions consistently with the equation of state for matter not. in statistical equilibrium in general. The methodology is similar to our previous work, but is somehow improved. In this paper, we studied the influence of the progenitor structure on the dynamics systematically. In order to expedite our understanding of the systematics, we constructed six parametric progenitor models, which are different in masses of Fe iron core and Si+S layer, instead of employing realistic models provided by stellar evolution calculations, which are sometimes of stochastic nature as a function of stellar mass on the main sequence. We found that the explosion energy is tightly correlated with the mass accretion rate at shock revival irrespective of dimension and the progenitors with light iron cores but with rather high entropies, which have. yet to be produced by realistic stellar evolution calculations, may reproduce the canonical values of explosion energy and nickel mass. The mass of the Si+S layer is also important in the mass accretion history after bounce, on the other hand; the higher mass accretion rates and resultant heavier cores tend to hamper strong explosions.

We perform numerical experiments to investigate the influence of inelastic neutrino reactions with light nuclei on the standing accretion shock instability. The time evolutions of shock waves are calculated with a simple light-bulb approximation for the neutrino transport and a multi-nuclei equation of state. The neutrino absorptions and inelastic interactions with deuterons, tritons, helions and alpha particles are taken into account in the hydrodynamical simulations in addition to the ordinary charged-current interactions with nucleons. Axial symmetry is assumed but no equatorial symmetry is imposed. We show that the heating rates of deuterons reach as high as 10% of those of nucleons around the bottom of the gain region. On the other hands, alpha particles heat the matter near the shock wave, which is important when the shock wave expands and density and temperature of matter become low. It is also found that the models with heating by light nuclei have different evolutions from those without it in non-linear evolution phase. The matter in the gain region has various densities and temperatures and there appear regions that are locally rich in deuterons and alpha particles. These results indicate that the inelastic reactions of light nuclei, especially deuterons, should be incorporated in the simulations of core-collapse supernovae.

Some high-energy photons are thought to be produced by the inverse Compton scattering process in ultrarelativistic flows, and the high-energy component of spectra in gamma-ray bursts can be interpreted by the process. To examine numerically the trajectory of photons traveling in relativistic jets in detail, a coupled computation method of radiative transport with relativistic hydrodynamics is required. We have developed a three-dimensional code of radiative transport on a background with a relativistic flow using Monte Carlo method. Radiative transfer simulations have been implemented in different inertial frames which are described as a shock rest frame or shock moving frames, and obtained results are compared in the shock rest frame to identify a consistent transformation among different frames. Optical depth tau for every directions agrees among each frame if a time duration of the computation is small enough to resolve photon path close to a shock front with almost the speed of light. Although the obtained results of the direction distribution and the spectrum of the escaped photons from the computational domain in each frame show discrepancies due to different flow velocities, they are identical after Lorentz transforming to the shock rest frame. We found the second peak of energy in the high-energy side of the spectra if the simulation condition is determined to allow the scattering process in the upstream side of the shock, and this peak is formed by the inverse Compton scattering process. (C) 2014 Elsevier B.V. All rights reserved.

Aiming to distinguish two types of progenitors of core-collapse supernovae, i.e., one with a core composed mainly of oxygen and neon (abbreviated as ONe core) and the other with an iron core (or Fe core), we calculated the luminosities and spectra of neutrinos emitted from these cores prior to gravitational collapse, taking neutrino oscillation into account. We found that the total energies emitted as (nu) over bar (e) from the ONe core are less than or similar to 10(46) erg, which is much smaller than similar to 10(47) erg for Fe cores. The average energy, on the other hand, is twice as large for the ONe core as those for the Fe cores. The neutrinos produced by the plasmon decays in the ONe core are more numerous than those from the electron-positron annihilation in both cores, but they have much lower average energies less than or similar to 1 MeV. Although it is difficult to detect the pre-supernova neutrinos from the ONe core even if it is located within 200 pc from Earth, we expect similar to 9-43 and similar to 7-61 events for Fe cores at KamLAND and Super-Kamiokande, respectively, depending on the progenitor mass and neutrino-mass hierarchy. These numbers might be increased by an order of magnitude if we envisage next-generation detectors such as JUNO. We will hence be able to distinguish the two types of progenitors by the detection or nondetection of the pre-supernova neutrinos if they are close enough (less than or similar to 1 kpc).

We investigate the possible effects of the supernova (SN) ejecta hitting the companion star in iPTF 13bvn, focusing on the observable features when it becomes visible. iPTF 13bvn is a type Ib SN that may become the first case in which its progenitor is identified as a binary (by observations in the near future). According to calculations by Bersten et al. the progenitor should have a mass approximate to 3.5 M-circle dot to reproduce the SN light curve, and such compact stars can only be produced via binary evolution. This is one of the reasons that we expect the progenitor to be a binary, but this. should be confirmed by observing the remaining companion after the SN. Bersten et al.'s evolutionary calculations suggest that the companion star will be an overluminous OB star at the moment of SN. With a combination of hydrodynamical and evolutionary simulations, we find that the secondary star will be heated by the SN ejecta and expand to have larger luminosities and lower surface effective temperatures. The star will look like a red supergiant. and this should be taken into account when searching for the companion star in the SN ejecta in future observations.

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This Letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of O(10(-4)) in the virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.

We study the multi-dimensional properties of neutrino transfer inside supernova cores by solving the Boltzmann equations for neutrino distribution functions in genuinely six-dimensional phase space. Adopting representative snapshots of the post-bounce core from other supernova simulations in three dimensions, we solve the temporal evolution to stationary states of neutrino distribution functions using our Boltzmann solver. Taking advantage of the multi-angle and multi-energy feature realized by the S-n method in our code, we reveal the genuine characteristics of spatially three-dimensional neutrino transfer, such as nonradial fluxes and nondiagonal Eddington tensors. In addition, we assess the ray-by-ray approximation, turning off the lateral-transport terms in our code. We demonstrate that the ray-by-ray approximation tends to propagate fluctuations in thermodynamical states around the neutrino sphere along each radial ray and overestimate the variations between the neutrino distributions on different radial rays. We find that the difference in the densities and fluxes of neutrinos between the ray-by-ray approximation and the full Boltzmann transport becomes similar to 20%, which is also the case for the local heating rate, whereas the volumeintegrated heating rate in the Boltzmann transport is found to be only slightly larger (similar to 2%) than the counterpart in the ray-by-ray approximation due to cancellation among different rays. These results suggest that we should carefully assess the possible influences of various approximations in the neutrino transfer employed in current simulations of supernova dynamics. Detailed information on the angle and energy moments of neutrino distribution functions will be profitable for the future development of numerical methods in neutrino-radiation hydrodynamics.

We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled to hydrodynamics equations. It is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of advection and collision terms in the Boltzmann equations is the source of difficulties, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce and shock-stall for a 15M(circle dot) progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects in our method.

We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind an application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch & Ott demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of a Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15M(circle dot) progenitor model by Woosley & Heger, which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically show that the growth rate is proportional to l, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.

The majority of massive stars are formed in binary systems. It is hence reasonable to expect that most core-collapse supernovae (CCSNe) take place in binaries and the existence of a companion star may leave some imprints in observed features. Having this in mind, we have conducted two-dimensional hydrodynamical simulations of the collisions of CCSNe ejecta with the companion star in an almost-equal-mass (similar to 10 M-circle dot) binary to find out possible consequences of such events. In particular we pay attention to the amount of mass removed and its dependence on the binary separation. In contrast to the previous surmise, we find that the companion mass is stripped not by momentum transfer but by shock heating. Up to 25% of the original mass can be removed for the closest separations and the removed mass decreases as M-ub alpha a(-4.3) with the binary separation a. By performing some experimental computations with artificially modified densities of incident ejecta, we show that if the velocity of ejecta is fixed, the density of incident ejecta is the single important parameter that actually determines the removed mass as M-ub alpha rho(1.4)(ej). On the other hand, another set of simulations with modified velocities of incident ejecta demonstrate that the strength of the forward shock, which heats up the stellar material and causes the mass loss of the companion star, is actually the key parameter for the removed mass.

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 not equal 0 modes of neutrino-driven convection or SASI are important for shock revival around the critical surface.

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.

We have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of non-regular shocks: intermediate shocks and switch-on/off shocks. Furthermore, the initial conditions with vanishing normal or transverse magnetic fields can be handled, although the code is partly based on the algorithm proposed by Torrilhon (2002) (Torrilhon, M. 2002 Exact solver and uniqueness condition for Riemann problems of ideal magnetohydrodynamics. Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich, Switzerland), which cannot deal with all types of non-regular waves nor the initial conditions without normal or transverse magnetic fields. Our solver can find all the solutions for a given Riemann problem, and hence, as demonstrated in this paper, one can investigate the structure of the solution space in detail. Therefore, the solver is a powerful instrument to solve the outstanding problem of existence and uniqueness of solutions of MHD Riemann problems. Moreover, the solver may be applied to numerical MHD schemes like the Godunov scheme in the future.

We derive a conservative form of Boltzmann's equation in general relativity, which is concisely written. Several explicit forms of this equation are written for black-hole spacetime with several coordinate conditions in real spacetime and momentum-space coordinates.

We investigated the impact of magnetorotational instability (MRI) on the dynamics of weakly magnetized, rapidly rotating core-collapse supernovae by conducting high-resolution axisymmetric MHD simulations with simplified neutrino transfer. We found that an initially sub-magnetar-class magnetic field is drastically amplified by MRI and substantially affects the dynamics thereafter. Although the magnetic pressure is not strong enough to eject matter, the amplified magnetic field efficiently transfers angular momentum from small to large radii and from higher to lower latitudes, which causes the expansion of the heating region due to the extra centrifugal force. This then enhances the efficiency of neutrino heating and eventually leads to neutrino-driven explosion. This is a new scenario of core-collapse supernovae that has never been demonstrated by past numerical simulations.

We investigate the r-process nucleosynthesis in the ejecta of core-collapse supernovae driven by rotation and magnetic fields. We adopt an explosion model based on axi-symmetric magneto- hydrodynamical simulation with the effects of magneto-rotational instability, which has been mostly ignored in previous studies. The hydrodynamics simulation also employs a very simplified treatment of neutrino transport on explosion dynamics, which includes the increase of explosion energy due to neutrino heating. We found that very neutron-rich matter in the jet-like explosion, producing heavy r-process nuclei, is ejected along the rotational axis driven by strong magnetic pressure. On the other hand, moderate neutron-rich matter is also ejected in the direction of the equatorial plane due to neutrino-heating associated with the magneto-rotational instability. This ejecta produces lighter and intermediate r-process nuclei rather than heavy isotopes A &gt
130. We compare these results with observed r-process abundances pattern.

We suggest a new experimental approach to conduct a systematic study in core collapse supernovae (CCSNe) theory. We provide toy pre-supernova stages with controlled core and silicon sulfer (Si+S) layer masses solving NSE and QSE compostions respectively. We also demonstrated 1D hydrodynamic simulations with light bulb approximation using 6 models from core collapse to explosion in order to study the dependence of the interior structures of pre-supernova stages on both explosion energies and nickel masses. During the core collapse our simulation showed that Si+S layer masses are most important in deciding the time evolution of mass accretion rates after bounce. We also found that the lighter core mass models produce the more energetic explosions and larger amounts of nickel masses. When the Si+S layer masses are lighter, mass accretion rates are enhanced so that the heavy core mass models are prevented from producing powerful explosions. Our simulation shows neccesity of early time explosion to reproduce 1051 erg .

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This Letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of O(10&lt
sup&gt
-4&lt
/sup&gt
) in the virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.

We have developed an entirely new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. It is based on the Lagrangian variational principle and, as a consequence, will allow us to apply it to stellar evolution calculations rather easily. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional. We also present the analogies between the study on rotating stellar configurations and the one on deformed nuclei. Possible applications are not limited to main sequence stars but will be extended to e.g. compact stars, proto-stars and planets. We believe that our formulation will be a major break-through then.

We perform numerical experiments to investigate the influence of inelastic neutrino reactions with light nuclei on the standing accretion shock instability. The time evolutions of shock waves are calculated with a simple light-bulb approximation for the neutrino transport and a multi-nuclei equation of state. The neutrino absorptions and inelastic interactions with deuterons, tritons, helions and alpha particles are taken into account in the hydrodynamical simulations in addition to the ordinary charged-current interactions with nucleons. Axial symmetry is assumed but no equatorial symmetry is imposed. We show that the heating rates of deuterons reach as high as 10% of those of nucleons around the bottom of the gain region. On the other hands, alpha particles heat the matter near the shock wave, which is important when the shock wave expands and density and temperature of matter become low. It is also found that the models with heating by light nuclei have different evolutions from those without it in non-linear evolution phase. The matter in the gain region has 1/allot's densities and temperatures and there appear regions that are locally rich in deuterons and alpha particles. These results indicate that the inelastic reactions of light nuclei, especially deuterons, should be incorporated in the simulations of core-collapse supernovae.

We perform numerical experiments to investigate the influence of inelastic neutrino reactions with light clusters in hot nuclear matter on core-collapse supernova simulations. These interactions have been neglected in most hydrodynamical supernova simulations. The neutrino absorptions and inelastic interactions with deuterons, tritons, helions and alpha particles are taken into account in the hydrodynamical simulations in addition to the ordinary charged-current interactions with nucleons. Axial symmetry is assumed but no equatorial symmetry is imposed. The time evolutions of shock waves are calculated with a simple light-bulb approximation for the neutrino transport and a multi-nuclei equation of state. We show that the heating rates of deuterons reach as high as similar to 10% of those of nucleons around the bottom of the gain region. On the other hand, alpha particles heat the matter near the shock wave, which is important when the shock wave expands and density and temperature of matter become low. It is also found that the models with heating by light clusters have different evolutions from those without it in non-linear evolution phase. The matter in the gain region has various densities and temperatures and there appear regions that are locally rich in deuterons and alpha particles. These results indicate that the inelastic reactions of light clusters, especially deuterons, should be incorporated in the simulations of core-collapse supernovae.

We have built a new exact Riemann solver for ideal magnetohydrodynamics (MHD) that can handle all types of the non-regular waves, such as intermediate shocks and switch-on/off waves. This code can find all the exact solutions for a given MHD Riemann problem. Using the solver, we found that there are uncountably many non-regular solutions for the Brio & Wu problem, which is one of the best-known MHD Riemann problems as it is used as a test problem for numerical codes. This result has cast a question on the numerical MHD simulations: Why do most of the numerical MHD codes always produce a typical non-regular solution which consists of a compound wave?

We explore photospheric emissions from stratified two-component jets, wherein a highly relativistic spine outflow is surrounded by a wider and less relativistic sheath outflow. Thermal photons are injected in regions of high optical depth and propagated until the photons escape at the photosphere. Because of the presence of shear in velocity (Lorentz factor) at the boundary of the spine and sheath region, a fraction of the injected photons are accelerated using a Fermi-like acceleration mechanism such that a high-energy power-law tail is formed in the resultant spectrum. We show, in particular, that if a velocity shear with a considerable variance in the bulk Lorentz factor is present, the high-energy part of observed gamma-ray bursts (GRBs) photon spectrum can be explained by this photon acceleration mechanism. We also show that the accelerated photons might also account for the origin of the extra-hard power-law component above the bump of the thermal-like peak seen in some peculiar bursts (e.g., GRB 090510, 090902B, 090926A). We demonstrate that time-integrated spectra can also reproduce the low-energy spectrum of GRBs consistently using a multi-temperature effect when time evolution of the outflow is considered. Last, we show that the empirical E _p-L _p relation can be explained by differences in the outflow properties of individual sources....

Context. Hadronic matter undergoes a deconfinement transition to quark matter at high temperature and/or high density. It would be realized in collapsing cores of massive stars.
Aims. In the framework of theMIT bag model, the ambiguities of the interaction are encapsulated in the bag constant. Some progenitor stars that invoke the core collapses explode as supernovae, and other ones become black holes. The fates of core collapses are investigated for various cases.
Methods. Equations of state including the hadron- quark phase transition are constructed for the cases of the bag constant B = 90, 150, and 250 MeV fm- 3. To describe the mixed phase, the Gibbs condition is used. Adopting the equations of state with different bag constants, the core collapse simulations are performed for the progenitor models with 15 and 40 M-circle dot.
Results. If the bag constant is small, for example B = 90 MeV fm(-3), the interval between the bounce and black hole formation is shortened drastically for the model with 40 M-circle dot, and the second bounce revives the shock wave leading to explosion for the model with 15 M-circle dot.

We perform numerical experiments to investigate the influence of inelastic neutrino reactions with light nuclei on the standing accretion shock instability (SASI). The time evolution of shock waves is calculated with a simple light-bulb approximation for the neutrino transport and a multi-nuclei equation of state. The neutrino absorptions and inelastic interactions with deuterons, tritons, helions, and alpha particles are taken into account in the hydrodynamical simulations. In addition, the effects of ordinary charged-current interactions with nucleons is addressed in the simulations. Axial symmetry is assumed but no equatorial symmetry is imposed. We show that the heating rates of deuterons reach as high as similar to 10% of those of nucleons around the bottom of the gain region. On the other hand, alpha particles are heated near the shock wave, which is important when the shock wave expands and the density and temperature of matter become low. It is also found that the models with heating by light nuclei evolve differently in the non-linear phase of SASI than do models that lack heating by light nuclei. This result is because matter in the gain region has a varying density and temperature and therefore sub-regions appear that are locally rich in deuterons and alpha particles. Although the light nuclei are never dominant heating sources and they work favorably for shock revival in some cases and unfavorably in other cases, they are non-negligible and warrant further investigation.

We construct new equations of state for baryons at subnuclear densities for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with thermodynamic quantities. A model free energy is constructed, based on the relativistic mean field theory for nucleons and the mass formula for nuclei with the proton number up to similar to 1000. The formulation is an extension of the previous model, in which we adopted the liquid drop model to all nuclei under the nuclear statistical equilibrium. We reformulate the new liquid drop model so that the temperature dependences of bulk energies could be taken into account. Furthermore, we extend the region in the nuclear chart, in which shell effects are included, by using theoretical mass data in addition to experimental ones. We also adopt a quantum-theoretical mass evaluation of light nuclei, which incorporates the Pauli- and self-energy shifts that are not included in the ordinary liquid drop model. The pasta phases for heavy nuclei are taken into account in the same way as in the previous model. We find that the abundances of heavy nuclei are modified by the shell effects of nuclei and temperature dependence of bulk energies. These changes may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. The abundances of light nuclei are also modified by the new mass evaluation, which may affect the heating and cooling rates of supernova cores and shocked envelopes.

We perform experimental simulations with spherical symmetry and axisymmetry to understand the post-shock-revival evolution of core-collapse supernovae. Assuming that the stalled shock wave is relaunched by neutrino heating and employing the so-called light bulb approximation, we induce shock revival by raising the neutrino luminosity up to the critical value, which is determined by dynamical simulations. A 15 M-circle dot progenitor model is employed. We incorporate nuclear network calculations with a consistent equation of state in the simulations to account for the energy release by nuclear reactions and their feedback to hydrodynamics. Varying the shock-relaunch time rather arbitrarily, we investigate the ensuing long-term evolutions systematically, paying particular attention to the explosion energy and nucleosynthetic yields as a function of relaunch time, or equivalently, the accretion rate at shock revival. We study in detail how the diagnostic explosion energy approaches the asymptotic value and which physical processes contribute in what proportions to the explosion energy. Furthermore, we study the dependence of physical processes on the relaunch time and the dimension of dynamics. We find that the contribution of nuclear reactions to the explosion energy is comparable to or greater than that of neutrino heating. In particular, recombinations are dominant over burnings in the contributions of nuclear reactions. Interestingly, one-dimensional (1D) models studied in this paper cannot produce the appropriate explosion energy and nickel mass simultaneously; nickels are overproduced. This problem is resolved in 2D models if the shock is relaunched at 300-400 ms after the bounce.

We performed the first global numerical simulations of magnetorotational instability from a sub-magnetar-class seed magnetic field in core-collapse supernovae. As a result of axisymmetric ideal MHD simulations, we found that the magnetic field is greatly amplified to magnetar-class strength. In the saturation phase, a substantial part of the core is dominated by turbulence, and the magnetic field possesses dominant large-scale components, comparable to the size of a proto-neutron star. A pattern of coherent channel flows, which generally appears during the exponential growth phase in previous local simulations, is not observed in our global simulations. While the approximate convergence in the exponential growth rate is attained by increasing spatial resolution, that of the saturation magnetic field is not achieved due to still large numerical diffusion. Although the effect of the magnetic field on the dynamics is found to be mild, a simulation with a high enough resolution might result in a larger impact. © 2013. The American Astronomical Society. All rights reserved.

We have built a code to numerically solve the Riemann problem in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition to investigate a variety of solutions more thoroughly. The code can handle not only regular solutions, in which no intermediate shocks are involved, but also all types of non-regular solutions if any. As a first application, we explored the neighborhood of the initial condition that was first picked up by Brio and Wu (1988) (Brio, M. and Wu, C. C. 1988 An upwind differencing scheme for the equation of ideal magnetohydrodynamics. J. Comput. Phys. 75, 400-422) and has been frequently employed in the literature as a standard problem to validate numerical codes. Contrary to the conventional wisdom that there will always be a regular solution, we found an initial condition for which there is no regular solution but a non-regular one. The latter solution has only regular solutions in its neighborhood and actually sits on the boundary of regular solutions. This implies that the regular solutions are not sufficient to solve the ideal MHD Riemann problem and suggests that at least some types of non-regular solutions are physical. We also demonstrate that the non-regular solutions are not unique. In fact, we found for the Brio and Wu initial condition that there are uncountably many non-regular solutions. This poses an intriguing question: Why a particular non-regular solution is always obtained in numerical simulations? This has important ramifications to the discussion of which intermediate shocks are really admissible.

We present numerical attempts of radiative transfer in a relativistic scattering flow that can produce gamma rays using a three-dimensional Monte Carlo code. We prepared an initial background flowfield obtained from hydrodynamical simulation of a relativistic jet in which Thomson scattering dominates compared to absorption, and solved the radiative transfer equation for the background evolved by a simple expansion model. Since a large number of sample particles is required for an accurate computation, we have parallelized the Monte Carlo code in order to obtain solutions in a practical computational time even for a long-term simulation coupled with a time-dependent flowfield. Using this code, higher parallel efficiency is achieved with larger number of particles. The obtained light curve from the simple model shows a signal of the transition from the opaque post-shock flow to the transparent regime as the flow expands, and the high-energy photons are generated by not only the Doppler boosting but also the inverse Compton scattering. (c) 2013 Elsevier B.V. All rights reserved.

We compare three different statistical models for the equation of state (EOS) of stellar matter at sub-nuclear densities and temperatures (0.5-10 MeV) expected to occur during the collapse of massive stars and supernova explosions. The models introduce the distributions of various nuclear species in nuclear statistical equilibrium, but use somewhat different nuclear physics inputs. It is demonstrated that the basic thermodynamical quantities of stellar matter under these conditions are similar, except in the region of high densities and low temperatures. We demonstrate that mass and isotopic distributions have considerable differences related to the different assumptions of the models on properties of nuclei at these stellar conditions. Overall, the three models give similar trends, but the details reflect the uncertainties related to the modeling of medium effects, such as the temperature and density dependence of surface and bulk energies of heavy nuclei, and the nuclear shell structure effects. We discuss importance of new physics inputs for astrophysical calculations from experimental data obtained in intermediate energy heavy-ion collisions, in particular, the similarities of the conditions reached during supernova explosions and multifragmentation reactions. (c) 2013 Elsevier B.V. All rights reserved.

We present a new series of supernova neutrino light curves and spectra calculated by numerical simulations for a variety of progenitor stellar masses (13-50 M-circle dot) and metallicities (Z = 0.02 and 0.004), which would be useful for a broad range of supernova neutrino studies, e. g., simulations of future neutrino burst detection by underground detectors or theoretical predictions for the relic supernova neutrino background. To follow the evolution from the onset of collapse to 20 s after the core bounce, we combine the results of neutrino-radiation hydrodynamic simulations for the early phase and quasi-static evolutionary calculations of neutrino diffusion for the late phase, with different values of shock revival time as a parameter that should depend on the still unknown explosion mechanism. We describe the calculation methods and basic results, including the dependence on progenitor models and the shock revival time. The neutrino data are publicly available electronically.

We develop a new semi-dynamical method to study shock revival by neutrino heating in core-collapse supernovae. Our new approach is an extension of the previous studies that employ spherically symmetric, steady, shocked accretion flows together with the light-bulb approximation. The latter has been widely used in the supernova community for the phenomenological investigation of the criteria for successful supernova explosions. In the present approach, we get rid of the steady-state condition and take into account shock wave motions instead. We have in mind a scenario in which it is not the critical luminosity but the critical fluctuation generated by hydrodynamical instabilities such as standing accretion shock instability and neutrino-driven convection in the post-shock region that determines the onset of shock revival. After confirming that the new approach indeed captures the dynamics of revived shock wave qualitatively, we then apply the method to various initial conditions and find that there is a critical fluctuation for shock revival, which can be well fit by the following formula: f(crit) similar to 0.8 x (M-in/1.4 M-circle dot) x {1 - (r(sh)/10(8) cm)}, where f(crit) denotes the critical pressure fluctuation normalized by the unperturbed post-shock value. M-in and r(sh) stand for the mass of the central compact object and the shock radius, respectively. The critical fluctuation decreases with the shock radius, whereas it increases with the mass of the central object. We discuss the possible implications of our results for three-dimensional effects on shock revival, which is currently controversial in the supernova community.

We studied the role of turbulent resistivity in the core-collapse of a strongly magnetized massive star, carrying out two-dimensional resistive-MHD simulations. Three cases with different initial strengths of magnetic field and rotation are investigated: (1) a strongly magnetized rotating core, (2) a moderately magnetized rotating core, and (3) a very strongly magnetized non-rotating core. In each case, one ideal-MHD model and two resistive-MHD models are computed. As a result of these computations, each model shows an eruption of matter assisted by magnetic acceleration (and also by centrifugal acceleration in the rotating cases). We found that resistivity attenuates the explosion in cases 1 and 2, while it enhances the explosion in case 3. We also found that in the rotating cases, the main mechanisms for the amplification of a magnetic field in the post-bounce phase are an outward advection of the magnetic field and a twisting of poloidal magnetic field lines by differential rotation, which are somewhat dampened down with the presence of resistivity. Although magnetorotational instability seems to occur in the rotating models, it plays only a minor role in magnetic field amplification. Another impact of resistivity is that on the aspect ratio. In the rotating cases, a large aspect ratio of the ejected matter, &gt
2.5, attained in an ideal-MHD model is reduced to some extent in a resistive model. These results indicate that resistivity possibly plays an important role in the dynamics of strongly magnetized supernovae. © 2013. The American Astronomical Society. All rights reserved.

We present results from the first phase of the KamLAND-Zen double-beta decay experiment, corresponding to an exposure of 89.5 kg yr of Xe136. We obtain a lower limit for the neutrinoless double-beta decay half-life of T1/20ν&gt;1.9×1025 yr at 90% C.L. The combined results from KamLAND-Zen and EXO-200 give T1/20ν&gt;3.4×1025 yr at 90% C.L., which corresponds to a Majorana neutrino mass limit of mββ &lt;(120-250) meV based on a representative range of available matrix element calculations. Using those calculations, this result excludes the Majorana neutrino mass range expected from the neutrinoless double-beta decay detection claim in Ge76, reported by a part of the Heidelberg-Moscow Collaboration, at more than 97.5% C.L. © 2013 American Physical Society.

We investigate the nucleosynthesis in a massive star of 70 M_{☉} with solar metallicity in the main sequence stage. The helium core mass after hydrogen burning corresponds to 32 M_{☉}. Nucleosynthesis calculations have been performed during the stellar evolution and the jetlike supernova explosion of a collapsar model. We focus on the production of elements heavier than iron group nuclei. Nucleosynthesis calculations have been accomplished consistently from hydrostatic to dynamic stages by using large nuclear reaction networks, where the weak s-, p-, and r-processes are taken into account. We confirm that s-elements of 60 &lt; A &lt; 90 are highly overproduced relative to the solar abundances in the hydrostatic nucleosynthesis. During oxygen burning, p-elements of A &gt; 90 are produced via photodisintegrations of seed s-elements. However, the produced p-elements are disintegrated in later stages except for ^{180}Ta. In the explosive nucleosynthesis, elements of 90 &lt; A &lt; 160 are significantly overproduced relative to the solar values owing to the r-process, which is very different from the results of spherical explosion models. Only heavy p-elements (N &gt; 50) are overproduced via the p-process because of the low peak temperatures in the oxygen- and neon-rich layers. Compared with the previous study of r-process nucleosynthesis calculations in the collapsar model of 40 M_{☉} by Fujimoto et al. [S. Fujimoto, M. Hashimoto, K. Kotake and S. Yamada, Astrophys. J. 656 (2007), 382; S. Fujimoto, N. Nishimura and M. Hashimoto, Astrophys. J. 680 (2008), 1350], our jet model cannot contribute to the third peak of the solar r-elements and intermediate p-elements, which have been much produced because of the distribution of the lowest part of electron fraction in the ejecta. Averaging the overproduction factors over the progenitor masses with the use of Salpeter's IMF, we suggest that the 70 M_{☉} star could contribute to the solar weak s}-elements of 60 &lt; A &lt; 90 and neutron-rich elements of 90 &lt; A &lt; 160. We confirm the primary synthesis of light p-elements in the ejected matter of high peak temperature. The ejected matter has [Sr/Eu] ̃ -0.4, which is different from that of a typical r-process-enriched star CS22892-052 ([Sr/Eu] ̃ -1). We find that Sr-Y-Zr isotopes are primarily synthesized in the explosive nucleosynthesis in a similar process of the primary production of light p-elements, which has been considered as one of the sites of a lighter element primary process (LEPP). <P />...

We develop a numerical code to calculate the neutrino transfer with multi-energy and multi-angle in three dimensions (3D) for the study of core-collapse supernovae. The numerical code solves the Boltzmann equations for neutrino distributions by the discrete-ordinate (S-n) method with a fully implicit differencing for time advance. The Boltzmann equations are formulated in the inertial frame with collision terms being evaluated to the zeroth order of v/c. A basic set of neutrino reactions for three neutrino species is implemented together with a realistic equation of state of dense matter. The pair process is included approximately in order to keep the system linear. We present numerical results for a set of test problems to demonstrate the ability of the code. The numerical treatments of advection and collision terms are validated first in the diffusion and free-streaming limits. Then we compute steady neutrino distributions for a background extracted from a spherically symmetric, general relativistic simulation of a 15M(circle dot) star and compare them with the results in the latter computation. We also demonstrate multi-dimensional capabilities of the 3D code solving neutrino transfers for artificially deformed supernova cores in 2D and 3D. Formal solutions along neutrino paths are utilized as exact solutions. We plan to apply this code to the 3D neutrino-radiation hydrodynamics simulations of supernovae. This is the first article in a series of reports on the development.

We investigate the emergence of hyperons in black-hole-forming failed supernovae, which are caused by the dynamical collapse of nonrotating massive stars. We perform neutrino-radiation hydrodynamical simulations in general relativity, adopting realistic hyperonic equation of state. Attractive and repulsive cases are examined for the potential of S hyperons. Since hyperons soften the EOS, they shorten the time interval from bounce to black hole formation, which corresponds to the duration of neutrino emission. This effect is more pronounced in the attractive case than in the repulsive case because S hyperons appear more easily. In addition, we investigate the impacts of pions to find that they also promote recollapse toward black hole formation.

We construct the equations of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with the ther-modynamic quantities. The formulation is the NSE description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with the atomic number up to ∼ 1000. We have also taken into account the pasta phase for heavy nuclei and the contribution of Pauli energies between free nucleons to binding energies to light nuclei. The experimental and theoretical mass data are employed to evaluate the shell effects of nuclei. We find that the abundance of heavy nuclei is different depending on shell effects of nuclei, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. The Pauli and self energy shifts also affect the abundance of light nuclei by comparing with ordinary nuclear statistical equilibrium results, which may affect the heating and cooling rates of supernova cores and shocked envelopes. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

We develop a new numerical code of the multi-energy and multi-angle neutrino radiation transfer in three dimensions (3D) for core-collapse supernovae. Our 3D code to solve the Boltzmann equations is based on the discretized-ordinate (S-N) method with a fully implicit differencing for time advance. A basic set of neutrino reactions is implemented in the collision terms together with a realistic equation of state. By following the time evolution of neutrino distributions in six dimensions (3 spatial and 3 momentum-space) by the 3D Boltzmann solver, we study the 3D feature of neutrino transfer for given background models of supernova cores in order to understand the explosion mechanism through neutrino heating in multi dimensions.

We investigate a proto-neutron star kick velocity estimated from kinetic momentum of a flow around the proto-neutron star after the standing accretion shock instability grows. In this study, ten different types of random perturbations are imposed on the initial flow for each neutrino luminosity. We found that the kick velocities of proto-neutron star are widely distributed from 40 km s(-1) to 180 km s(-1) when the shock wave reaches 2000 km away from the center of the star. The average value of kick velocity is 115 km s(-1), whose value is smaller than the observational ones. The kick velocities do not depend on the neutrino luminosity.

We construct a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is based on the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by using relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to similar to 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far.

Most of the sophisticated numerical simulations of the collapse-driven supernova explosions are performed until 1-2 seconds after bounce. On the other hand, we caluclate long term evolution of supernovae using spherical symmetric models and approximate neutrino transfer. We applied this scheme to the systematic study on evaluation of explosion energy E-exp.

We calculate a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to similar to 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.

We investigate the nucleosynthesis during the stellar evolution and the jet-like supernova explosion of a massive star of 70 M-circle dot having the solar metallicity in the main sequence stage. The nucleosynthesis calculations have been performed with large nuclear reaction networks, where the weak s-, p-, and r-processes are taken into account. As a result s-elements of 60 &lt; A &lt; 90 and r-elements of 90 &lt; A &lt; 160 are highly overproduced relative to the solar system abundances. We find that the Sr-Y-Zr isotopes are primarily synthesized in the explosive nucleosynthesis which could be one of the sites of the lighter element primary process (LEPP).

This is a status report on our endeavor to reveal the mechanism of core-collapse supernovae (CCSNe) by large-scale numerical simulations. Multi-dimensionality of the supernova engine, general relativistic magnetohydrodynamics, energy and lepton number transport by neutrinos emitted from the forming neutron star, as well as nuclear interactions there, are all believed to play crucial roles in repelling infalling matter and producing energetic explosions. These ingredients are non-linearly coupled with one another in the dynamics of core collapse, bounce, and shock expansion. Serious quantitative studies of CCSNe hence make extensive numerical computations mandatory. Since neutrinos are neither in thermal nor in chemical equilibrium in general, their distributions in the phase space should be computed. This is a six-dimensional (6D) neutrino transport problem and quite a challenge, even for those with access to the most advanced numerical resources such as the "K computer". To tackle this problem, we have embarked on efforts on multiple fronts. In particular, we report in this paper our recent progresses in the treatment of multidimensional (multi-D) radiation hydrodynamics. We are currently proceeding on two different paths to the ultimate goal. In one approach, we employ an approximate but highly efficient scheme for neutrino transport and treat 3D hydrodynamics and/or general relativity rigorously; some neutrino-driven explosions will be presented and quantitative comparisons will be made between 2D and 3D models. In the second approach, on the other hand, exact, but so far Newtonian, Boltzmann equations are solved in two and three spatial dimensions; we will show some example test simulations. We will also address the perspectives of exascale computations on the next generation supercomputers.

We calculate a new equation of state for baryons at sub-nuclear densities meant for the use in core-collapse simulations of massive stars. The abundances of various nuclei are obtained together with the thermodynamic quantities. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to similar to 1000. We have also taken into account the pasta phase, thanks to which the transition to uniform nuclear matter in our equation of state (EOS) occurs in the conventional manner: nuclei are not dissociated into nucleons but survive right up to the transition to uniform nuclear matter. We find that the free energy and other thermodynamical quantities are not very different from those given in the H. Shen&apos;s EOS, one of the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important ramification to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far. The EOS table is currently under construction, which will include the weak interaction rates.

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.

We explore the evolution of emissions by accelerated electrons in shocked shells driven by jets in active galactic nuclei. Focusing on powerful sources which host luminous quasars, we evaluated the broadband emission spectra by properly taking into account adiabatic and radiative cooling effects on the electron distribution. The synchrotron radiation and inverse Compton (IC) scattering of various photons that are mainly produced in the accretion disk and dusty torus are considered as radiation processes. We show that the resultant radiation is dominated by the IC emission for compact sources (less than or similar to 10 kpc), whereas the synchrotron radiation is more important for larger sources. We also compare shell emissions with those expected from the lobe under the assumption that the fractions of the energy deposited in the shell and lobe carried by non-thermal electrons are epsilon(e) similar to 0.01 and epsilon(e),(lobe) similar to 1, respectively. We find that shell emissions are brighter than lobe ones at infrared and optical bands when the source size is greater than or similar to 10 kpc, and the IC emissions from the shell at greater than or similar to 10 GeV can be observed with an absence of contamination from the lobe irrespective of the source size. In particular, it is predicted that, for most powerful nearby sources (L-j similar to 10(47) erg s(-1)), similar to TeV gamma-rays produced via IC emissions can be detected by modern Cherenkov telescopes such as MAGIC, HESS, and VERITAS.

We investigate the possibility of the r-process during the magnetohydrodynamical (MHD) explosion of supernova in a massive star of 13 M-circle dot with the effects of neutrinos included. Contrary to the case of the spherical explosion, jet-like explosion due to the combined effects of rotation and magnetic field lowers the electron fraction significantly inside the layers. We find that the ejected material of low electron fraction responsible for the r-process comes out from the inner deep region of the core that is made up of iron-group nuclei. This leads to the production of the second to third peak in the solar r-process elements. We suggest that there are some variations in the r-process nucleosynthesis according to the initial conditions of rotational and magnetic fields.

We investigate the heavy-element nucleosynthesis of a massive star whose mass in the main sequence stage is M-ms = 70 M-circle dot. Detailed calculations of the nucleosynthesis are performed during the hydrostatic stellar evolution until the core composed of iron-group nuclei begins to collapse. As a supernova explosion model, a collapsar model is constructed whose jets are driven by magnetohydrodynamical effects of a differentially rotating core. The heavy-element nucleosynthesis inside the jet of a collapsar model is followed along the trajectories of stream lines of the jet. We combine the results of both hydrostatic and heavy-element nucleosyntheses to compare with the solar abundances. We find that neutron-rich elements of 70 &lt; A &lt; 140 are highly overproduced relative to the solar abundances. Therefore, we conclude that this scenario should be rare and elements of A less than or similar to 70 are compensated for other supernova explosion models. We find also that different mass formula changes significantly the production of elements of A &gt; 140.

We numerically investigated the gravitational collapse of a rapidly rotating massive star and the subsequent propagation of relativistic jets, varying the timing of jet injection. In this study, we pay particular attention to observational consequences of the difference in the timing of jet injection. In order to discuss them, the light curve of photospheric emissions is also calculated by the post process. In calculating optical depths to find the location of the photosphere, we take into account the relativistic effect such as the time retardation accurately. We find that, as a consequence of rotating massive star collapse, the centrifugal shock wave (CSW) is formed, then it propagates outwards and breaks out of the envelope into the stellar wind. Which of the jet and CSW breaks out earlier depends on the timing of jet injection. If the CSW breakout occurs first owing to later jet injection, the jet propagation and subsequent photospheric emissions are affected substantially.

In the formation process of black holes, the density and temperature of matter become sufficiently high for quarks and pions to appear. In this study, we numerically investigate stellar core collapse and black hole formation taking into account the equations of state involving quarks and/or pions. In our simulations, we utilize a code that solves the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail under spherical symmetry. Initial models with three different masses, namely, 40, 100, and 375 M(circle dot), are adopted. Our results show that quarks and pions shorten the duration of neutrino emission if the collapse bounces before black hole formation. In addition, pions increase the luminosity and average energy of neutrinos before black hole formation. We also find that the hadron-quark phase transition leads to an interesting evolution of temperature. Moreover, the neutrino event number is evaluated for the currently operating neutrino detector, SuperKamiokande, to confirm that it is not only detectable but also affected by the emergence of quarks and pions for Galactic events. While there are some issues, such as hyperons, beyond the scope of this study, this is the first serious attempt to assess the impact of quarks and pions in dynamical simulations of black hole formation and will serve as an important foundation for future studies.

We present a new formula to numerically construct configurations in rotational equilibrium, which consists of multiple layers. Each layer rotates uniformly or differentially according to cylindrical rotation laws that are different from layer to layer. Assuming a different barotropic equation of state (EOS) for each layer, we solve the Bernoulli equation in each layer separately and combine the solutions by imposing continuity of the pressure at each boundary of the layers. It is confirmed that a single continuous barotropic EOS is incompatible with the junction condition. Identifying appropriate variables to be solved, we construct a convergent iteration scheme. For demonstration, we obtain two-layered configurations, each layer of which rotates rapidly with either an "Omega-constant law" or a "j-constant law" or a "v-constant law." Other rotation laws and/or a larger number of layers can be treated similarly. We hope that this formula will be useful in studying the stellar evolution in multi-dimension with the non-spherical configuration induced by rotation being fully taken into account.

We explore the emissions by accelerated electrons in shocked shells driven by jets in active galactic nuclei (AGNs). Focusing on powerful sources which host luminous quasars, the synchrotron radiation and inverse-Compton (IC) scattering of various photons that are mainly produced in the core are considered as radiation processes. We show that the radiative output is dominated by the IC emission for compact sources (less than or similar to 30 kpc), whereas the synchrotron radiation is more important for larger sources. It is predicted that, for powerful sources (L(j) similar to 10(47) ergs s(-1)), GeV-TeV gamma-rays produced via the IC emissions can be detected by the Fermi satellite and modern Cherenkov telescopes such as MAGIC, HESS and VERITAS if the source is compact.

We study how the influence of the shock wave appears in neutrino oscillations and the neutrino spectrum by using the density profile of the adiabatic explosion model of a core-collapse supernova, which is calculated in an implicit Lagrangian code for general relativistic spherical hydrodynamics. We calculate expected event rates of neutrino detection at Super-Kamiokande (SK) and Sudbury Neutrino Observatory (SNO) for various theta(13) values and both normal and inverted hierarchies. The predicted event rates of (nu) over bar (e) and nu(e) depend on the mixing angle theta(13) for the inverted and normal mass hierarchies, respectively, and the influence of the shock wave appears for about 2-8 s when sin(2)2 theta(13) is larger than 10(-3). These neutrino signals for the shock-wave propagation is decreased by less than or similar to 30% for (nu) over bar (e) in inverted hierarchy (SK) or by less than or similar to 15% for nu(e) in normal hierarchy (SNO) compared with the case without shock. The obtained ratio of the total event for high-energy neutrinos (20 MeV &lt;= E-v &lt;= 60 MeV) to low-energy neutrinos (5 MeV less than or similar to E &lt;= 20 MeV) is consistent with the previous studies in schematic semianalytic or other hydrodynamic models of the shock propagation. The time dependence of the calculated ratio of the event rates of high-energy neutrinos to the event rates of low-energy neutrinos is a very useful observable which is sensitive to theta(13) and mass hierarchies. Namely, the time-dependent ratio shows a clearer signal of the shock-wave propagation that exhibits a remarkable decrease by at most a factor of similar to 2 for (nu) over bar (e) in inverted hierarchy (SK), whereas it exhibits a smaller change by similar to 10% for nu(e) in normal hierarchy (SNO). Observing the time-dependent high-energy to low-energy ratio of the neutrino events thus would provide a piece of very useful information to constrain theta(13) and mass hierarchy and eventually help understand how the shock wave propagates inside the star.

We present that the appearance of hyperons plays a crucial role in failed supernovae from massive stars of similar to 40M(circle dot). The quick dynamics front the gravitational collapse to the black hole leads to extreme conditions, reaching high densities and temperatures to have strangeness particles, within 1 s after the core bounce. The associated neutrino bursts are short and energetic, being different from ordinary supernova neutrinos, and may provide the information on the strangeness in dense matter. The end point of the duration of neutrino burst is determined by the stiffness of EOS and the appearance of new particle is the trigger of the termination due to the black hole formation. By measuring the duration of burst and the energy spectrum, one can constrain the appearance of exotics. The event numbers of neutrinos from the black-hole-forming collapse at the terrestrial detector are found large enough to utilize this phenomena as a target of neutrino astronomy and a probe of dense matter with strangeness.

We discuss the properties of the supernova matter equation of state (EOS) including hyperons, and the emergence of hyperons in dynamical core-collapse processes. The recently tabulated EOS including hyperons is based on an SUf(3) extended relativistic mean field (RMF) model, in which the coupling constants of hyperons with scalar mesons are determined to fit the hyperon potential depths in nuclear matter, (U-Sigma, U-Xi) = (+30MeV, -15 MeV), which are suggested from recent analyses of hyperon production reactions. Hyperon effects are found to be small in the core-collapse and bounce stages, but abundant hyperons appear when the temperature becomes high during black hole formation and promote earlier collapse of the accreting proto-neutron star. The maximum mass of a hot proto-neutron star is discussed, and we give a rough estimate of the critical mass of the accreting proto-neutron star, at which the proto-neutron star re-collapses to a black hole.

The detection of neutrinos from massive stellar collapses can teach us a great deal not only about source objects but also about microphysics working deep inside them. In this study we discuss quantitatively the possibility to extract information on the properties of dense and hot hadronic matter from neutrino signals coming out of black-hole-forming collapses of nonrotational massive stars. Based on our detailed numerical simulations we evaluate the event numbers for SuperKamiokande, with neutrino oscillations fully taken into account. We demonstrate that the event numbers from a Galactic event are large enough not only to detect but also to distinguish one hadronic equation of state from another by our statistical method, assuming the same progenitor model and nonrotation. This means that the massive stellar collapse can be a unique probe into hadron physics and will be a promising target of the nascent neutrino astronomy.

We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading to highly eccentric orbital motions or ejections of some of the planets. In this paper, we are concerned with the underlying physics for this quasi-stability as well as the subsequent instability and advocate the so-called stagnant motion in the phase space, which has been explored in the field of a dynamical system. We employ the Lyapunov exponent, the power spectra of orbital elements, and the distribution of the durations of quasi-stable motions to analyze the phase-space structure of the three-planet system, the simplest and hopefully representative one that shows the instability. We find from the Lyapunov exponent that the system is almost non-chaotic in the initial quasi-stable state whereas it becomes intermittently chaotic thereafter. The non-chaotic motions produce the horizontal dense band in the action-angle plot whereas the voids correspond to the chaotic motions. We obtain power laws for the power spectra of orbital eccentricities. Power-law distributions are also found for the durations of quasi-stable states. With all these results combined together, we may reach the following picture: the phase space consists of the so-called KAM tori surrounded by satellite tori and imbedded in the chaotic sea. The satellite tori have a self-similar distribution and are responsible for the scale-free power-law distributions of the duration times. The system is trapped around one of the KAM torus and the satellites for a long time (the stagnant motion) and moves to another KAM torus with its own satellites from time to time, corresponding to the intermittent chaotic behaviors.

We investigate the possibility of the r-process during the magnetohydrohynamical explosion of supernova in a massive star of 13 solar mass with the effects of neutrinos induced. We adopt five kinds of initial models which include properties of rotation and the toroidal component of the magnetic field. The simulations which succeed the explosions are limitted to a concentrated magnetic field and strong differential rotation. Low Ye ejecta produce heavy elements and the third peak can be reproduced. However, the second peak is low because Ye distribution as a function of radius is steep and ejecta corresponding to middle Ye is very few.

We numerically investigate the effects of electrical resistivity on the dynamics of core-collapse supernovae. Initially strong magnetic fields and rapid rotations are assumed together with high resistivities. We find that resistivity acts as a negative reinforcer for the explosion. Although the thermal pressure is produced due to the Joule heating, an inefficiency of magnetic field amplification result in weaker total stress than that of the ideal magnetohydrodynamic computation and leads to less energetic explosion.

In this study we investigate numerically the stellar core collapse and black hole formation taking into account the EOS's involving quarks and/or pions. In our simulations, we utilize the code which solves the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail under spherical symmetry. Our results show that quarks and pions shorten the duration of neutrino emission if the collapse is bounced before the black hole formation. In addition, pions make the luminosity and average energy of neutrinos higher before the black hole formation.

We propose a new candidate for nuclear shapes at subnuclear densities in analogy with polymer shapes. We then find that the new candidate, gyroid morphology, may appear near the transition point from a cylinder to a slab as well as that from a slab to a cylindrical hole. Since this analogy between the nuclear and polymer systems is not only qualitative but also quantitative, our findings may offer a new field of interest. Further details of this study are seen in our lately published letter [1].

We have performed several simulations on non-rotational core-collapses of a star with 40M(circle dot) by a general relativistic v-radiation-hydrodynamics code and computed quantitatively the dynamics up to the black hole formation as well as the neutrino luminosities and spectra. Employing different hadronic equations of state (EOS), we have demonstrated that the duration of neutrino emissions from this event is sensitive to the stiffness of EOS at supra-nuclear densities and, therefore, that the observation of neutrinos from such an event will provide us with valuable information on the properties of dense and hot hadronic matter as well as on the maximum mass of proto-neutron stars. However, this approach can not distinguish EOS's with a similar stiffness: a soft nucleonic EOS and a hyperonic EOS, for example. In this study, we attempt to break this degeneracy by analyzing more in detail the time variation of neutrino numbers observed at a terrestrial detector. Performing the Kolmogolov-Smimov test, which is free from the ambiguity of the distance to the progenitor, we show that the break-up of the degeneracy of hadronic EOS's is indeed feasible for Galactic events.

We investigate the heavy-element nucleosynthesis of a massive star whose mass in the main sequence stage is M-ms = 70 M-circle dot. Numerical calculations of the nucleosynthesis are performed during the stage of hydrostatic stellar evolution until the core composed of iron-group nuclei begins to collapse. As a supernova explosion model, a collapsar model is constructed whose jets are driven by magnetohydrodynamical effects of a differentially rotating core. The heavy-element nucleosynthesis inside the jet of a collapsar model is followed along the trajectories of stream lines of the jet. We combine the results of both detailed hydrostatic and heavy-element nucleosyntheses to compare with the solar abundances. We find that neutron-rich elements of 70 &lt; A &lt; 160 are highly overproduced to the solar abundances. Therefore, we conclude that this scenario should be rare and elements of A less than or similar to 70 are compensated for other supernova explosion models.

We investigate the nucleosynthesis of a massive star whose mass in the main sequence stage is M_{ms} = 70 M_{☉} that corresponds to the helium core or helium star of M_α = 32 M_{☉}. Numerical calculations of the nucleosynthesis are performed during the stage of hydrostatic stellar evolution until the core composed of iron-group nuclei (Fe core) begins to collapse. A collapsar model whose jets are driven by two-dimensional magnetohydrodynamical effects of a differentially rotating core is constructed. The explosive nucleosynthesis inside the jets of a specified collapsar model is followed along the trajectories of stream lines. We combine the results of both detailed hydrostatic and explosive nucleosyntheses to compare the solar system abundances. We show that the agreement is considerably improved compared with the case without the detailed hydrostatic nucleosynthesis included. We suggest that many radioactive nuclei such as ^{44}Ti and ^{56,57}Ni <P />are produced if the jets continue for more than 10 s, which would become crucial for the observation of abundance distribution in young supernova remnants. <P />...

Nuclear matter is considered to be inhomogeneous at subnuclear densities that are realized in supernova cores and neutron star crusts, and the structures of nuclear matter change from spheres to cylinders, slabs, cylindrical holes, and spherical holes as the density increases. In this Letter, we discuss other possible structures, that is, gyroid and double-diamond morphologies, which are periodic bicontinuous structures discovered in a block copolymer. Utilizing the compressible liquid drop model, we show that there is a chance of gyroid appearance near the transition point from a cylinder to a slab and the volume fraction at this point is also similar for nuclear and polymer systems. Although the five shapes listed initially have been long thought to be the only major constituents of so-called nuclear pasta at subnuclear densities, our findings imply that this belief needs to be reconsidered.

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.

This paper is a sequel to our previous work for accretion onto a Schwarzschild black hole and the so-called standing accretion shock instability; in this paper, we investigate nonaxisymmetric perturbations for a Kerr black hole. The linear and nonlinear phases for the shock evolution are analyzed in detail by both two-dimensional general relativistic hydrodynamical simulations and linear analysis. Since the structure of steady axisymmetric accretion flows with a standing shock wave is very sensitive to the inner transonic flow, their properties such as Mach numbers, which are important for the stability, depend on the Kerr parameter very much. Although the essential features of the instability do not differ from the previous results for the Schwarzschild black hole, the frame-dragging effects specific to the Kerr black hole are also evident. Interestingly, the oscillation periods of the fundamental unstable modes are dependent only on the shock radius irrespective of the injection parameters.

We investigate the emergence of strange baryons in the dynamical collapse of a nonrotating massive star to a black hole using neutrino-radiation hydrodynamical simulations in general relativity. By following the dynamical formation and collapse of a nascent proto-neutron star from the gravitational collapse of a 40 M(circle dot) star adopting a new hyperonic equation-of-state (EOS) table, we show that the hyperons do not appear at the core bounce but populate quickly similar to 0.5-0.7 s after the bounce to trigger the recollapse to a black hole. They start to show up off center owing to high temperatures and later prevail at center when the central density becomes high enough. The neutrino emission from the accreting proto-neutron star with the hyperonic EOS stops much earlier than the corresponding case with a nucleonic EOS, while the average energies and luminosities are quite similar in the two cases. These features of the neutrino signal are a potential probe of the emergence of new degrees of freedom inside the black hole forming collapse.

We study the gravitational collapse of non-rotating massive stars (40-50Modot;) and the associated neutrino burst by general relativistic v-radiation hydrodynamics. We show that the neutrino burst from the accreting proto-neutron star till the black hole formation is short and energetic in a situation of failed explosion. This unique characteristics is a hallmark of black hole formation and distinguishable from the neutrino signal of ordinary supernovae. Adopting the sets of physical equation of state of dense matter, we demonstrate that the duration of neutrino emission depends crucially on the equation of state. Future detection of neutrinos from the failed supernovae can be used to probe the stiffness of dense matter with possible emergence of hyperons. Speaker. ? Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence.

We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole using two-dimensional general relativistic hydrodynamic simulations, as well as linear analysis, in the equatorial plane. We demonstrate that the accretion shock is stable against axisymmetric perturbations but becomes unstable to nonaxisymmetric perturbations. The results of the dynamical simulations show good agreement with the linear analysis on the stability and the oscillation and growth timescales. A comparison of different wave-travel times with the growth timescales of the instability suggests that it is likely to be of the Papaloizou-Pringle type, induced by the repeated propagations of acoustic waves. However, the wavelengths of the perturbations are too long to allow a clear definition of the reflection point. By analyzing the nonlinear phase in the dynamical simulations, we show that quadratic mode couplings precede the nonlinear saturation. It is also found that not only short-term random fluctuations due to turbulent motion, but also quasi-periodic oscillations on longer timescales, take place in the nonlinear phase. We give some possible implications of the instability for black hole quasi-periodic oscillations and the central engine in gamma-ray bursts.

We study the progenitor dependence of black hole formation and its associated neutrino signal due to the gravitational collapse of a nonrotating massive star, following on our previous study of a single progenitor model. We aim to clarify whether the dynamical evolution toward black hole formation occurs in the same manner for different progenitors and to examine whether the characteristic of neutrino bursts having short duration and rapidly increasing average energies is a general one. We perform numerical simulations using general relativistic neutrino radiation hydrodynamics to follow the dynamical evolution from the collapse of 40 and 50 M-circle dot presupernova models to black hole formation via contracting proto-neutron stars. For the three progenitor models studied in this paper, we find that black hole formation occurs similar to 0.4-1.5 s after core bounce through an increase of the proto-neutron star mass, accompanied by a short and energetic neutrino burst. The density profile of the progenitor is important in determining the accretion rate onto the proto-neutron star and, therefore, the duration of the neutrino burst. We compare the neutrino bursts of black hole-forming events from different progenitors and discuss whether they can be used to probe clearly the progenitor and the dense matter.

We investigate the emergence of strange baryons in the dynamical collapse of a non-rotating massive star to a black hole by the neutrino-radiation hydrodynamical simulations in general relativity. By following the dynamical formation and collapse of nascent proto-neutron star from the gravitational collapse of a 40Msun star adopting a new hyperonic EOS table, we show that the hyperons do not appear at the core bounce but populate quickly at ~0.5-0.7 s after the bounce to trigger the re-collapse to a black hole. They start to show up off center owing to high temperatures and later prevail at center when the central density becomes high enough. The neutrino emission from the accreting proto-neutron star with the hyperonic EOS stops much earlier than the corresponding case with a nucleonic EOS while the average energies and luminosities are quite similar between them. These features of neutrino signal are a potential probe of the emergence of new degrees of freedom inside the black hole forming

We investigate the total kinetic power (L-j) and age (t(age)) of powerful jets in FR II radio galaxies by comparison of the dynamical model of expanding cocoons with observations. We select four FR II radio sources (Cygnus A, 3C 223, 3C 284, and 3C 219), for which the mass-density profiles of the intracluster medium (ICM) are known in the literature. It is found that large fractions greater than or similar to 0.02-0.7 of the Eddington luminosity (L-Edd) are carried away as kinetic power of jets. The upper limit of estimated 2L(j)/L-Edd is larger than unity (less than or similar to 10) for some sources, suggesting the possibility of super-Eddington mass accretions. As a consequence of the large powers, we also find that the total energy stored in the cocoon (E-c) exceeds the energy derived from the minimum energy condition for the energy of radiating nonthermal electrons and magnetic fields (E-min): 4 &lt; E-c/E-min &lt; 310. This implies that most of the energy in the cocoon is carried by invisible components such as thermal leptons (electron and positron) and/or protons.

Recently, stellar collapse involving black-hole formation from massive stars is suggested to emit enormous fluxes of neutrinos on par with ordinary core-collapse supernovae. We investigate their detectability for the currently operating neutrino detector, SuperKamiokande. Neutrino oscillation is also taken into account for the evaluation. We find that the event number is larger than or comparable to that of supernova neutrinos and, hence, black-hole formation is also a candidate for neutrino astronomy. Moreover, we find that the event number depends dominantly on the equation of state used in the computations of the black-hole formation. This fact implies that the detection of neutrinos emitted from the black hole progenitors is very valuable to probe the properties of the equation of state for hot and/or dense matter.

We present sets of equation of state (EOS) of nuclear matter including hyperons using an SUf(3) extended relativistic mean field (RMF) model with a wide coverage of density, temperature and charge fraction for numerical simulations of core-collapse supernovae. Coupling constants of Sigma and Xi hyperons with the sigma meson are determined to fit the hyperon potential depths in nuclear matter, U-Sigma(rho(0)) similar or equal to + 30MeV and U-Xi(rho(0)) similar or equal to - 15 MeV, which are suggested from recent analyses of hyperon production reactions. At low densities, the EOS of uniform matter is connected with the EOS by Shen et al, in which the formation of finite nuclei is included in the Thomas - Fermi approximation. In the present EOS, the maximum mass of neutron stars decreases from 2.17M(circle dot) (Ne mu) to 1.63 M-circle dot (NY e mu) when hyperons are included. In a spherical, adiabatic collapse of a 15M(circle dot) star by the hydrodynamics without neutrino transfer, hyperon effects are found to be small, since the temperature and density do not reach the region of hyperon mixture, where the hyperon fraction is above 1 % (T &gt; 40 MeV or rho(B) &gt; 0.4 fm(-3)).

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 (similar to 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-l(m), just as expected for a spherically symmetric background; (2) nonlinear mode couplings produce only m = 0 modes for axisymmetric perturbations, whereas m not equal 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 investigate the role of Alfven waves in a core-collapse supernova (SN) explosion. We assume that Alfven waves are generated by convections inside a proto-neutron star (PNS) and emitted from its surface. These waves then propagate outward, dissipate via nonlinear processes, and heat up matter around a stalled prompt shock. To quantitatively assess the importance of this process for the revival of the stalled shock, we perform one-dimensional time-dependent hydrodynamical simulations, taking into account the heating via the dissipation of Alfven waves that propagate radially outward along open flux tubes. We show that shock revival occurs if the surface field strength is larger than similar to 2 x 10(15) G and if the amplitude of the velocity fluctuation at the PNS surface is larger than similar to 20% of the local sound speed. Interestingly, the Alfven wave mechanism is self-regulating in the sense that the explosion energy is not very sensitive to the surface field strength or initial amplitude of Alfven waves, as long as they are larger than the threshold values given above.

We construct an equation of state including the hadron-quark phase transition. The mixed phase is obtained by the Gibbs conditions for finite temperature. We adopt the equation of state based on the relativistic mean field theory for the hadronic phase, taking into account pions. As for the quark phase, the MIT bag model of the deconfined 3-flavor strange quark matter is used. As a result, our equation of state is thermodynamically stable and qualitatively exhibits the desired properties of hadron-quark mixed matter, such as the temperature dependence of the transition density. The pions raise the transition density because they make the equation of state softer. Using the equation of state constructed here, we study its astrophysical implications. The maximum mass of compact stars is investigated, and our equation of state is consistent with recent observations. We also compute the collapse of a massive star with 100 solar masses (M(circle dot)) using our equation of state and find that the interval time from the bounce to the black hole formation becomes shorter for the model with pions and quarks. The pions and quarks affect the total energy of the emitted neutrinos because the duration time of the neutrino emission becomes shorter. The neutrino luminosity rises under the effect of pions since the density of the proto-neutron star becomes high.

We performed 2.5 dimensional numerical simulations of magnetized rotational core-collapse. From the observational fact, it is probable that gamma-ray bursts and core-collapse supernovae have same origin. And the very collimated jet is preferable to explain the light curve of their afterglow. How this collimated jet is produced due to the process of core-collapse of massive star? There are two main energy-sources for this explosion. One is neutrino pair annihilations and another is magneto-hydrodynamical process. In this time we concentrate the magneto-hydrodynamical process. We found a jet-like shock wave is launched in the direction of the pole. The strength of initial magnetic field determine the profile of jet. We found common structures of these jets. We continue the simulation that the jet-like shock wave produced at the center propagate to the surface of the star. Since the previous works are performed separately at each stage such as core-collapse and jet-propagation, many initial uncertainty remains in each stage. However we have performed the simulations from the magnetized core-collapse to the jet-propagation totally. This study gives us deeper knowledge on the relation between the profile of the jet and the progenitor. © 2008 World Scientific Publishing Co. Pte. Ltd.

We have investigated nucleosynthesis inside the jets from a 35 M ⊙, low-metallicity collapsar before the formation of a black hole, based on a two-dimensional magneto-hydrodynamic (MHD) simulation of the collapsar, taking into account neutrino interactions both on the MHD simulation and nucleosynthesis. We find that jets are ejected via the magnetic pressure, and that r-process operates in the jets even if the neutrino absorption is taken into account in the nucleosynthesis calculation. This is due to efficient electron captures in the high-density (∼ 1011 gcm-3) region near the rotational axis, fast ejection (&gt
0.2 in units of speed of light), and relatively low neutrino luminosity (&lt
5 × 10 52ergss-1). Chemical composition of the neutron-rich nuclei in jets from collapsars with different mass and rotation could be largely different from each other. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence.

We try to constrain the neutrino oscillation parameters by studying the MSW matter effect on supernova neutrinos. Using an implicit Lagrangian code for general relativistic spherical hydrodynamics (Yamada, 1997), we calculate the propagation of shock waves passing through the stellar envelopes over dozens of seconds, which is based on modeling the adiabatic collapse of iron core. We study how quantitatively the influence of the shock propagation appears in the deformation of neutrino energy spectrum. In addition, we are able to examine the θ13 dependence of time evolution of the neutrino detection rates at SK. Using our supernova model, we found that the MSW effect appears, at first, from low-energy region and moves toward high-energy region as the shock wave propagates. We find that the shock propagation has strong influence on the supernova neutrino oscillation through the evolution of density profile induced by the shock propagation.

We compute the collapse of Population III (Pop III) massive stars with 300 - 13500 M⊙ for 18 models. In this study, we solve the general relativistic hydrodynamics and the neutrino transfer equations simultaneously to follow the evolution of space time under spherical symmetry. As a result, it is shown that the neutrino transfer plays a crucial role in the dynamics of the gravitational collapse and the emitted neutrino spectrum does not become harder for more massive stars. We also evaluate the flux of the relic neutrino background from Pop III massive stars and discuss the possibility to study the Pop III star formation history. © 2008 Springer-Verlag Berlin Heidelberg.

We construct an equation of state (EOS) including the hadron-quark phase transition by the Gibbs conditions for finite temperature. We adopt the equation of state based on the relativistic mean field theory for the hadronic phase taking into account pions and the MIT bag model of the deconfined 3-flavor strange quark matter for the quark phase.
The gravitational collapse of a massive star is computed using our equation of state and we find that the interval time from the bounce to the black hole formation, namely the duration time of the neutrino emission, becomes shorter for the model with pions and quarks. This fact implies that we may be able to probe observationally the EOS of hot dense matter in future.

We construct an equation of state (EOS) including the hadron-quark phase transition by the Gibbs conditions for finite temperature. We adopt the EOS based on the relativistic mean field theory for the hadronic phase and the MIT bag model of the deconfined 3-flavor strange quark matter for the quark phase. Moreover, the gravitational collapse of massive stars with several masses is computed using our EOS and we find that the phase transition makes the interval time from the bounce to the black hole formation, namely the duration time of the neutrino emission, shorter for the model with a bounce. This fact implies that we may be able to probe observationally the EOS of hot and dense matter in future.

We investigate hyperon potentials in nuclear matter through hyperon production reactions, and construct several sets of equation of state (EOS) of nuclear matter including hyperons for numerical simulations of core collapse supernovae.

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.

We studied the standing accretion shock instability (SASI) for a core-collapse supernova explosion. SASI induces a nonspherically symmetric motion of a standing spherical shock wave. In order to investigate the growth of SASI, we solved the three-dimensional compressible Euler equations using ZEUS-MP/2 code based on the finite-difference method with a staggered mesh of spherical polar geometry. Although the von Neumann and Richtmyer artificial viscosity is used in ZEUS-MP/2 code to capture shock waves, we propose utilizing a tensor artificial viscosity in order to overcome the numerical instability regarded as the carbuncle phenomenon. This numerical instability emerges around the grid polar axis and precludes mode analysis of SASI.

A series of numerical simulations of magnetorotational core-collapse supernovae are carried out. Dipole-like configurations which are offset northward are assumed for the initially strong magnetic fields, along with rapid differential rotations. The aim of our study is to investigate the effects of the offset magnetic field on magnetar kicks and on supernova dynamics. Note that we study a regime where the proto-neutron star formed after collapse has a large magnetic field strength approaching that of a "magnetar," a highly magnetized slowly rotating neutron star. As a result, equatorially asymmetric explosions occur with the formation of the bipolar jets. We find that the jets are fast and light in the north and slow and heavy in the south for rapid cases, while they are fast and heavy in the north and slow and light in the south for slow-rotation cases. The resulting magnetar kick velocities are similar to 300-1000 km s(-1). We find that the acceleration is mainly due to the magnetic pressure, while the somewhat weaker magnetic tension works in the opposite direction, due to the stronger magnetic field in the northern hemisphere. Note that observations of magnetar proper motions are very scarce; our results supply a prediction for future observations. Namely, magnetars possibly have large kick velocities, several hundred km s(-1), as ordinary neutron stars do, and in extreme cases they could have kick velocities up to 1000 km s(-1). In each model, the formed protomagnetar is a slow rotator with a rotational period of more than 10 ms. It is also found that, in rapid-rotation models, the final configuration of the magnetic field in the protomagnetar is a collimated dipole-like field pinched by the torus of toroidal field lines, whereas in the protomagnetar produced in the slow-rotation model the poloidal field is totally dominant.

We investigate the total kinetic powers (L (j)) and ages (t (age)) of powerful jets of four FR II radio sources (Cygnus A, 3C 223, 3C 284, and 3C 219) by the detail comparison of the dynamical model of expanding cocoons with observed ones. It is found that these sources have quite large kinetic powers with the ratio of L (j) to the Eddington luminosity (L-Edd) resides in 0.02 &lt; L-j/L (Edd)&lt; 10. Reflecting the large kinetic powers, we also find that the total energy stored in the cocoon (E (c)) exceed the energy derived from the minimum energy condition (E-min): 2 &lt; E-c/E-min &lt; 160. This implies that a large amount of kinetic power is carried by invisible components such as thermal leptons (electron and positron) and/or protons.

The existence of various anomalous stars, such as the first stars in the universe or stars produced by stellar mergers, has been proposed recently. Some of these stars will result in black hole formation. In this study we investigate iron-core collapse and black hole formation systematically for the iron-core mass range of 3-30 M-circle dot, which has not been studied well so far. Models used here are mostly isentropic iron cores that may be produced in merged stars in the present universe, but we also employ a model that is meant for a Population III star and is obtained by evolutionary calculation. We solve numerically the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail under spherical symmetry. As a result, we find that massive iron cores with similar to 10 M-circle dot unexpectedly produce a bounce, owing to the thermal pressure of nucleons before black hole formation. The features of neutrino signals emitted from such massive iron cores differ in time evolution and spectrum from those of ordinary supernovae. First, the neutronization burst is less remarkable or disappears completely for more massive models, because the density is lower at the bounce. Second, the spectra of neutrinos, except the electron type, are softer, owing to the electron-positron pair creation before the bounce. We also study the effects of the initial density profile, finding that the larger the initial density gradient is, the more steeply the neutronization burst declines. Furthermore, we suggest a way to probe into the black hole progenitors from the neutrino emission and estimate the event number for the currently operating neutrino detectors.

We present the results of numerical experiments, in which we have investigated the influence of the inelastic neutrino-helium interactions on the standing accretion shock instability supposed to occur in the postbounce supernova core. The axisymmetric hydrodynamical simulations of accretion flows through the standing accretion shock wave onto the proto-neutron star show that the interactions are relatively minor and the linear growth of the shock instability is hardly affected. The extra heating given by the inelastic reactions becomes important for the shock revival after the instability enters the nonlinear regime, but only when the neutrino luminosity is very close to the critical value at which the shock would be revived without the interactions. We have also studied the dependence of the results on the initial amplitudes of perturbation and the temperatures of mu and tau neutrinos.

We study black hole formation and the neutrino signal from the gravitational collapse of a nonrotating massive star of 40 M-circle dot. Adopting two different sets of realistic equations of state (EOSs) for dense matter, we perform numerical simulations of general relativistic nu-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.

The acoustic-revival mechanism in core-collapse supernovae, proposed recently by the Arizona group led by A. Burrows, is an interesting new scenario. With an aim to understanding the elementary processes involved in this mechanism, we have calculated the eigenfrequencies and eigenfunctions for the g-mode oscillations of a nonrotating proto-neutron star. The possible excitation of these modes by the standing accretion shock instability, or SASI, is discussed. We have formulated the forced oscillations of g-modes due to external pressure perturbations exerted on the proto-neutron star's surface. The driving pressure fluctuations have been adopted from our previous computations of axisymmetric SASI in the nonlinear regime. We pay particular attention to low-l modes, since these are the modes that are dominant in SASI and what Burrows et al. claim to have played an important role in their acoustic-revival scenario. Here l is the index of the spherical harmonic functions, Y-l(m). Although the frequency spectrum of nonlinear SASI is broadened substantially by nonlinear couplings, the typical frequency is still much smaller than those of the g-modes, leading to a severe impedance mismatch. As a result, the excitations of various g-modes are rather inefficient, and the energy of the saturated g-modes is similar to 10(50) ergs or less, with the g(2) mode being the largest in our model. Here the g(2) mode has two radial nodes and is confined to the interior of the convective region. The energy transfer rate from the g-modes to outgoing sound waves is estimated from the growth of the g-modes to be similar to 10(51) ergs s(-1) in the models studied in this paper.

We perform two-dimensional, magneto-hydrodynamical core-collapse simulations of massive stars accompanying the QCD phase transition. We study how the phase-transition affects the gravitational waveforms near the epoch of core-bounce. As for initial models, we change the strength of rotation and magnetic fields. Particularly, the degree of differential rotation in the iron core (Fe-core) is changed parametrically. As for the microphysics, we adopt a phenomenological equation of state above the saturation density, including two parameters to change the hardness before the transition. We assume the first order phase transition, where the conversion of bulk nuclear matter to a chirally symmetric quark-gluon phase is described by the MIT bag model. Based on these computations, we find that the phase transition can make the maximum amplitudes larger up to similar to 10 percents than the ones without the phase transition. On the other hand, when the degree of the differential rotation becomes larger, the maximum amplitudes become smaller up to similar to 10 percents owing to the phase transition. We find that even extremely strong magnetic fields similar to 10(17) G in the protoneutron star do not affect these results.

With an eye toward application to the theory of core-collapse supernovae, we perform a global linear analysis of the stability of spherically symmetric accretion flows through a standing shock wave onto a proto-neutron star. For the unperturbed flows, we adopt spherically symmetric, steady solutions obtained with a realistic equation of state and realistic neutrino reaction rates. These solutions are characterized by the mass accretion rate and neutrino luminosity. Then we solve the equations for linear perturbations numerically, obtaining the eigenfrequencies and eigenfunctions. We find the following: (1) The flows are stable for all modes if the neutrino luminosity is lower than a certain value, e.g., similar to 1 x 10(52) ergs s(-1) for. M = 1.0M(circle dot) s(-1). (2) For higher luminosities, nonradial instabilities are induced, probably through advective-acoustic cycles. Interestingly, modes with l = 2 and l = 3 first become unstable for relatively low neutrino luminosities, e. g., similar to(2-3); 10(52) ergs s(-1) for the same accretion rate, whereas the l = 1 mode is the most unstable for higher luminosities, similar to(3-7); 10(52) ergs s(-1). These are all oscillatory modes. (3) For still larger luminosities, greater than or similar to 7 x 10(52) ergs s(-1) for. M = 1.0M(circle dot) s(-1), nonoscillatorymodes, both radial and nonradial, become unstable. These nonradial modes are identified as convective, and their growth rates have a peak at l = 5-11, depending on the luminosity. We confirm the result from numerical simulations that the instabilities induced by advective-acoustic cycles are more important than convection for lower neutrino luminosities. Furthermore, we investigate changing the inner boundary conditions and find that while the effects are nonnegligible, the existence of the instabilities does not qualitatively change for a variety of conditions.

We have made detailed calculations of the composition of magnetically driven jets ejected from a collapsar, based on long-term, magnetohydrodynamic simulations of a rapidly rotating, massive (40 M-.) star during core collapse. We follow the evolution of the abundances of about 4000 nuclides from the collapse phase to the ejection phase and through the jet generation phase using two large nuclear reaction networks. We find that the r-process successfully operates in the jets, so that U and Th are synthesized abundantly when the progenitor has a large magnetic field (10(12) G) and a rapidly rotating core. The abundance pattern inside the jets is similar to that of the r-elements in the solar system. About 0.01 M-. of heavy, neutron-rich nuclei can be ejected from the collapsar. The detailed abundances depend on the nuclear properties of the mass model, beta-decay rate, and fission, for nuclei near the neutron drip line. Furthermore, we find that p-nuclei are produced without seeds: not only can light p-nuclei, such as Se-74, Kr-78, Sr-84, and Mo-92, be abundantly synthesized in the jets, but also heavy p-nuclei, In-113, Sn-115, and La-138. The amounts of p-nuclei in the ejecta are much greater than those in core-collapse supernovae. In particular, Mo-92, In-113, Sn-115, and La-138, which are deficient in these supernovae, are produced significantly in the collapsar ejecta.

We study the recoil of so-called "magnetars", highly magnetized slowly rotating neutron stars, doing series of numerical simulations on the core-collapse of massive stars in strong magnetic field and rapid rotation regime. We assume that the initial magnetic fields have a dipole-like configurations somewhat offset from the center of the cores. As a result, recoil velocities of ∼ 500 - 1000 km s-1 are obtained which suggest that magnetars could have substantial recoil velocities as ordinary pulsars. © 2007 American Institute of Physics.

We investigate nucleosynthesis in collapsars, based on long-term, magnetohydrodynamic simulations of a rapidly rotating massive star of 40M circle dot during the core collapse. We have calculated detailed composition of magnetically driven jets ejected from the collapsars, in which the magnetic fields before the collapse, are uniform and parallel to the rotational axis of the star and the magnitudes of the fields, B-0, are 10(10) G or 10(12) G. We follow the evolution of chemical composition up to, about 4000 nuclides inside the jets from the collapse phase to the ejection phase through the jet generation phase with use of a large nuclear reaction network. We find that the r-process successfully operates in the jets from the collapsar of B-0 = 10(12) G, so that U and Th are synthesized abundantly. Abundance pattern inside the jets is similar to that of r-elements in the solar system. Furthermore, we find that p-nuclei are produced without seed nuclei: not only light p-nuclei, such as Se-74, Kr-78, Sr-84, and Mo-92, but also heavy p-nuclei, In-113, Sn-115, and La-138, can be abundantly synthesized in the jets. The amounts of p-nuclei in the ejecta are much greater than those in core-collapse supernovae (SNe). In particular, Mo-92, In-113, Sn-115, and La-138 deficient in the SNe, are significantly produced in the ejecta. On the other hand, in the jets from the collapsar of B-0 = 10(10) G, the r-process cannot operate and Ni-56, Si-28, (32) S, and He-4 are abundantly synthesized in the jets, as in ejecta from inner layers of type II supernovae. An amount of Ni-56 is much smaller than that from SN 1987A.

We carry out series of numerical simulations on the magnetorotational supernovae in order to study about recoil of so-called "magnetars", highly magnetized slowly rotating neutron stars. We assume that the core initially rotates rapidly and is strongly magnetized. Presumed initial magnetic fields have dipole-like configurations somewhat offset from the center of the cores. As a result, equatorially asymmetric supernova explosions are produced and recoil velocities of similar to 500 - 1000 km s(-1) are obtained which suggest that magnetars possibly have large recoil velocities as ordinary pulsars.

The existence of various anomalous stars, such as the first stars in the universe or stars produced by stellar mergers, has been proposed recently. Some of these stars will result in black hole formation. In this study we investigate iron-core collapse and black hole formation systematically for the iron-core mass range of 3-30 M⊙, which has not been studied well so far. Models used here are mostly isentropic iron cores that may be produced in merged stars in the present universe, but we also employ a model that is meant for a Population III star and is obtained by evolutionary calculation. We solve numerically the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail under spherical symmetry. As a result, we find that massive iron cores with ∼ 10 M ⊙ unexpectedly produce a bounce, owing to the thermal pressure of nucleons before black hole formation. The features of neutrino signals emitted from such massive iron cores differ in time evolution and spectrum from those of ordinary supernovae. First, the neutralization burst is less remarkable or disappears completely for more massive models, because the density is lower at the bounce. Second, the spectra of neutrinos, except the electron type, are softer, owing to the electron-positron pair creation before the bounce. We also study the effects of the initial density profile, finding that the larger the initial density gradient is, the more steeply the neutralization burst declines. Furthermore, we suggest a way to probe into the black hole progenitors from the neutrino emission and estimate the event number for the currently operating neutrino detectors. © 2007. The American Astronomical Society. All rights reserved.

During the collapse of a massive star greater than 35-40 M-circle dot, stellar core is considered to promptly collapse to a black hole, and stellar material may fall onto the hole greater than several solar masses with extremely high accretion rates (&gt; 1 M-circle dot s(-1)). If the star has a sufficiently high angular momentum before the collapse, an accretion disk is likely to form around the black hole. Jets are suggested to be launched from the inner region of the accretion disk near the hole through magnetic and/or neutrino processes. Gamma-Ray Bursts (GRBs) are expected to be driven by the jets. This scenario of GRBs is called the collapsar model. Recently, magnetohydrodynamic (MHD) simulations were performed of the collapse of rapidly rotating, magnetized 25 M-circle dot and 40-M-circle dot stars in light of the collapsar model of GRBs (see papers listed at the end of the paper). For assumed angular velocity distributions and the uniform magnetic fields, the collapsars are shown to eject jets driven through the magnetic pressure. The simulations are however performed up to 4 s, which are shorter than durations of long GRBs similar to 10s. In the present work, we have performed long-term (similar to 10 s), two-dimensional, MHD simulations of the collapse of a rapidly rotating, magnetized 40 ME) star.

This is a sequel to the previous paper, in which we investigated the structure and stability of the spherically symmetric accretion flows through the standing shock wave onto the proto-neutron star in the postbounce phase of the collapse-driven supernova. Following the prescription in the previous paper, we assume that the accretion flow is in a steady state controlled by the neutrino luminosity and mass accretion rate that are kept constant. We obtain steady solutions for a wide range of neutrino luminosities and mass accretion rates. In so doing, as an extension to the previous models, we employ a realistic EOS and neutrino-heating rate. More importantly, we take into account the effect of convection phenomenologically. For each mass accretion rate, we find the critical neutrino luminosity, above which there exists no steady solution. These critical points are supposed to mark the onset of the shock revival. As the neutrino luminosity increases for a given mass accretion rate, there appears a convectively unstable region at some point before the critical value is reached. We introduce a phenomenological energy flux by convection so that the negative entropy gradient should be canceled out. We find that the convection lowers the critical neutrino luminosity substantially, which is in accord with the results of multidimensional numerical simulations done over the years. We also consider the effect of the self-gravity, which was neglected in the previous paper. It is found that the self-gravity is important only when the neutrino luminosity is high. The critical luminosity, however, is little affected if the energy transport by convection is taken into account.

The gravitational collapse of a nonrotating, black-hole-forming massive star is studied by nu-radiation-hydrodynamical simulations for two different sets of realistic equation of state of dense matter. We show that the event will produce as many neutrinos as the ordinary supernova, but with distinctive characteristics in luminosities and spectra that will be an unmistakable indication of black hole formation. More importantly, the neutrino signals are quite sensitive to the difference of equation of state and can be used as a useful probe into the properties of dense matter. The event will be unique in that they will be shining only by neutrinos (and, possibly, gravitational waves) but not by photons, and hence they should be an important target of neutrino astronomy.

Population III (Pop III) stars are the first stars in the universe. They do not contain metals, and their formation and evolution may be different from that of stars of later generations. In fact, according to the theory of star formation, Pop III stars might have very massive components (similar to 100-10000 M-circle dot). In this paper, we compute the spherically symmetric gravitational collapse of these Pop III massive stars. We solve the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail. Unlike supermassive stars (greater than or similar to 10(5) M-circle dot), the stars of concern in this paper become opaque to neutrinos. The collapse is simulated until after an apparent horizon is formed. We confirm that the neutrino transfer plays a crucial role in the dynamics of gravitational collapse and find also that the beta-equilibration leads to a somewhat unfamiliar evolution of electron fraction. Contrary to the naive expectation, the neutrino spectrum does not become harder for more massive stars. This is mainly because the neutrino cooling is more efficient and the outer core is more massive as the stellar mass increases. Here the outer core is the outer part of the iron core falling supersonically. We also evaluate the flux of relic neutrinos from Pop III massive stars. As expected, the detection of these neutrinos is difficult for the currently operating detectors. However, if ever observed, the spectrum will enable us to obtain information on the formation history of Pop III stars. We investigate 18 models covering the mass range of 300-10(4) M-circle dot, making this study the most detailed numerical exploration of spherically symmetric gravitational collapse of Pop III massive stars. This will also serve as an important foundation for multidimensional investigations.

We perform two-dimensional, axisymmetric, magnetohydrodynamic simulations of the collapse of a rotating star of 40 M-circle dot in light of the collapsar model of gamma-ray bursts. Considering two distributions of angular momentum, up to similar to 10(17) cm(2) s(-1), and the uniform vertical magnetic field, we investigate the formation of an accretion disk around a black hole and the jet production near the black hole. After material reaches the black hole with high angular momentum, the disk forms inside a surface of weak shock. The disk reaches a quasi-steady state for stars whose magnetic field is less than 10(10) G before the collapse. We find that the jet can be driven by the magnetic fields even if the central core does not rotate as rapidly as previously assumed as long as the outer layers of the star have sufficiently high angular momentum. The magnetic fields are chiefly amplified inside the disk due to the compression and the wrapping of the field. The fields inside the disk propagate to the polar region along the inner boundary near the black hole through the Alfven wave and eventually drive the jet. The quasi-steady disk is not an advection-dominated disk but a neutrino cooling-dominated one. Mass accretion rates in the disks are greater than 0: 01 M-circle dot s(-1) with large fluctuations. The disk is transparent for neutrinos. The dense part of the disk, which is located near the black hole, emits neutrinos efficiently at a constant rate of &lt; 8 x 10(51) ergs s(-1). The neutrino luminosity is much smaller than those from supernovae after the neutrino burst.

We investigate the r-process nucleosynthesis during a purely magnetohydrodynamic (MHD) explosion in a massive star of 13 M(circle dot). The two-dimensional MHD simulations have been carried out from the onset of the core collapse to the shock propagation to the silicon-rich layers (similar to 500 ms after bounce). Thereafter, using the compositions during the explosion, we calculate the r-process nucleosynthesis in the later phase by employing the two kinds of time extrapolations of the temperature and density. With these computations, we show that the jetlike explosion formed due to the combined effects of rapid rotation and strong magnetic field lowers the electron fraction significantly in the iron core, contrary to the spherical explosion. We demonstrate that the ejected material with low Ye in the jet coming out from the silicon layers is good for reproducing the third peak of the solar r-element pattern. In addition, we investigate the effects of fission using the full nuclear reaction network and the differences of two kinds of mass formulae on the r-process peaks obtained in the above MHD models. As a result, we find that both of them can reproduce the global abundance pattern up to the third peaks, although the detailed distributions are rather different. Finally, we discuss the effects of neutrino absorption reactions, which are not coupled to the above MHD simulations, on the possible reduction of Ye obtained in the above computations. We point out that there should be variations in the r-process nucleosynthesis in the supernova explosion if the MHD effects play an important role.

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.

In order to infer the effects of rotation on the revival of a stalled shock in supernova explosions, we investigated steady accretion flows with a standing shock. We first confirmed the results of preceding papers that, for a given mass accretion rate, there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution. We can identify the critical luminosity as the one, at which the stalled shock revives. If a collapsing star rotates, the accretion flow is non-spherical due to centrifugal forces. Flows are accelerated near the rotation axis whereas they are decelerated near the equatorial plane. As a result, the critical luminosity is lowered, that is, rotation assists the revival of a stalled shock. © 2006 IOP Publishing Ltd.

We present a series of axisymmetric, magneto-hydrodynamical simulations for the rotational core collapse of a massive star accompanying the QCD phase transition. To elucidate the implications of a phase transition against a supernova, we investigate the waveforms of gravitational wave derived from the quadrupole formula that includes the contributions from the electromagnetic fields. We adopt a phenomenological equation of state above the nuclear matter density ρ0 that includes two parameters to change the hardness of the matter before the transition. We assume that the first order phase transition is the conversion of bulk nuclear matter to a chirally symmetric quark-gluon phase described by the MIT bag model. In most models with the phase transition, the first peak amplitudes are higher by a few percents to nearly ten percents than those without the transition. However, it is found that under the condition of the very strong differential rotation, the height of the peak becomes lower by several percents if the phase transition is included. In the paper, we show the typical models of our calculations. © Copyright owned by the author(s).

Massive stars whose mass exceed 10 times the solar mass evolve until the Fe-core is formed. Since the nuclear reactions in the Fe-core do not proceed further, the core begins to collapse, which leads to the catastrophic explosion. The nucleosynthesis during the evolutions and subsequent explosions is responsible for the heavy element enrichment in our galaxy. We calculate heavy element nucleosynthesis during the magneto-hydrodynamical (MHD) explosion of supernova of a massive star. We consistently calculate all stages of the collapse of the Fe-core, the core bounce, and the shock wave propagation. When the shock wave propagate in the oxygen-neon layers, the p-process nucleosynthesis should occur. Until now, the p-process has been studied with use of spherical explosion models where significant deficiencies in some light p-elements compared to solar ones have been found. We present nonspherical effects on the production of p-elements using adiabatic MHD explosion model. © Copyright owned by the author(s).

In this study, we investigate the iron core collapses systematically for various masses, especially in the range which has not been studied well so far. Here, we solve the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail. We also estimate the neutrino event number from the black hole formation at the Galactic center for the currently operating detectors. As a result, we suggest that the probe into the black hole progenitors is possible by detecting the neutrinos emitted from them, because the more massive the progenitor is, the softer its v̄e spectrum becomes. Further details of this study are seen in our lately submitted nanuscript [1].

We propose a new mechanism for pulsar kicks, which is magnetohydrodynamically-induced kick. We carry out two-dimensional numerical simulations on the core-collapse of a massive star with differential rotation and initially large magnetic fields which have equatorially-asymmetric dipole-like configuration. As a result of the computations, we get transient large kick velocities which are up to 500 km/s. However, these large velocities are soon damped since surrounding matter prevent proto-neutron-stars from moving away and finally no substantial kicks are produced. This may be a crucial problem for all pulsar kick computations.

The MSW effect of supernova neutrino is one of foci of recent neutrino astrophysics. It is still an open question how the shock wave propagation affects the neutrino oscillation. Using an implicit Lagrangian code for general relativistic spherical hydrodynamics, we succeeded in numerical simulations of breakout of shock wave propagation through the stellar envelope. We first discuss our successful result of shock wave propagation which is generated by adiabatic collapse of iron core, and compare with non-adiabatic models. Secondly, we apply our model to the neutrino oscillation and calculate survival probabilities of three light-neutrino families. We discuss how the flux and energy spectrum of each neutrino species can change due to the MSW effect.

We study the fate of core-collapse supernovae from the massive stars by numerical simulations of neutrino-radiation hydrodynamics. We follow the long term evolution over I see after the core bounce from the initial gravitational collapse to examine the explosion mechanism and to reveal the formation of neutron star and black hole. We explore the effects of equation of state (EOS) in these simulations by adopting the two sets of realistic EOS for supernovae. For the case of a 40M(circle dot) star, we find that the formation of black hole occurs in different timing depending on the softness of EOS and resulting properties of emergent neutrinos appear differently from ordinary supernova neutrinos.

We carried out one-dinensional long-term numerical simulations of core-collapse supernovae imposing steady shock approximation. As a result of a computation, we found core does not explode and shock wave stalls within several hundreds milliseconds from bounce. However, we execute long-term numerical simulation until 3.5 seconds from bounce with short CPU time using Personal Computer.

We report a current status of our radiation-magnetohydrodynamic code for the study of core-collapse supernovae. In this contribution, we discuss the accuracy of our newly developed numerical code by presenting the test problem in a static background model. We also present the application to the spherically symmetric core-collapse simulations. Since close comparison with the previously published models is made, we are now applying it for the study of magnetorotational core-collapse supemovae.

We have performed the simulations from the magnetized core-collapse to the jet-propagation totally. This study gives us deeper knowledge on the relation between the profile of the jet and the progenitor.

We report a current status of our radiation-magnetohydrodynamic code for the study of core-collapse supernovae. In this contribution, we discuss the accuracy of our newly developed numerical code by presenting the test problem in a static background model. We also present the application to the spherically symmetric core-collapse simulations. Since close comparison with the previously published models is made, we are now applying it for the study of magnetorotational core-collapse supernovae.

We investigate nucleosynthesis inside jets in a gamma ray bursts (GRB). We have calculated detailed composition of magnetically driven jets related to GRBs with post-processing calculation, which is based on long-term, magneto-hydrodynamic simulations of a rapidly rotating massive star of 40M(circle dot) during core collapse. We follow abundance evolution of about 4000 nuclides inside the jets from the collapse phase to the ejection phase through the jet generation phase with a large nuclear reaction network. We find that the r-process successfully operates inside the jets, so that U and Th are synthesized abundantly. Abundance pattern inside the jets is similar compared to that of r-clements in the solar system. Heavy neutron-rich nuclei similar to 0.001M(circle dot) can be ejected through the jets. Furthermore, we find that p-nuclei are produced without seed nuclei: not only light p-nuclei, such as Se-74, Kr-84, Sr-84, and Mo-92, but also heavy p-nuclei, In-113, Sn-115, and La-138, can be abundantly synthesized in the jets. The amounts of p-nuclei in the ejecta are much greater than those in core collapse supernovae (SNe). In particular, Mo-92, In-113, Sn-115, and La-138 deficient in core collapse SNe, are significantly produced in the ejecta.

It is pointed out that shock wave propagation has influences on the supernova neutrino oscillation by changing density profile and neutrino survival probability (MSW effect). Using an implicit Lagrangian code for general relativistic spherical hydrodynamics, we succeeded in calculating propagation of shock waves which are generated by adiabatic collapse of iron cores and pass into the stellar envelopes. We apply our model to the neutrino oscillation and calculate neutrino energy spectra of three light-neutrino families. We examined how the influence of the shock wave appear in the neutrino spectra, and found that the influences of the shock wave in the neutrino spectra move from low-energy side to high-energy side according to the shock propagation.

We compute the collapse of Population III massive stars (the first stars in the universe) with 300 - 13500 M-circle dot. In this study, we solve the general relativistic hydrodynamics and the neutrino transfer equations simultaneously and we also solve the evolution of space time of the spherically symmetric model. As a result, it is shown that the neutrino transfer plays a crucial role in the dynamics of gravitational collapse and the emitted neutrino spectrum does not become harder for more massive stars. We also evaluate the flux of relic neutrino background from Pop III massive stars and discuss the possibility to III massive stars and discuss the possibility to study the Pop III star formation history.

By using analytical model of cocoon expansion, we examine the total power and age of jets in five FRII radio galaxies. The estimated total power is quite larger than those estimated in previous works based on observation of non-thermal emission from electrons. This might imply that the amount of unobservable particles (e.g. protons and thermal component) can not be ignored when considering jet dynamics.

For the rst time heavy element nucleosynthesis in the magneto-hydrodynamical (MHD) explosions of core-collapse supemovae are investigated using a massive star of 13M(circle dot) in a main sequence stage. Contrary to the case of the spherical explosion, jet-like explosion due to the combined effects of the rotation and magnetic eld lowers the electron fraction signi cantly inside the layers above the Fe-core. Then, the anisotropic shock waves pass through the oxygen rich layers. As a consequence, we nd that the nucleosynthesis of the r- and p-process proceeds appreciably compared to the models previously considered.

I will give an overview of the current status of our understanding on the machanism of collapse-driven supernovae and related phenomena, presenting some of our group's recent results. Included among the issues discussed in this article are (1) 1D simulations with the most detailed neutrino transport, (2) the global asymmetry of supernovae and its implications for the explosion mechanism, (3) hydrodynamical instabilities after the shock stagnation, and (4) gravitational collapse of more massive stars.

We investigate the effects of magnetic fields on proto-neutron star winds by performing numerical simulations. We assume that the atmosphere of a proto-neutron star has a homogenous magnetic field (ranging from 10(12)G to 5 x 10(15)G) perpendicular to the radial direction and examine the dependence of the three key quantities (the dynamical time scale tau(dyn), electron fraction Y-e, and entropy per baryon s) for the successful r-process on the magnetic field strength. Our results show that even with a magneter-class field strength, similar to 10(15)G, the features of the wind dynamics differ only little from those of non-magnetic winds and that the conditions for an effective r-process are not realized.

We perform two-dimensional numerical simulations on the core collapse of a massive star with strong magnetic fields and differential rotations using the numerical code ZEUS-2D. Changing field configurations and laws of differential rotation parametrically, we compute 14 models and investigate the effects of these parameters on the dynamics. In our models we do not solve the neutrino transport but instead employ a phenomenological parametric EOS that takes into account the neutrino emissions. As a result of the calculations, we find that the field configuration plays a significant role in the dynamics of the core if the initial magnetic field is large enough. Models with initially concentrated fields produce more energetic explosions and more prolate shock waves than the uniform field. Quadrupole-like fields produce a remarkably collimated and fast jet, which might be important for gamma-ray bursts (GRBs). The Lorentz forces exerted in the region where the plasma beta is less than unity are responsible for these dynamics. The pure toroidal field, on the other hand, does not lead to any explosion or matter ejection. This suggests that the presupernova models, in which toroidal fields are predominant are disadvantageous for the magnetorotation-induced supernova considered here. Models with initially weak magnetic fields do not lead to explosion or matter ejection, either. In these models magnetic fields play no role, as they do not grow on the timescale considered in this paper and the magnetic pressure could be comparable to the matter pressure. This is because the exponential field growth as expected in MRI is not seen in our models. The magnetic field is amplified mainly by field compression and field wrapping in our simulations.

We study the evolution of a supernova core from the beginning of the gravitational collapse of a 15M(circle dot) star up to 1 s after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic v-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 similar to 2 and a difference of similar to 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.

We study the explosion mechanism of collapse-driven supernovae by numerical simulations with a Dew nuclear EOS based on unstable nuclei. We report new results of simulations of general relativistic hydrodynamics together with the Boltzmann neutrino-transport in spherical symmetry. We adopt the new data set of relativistic EOS and the conventional set of EOS (Lattimer-Swesty EOS) to examine the influence on dynamics of core-collapse, bounce and shock propagation. We follow the behavior of stalled shock more than 500 ms after the bounce and compare the evolutions of supernova core.

We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of collapsars including a rotating black hole. Initially, we assume that the core collapse has failed in this star. A rotating black hole of a few solar masses is inserted by hand into the calculation. The simulation results show the formation of a disklike structure and the generation of a jetlike outflow near the central black hole. The jetlike outflow propagates and accelerated mainly by the magnetic field. The total jet velocity is similar to 0.3c. When the rotation of the black hole is faster, the magnetic field is twisted strongly owing to the frame-dragging effect. The magnetic energy stored by the twisting magnetic field is directly converted to kinetic energy of the jet rather than propagating as an Alfven wave. Thus, as the rotation of the black hole becomes faster, the poloidal velocity of the jet becomes faster.

In order to infer the effects of rotation on the revival of a stalled shock in supernova explosions, we investigate steady accretion flows with a standing shock. We first obtain a series of solutions for equations describing nonrotating, spherically symmetric flows and confirm the results of preceding papers, that for a given mass accretion rate, there is a critical luminosity of irradiating neutrinos above which there exists no steady solution. Below the critical value, we find two branches of solutions; one is stable and the other is unstable against radial perturbations. With a simple argument based on the Riemann problem, we can identify the critical luminosity as that at which the stalled shock revives. We also obtain a condition satisfied by the flow velocity for the critical luminosity, which can easily be applied to the rotational case. If a collapsing star rotates, the accretion flow is nonspherical as a consequence of centrifugal forces. Flows are accelerated near the rotation axis, whereas they are decelerated near the equatorial plane. As a result, the critical luminosity is lowered; that is, rotation assists the revival of a stalled shock. According to our calculations, the critical luminosity is similar to 25% lower for a mass accretion rate of 1 M-. s(-1) and a rotational frequency of 0.1 Hz at a radius of 1000 km than that for a spherically symmetric flow with the same mass accretion rate. We find that the condition on the flow velocity at the critical luminosity is first satisfied at the rotation axis. This suggests that shock revival is triggered on the rotation axis and a jetlike explosion ensues.

In the framework of RMF containing the full baryon octet [ I], we have made the EOS table at high densities combined with the relativistic nuclear EOS table [2] at lower densities. Both parts of the table is based on the TM1 parameter [31 of RMF, then the table covers wide range of nuclear densities, from 10(5.1)g/cc to 10(15.4)g/cc, smoothly. As a sample calculation by using this new EOS table, we perform 1-dim. spherical hydro-dynamical calculation [4] with the relativistic EOS of supenova matter including hyperons and discuss the EOS dependence of the explosion energy. For the most attractive Sigma potential case, we find that hyperons increase the explosion energy by about 4 % in the case of 15M(o) model. We also show the element composition around core bounce, where p similar to 1.6p At this density, hyperons can appear due to finite temperature effects. Although the hyperon ratio is small, it leads to the reduction of pressure by around 3 %. In this paper, we discuss the mechanism of hyperon admixture, and progenitor mass dependence on hyperon ratio.

We study the hydrodynamical effects of two colliding shells, adopted to model internal shocks in various relativistic outflows such as gamma-ray bursts and blazars. We find that the density profiles are significantly affected by the propagation of rarefaction waves. A split-feature appears at the contact discontinuity of the two shells. The shell spreading with a few ten percent of the speed of light is also shown to be a notable aspect. The conversion efficiency of the bulk kinetic energy to internal one shows deviations from the widely-used inelastic two-point-mass-collision model. Observational implications are also shortly discussed.

We perform a series of magnetohydrodynamic simulations of supernova cores. Since the distributions of the angular momentum and the magnetic fields of strongly magnetized stars are quite uncertain, we systematically change the combinations of the strength of the angular momentum, rotation law, degree of differential rotation, and profiles of the magnetic fields to construct the initial conditions. By so doing, we estimate how the rotation-induced anisotropic neutrino heating is affected by the strong magnetic fields through parity-violating effects and for the first time investigate how the north-south asymmetry of the neutrino heating in a strongly magnetized supernova core could be affected. As for the microphysics, we employ a realistic equation of state based on the relativistic mean field theory and take into account electron captures and the neutrino transport via a neutrino leakage scheme. With these computations, we find that the neutrino heating rates are reduced by less than or similar to0.5% over those without the magnetic fields as a result of the parity-violating effects in the vicinity of the north pole of a star, while they are enhanced by about less than or similar to0.5% in the vicinity of the south pole. If the global asymmetry of the neutrino heating in the both of the poles develops in the later phases, the newly born neutron star might be kicked toward the north pole in the subsequent period.

We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of collapsars including a rotating black hole. This paper is an extension of our previous paper. The current calculation focuses on the effect of black hole rotation using general relativistic MHD with simplified microphysics; i.e., we ignore neutrino cooling, physical equation of state, and photodisintegration. Initially, we assume that the core collapse has failed in this star. A rotating black hole of a few solar masses is inserted by hand into the calculation. We consider two cases, a corotating case and a counterrotating case with respect to the black hole rotation. Although the counterrotating case may be unrealistic for collapsars, we perform it as the maximally dragging case of a magnetic field. The simulation results show the formation of a disklike structure and the generation of a jetlike outflow near the central black hole. The jetlike outflow propagates outwardly with the twisted magnetic field and becomes collimated. We have found that the jets are generated and accelerated mainly by the magnetic field. The total jet velocity in the rotating black hole case is comparable to that of the nonrotating black hole case, similar to0.3c. When the rotation of the black hole is faster, the magnetic field is twisted strongly owing to the frame-dragging effect. The magnetic energy stored by the twisting magnetic field is directly converted to kinetic energy of the jet rather than propagating as an Alfven wave. Thus, as the rotation of the black hole becomes faster, the poloidal velocity of the jet becomes faster. In the rapidly rotating black hole case the jetlike outflow can be produced by the frame-dragging effect only through twisting of the magnetic field, even if there is no stellar rotation.

We study both analytically and numerically hydrodynamic effects of two colliding shells, the simplified models of internal shock in various relativistic outflows such as gamma-ray bursts and blazars. We pay particular attention to three interesting cases: a pair of shells with the same rest-mass density ("equal rest-mass density''), a pair of shells with the same rest mass ("equal mass''), and a pair of shells with the same bulk kinetic energy ("equal energy'') measured in the interstellar medium frame. We find that the density profiles are significantly affected by the propagation of rarefaction waves. A split feature appears at the contact discontinuity of two shells for the equal-mass case, while no significant split appears for the equal-energy and equal rest-mass density cases. The shell spreading within a few 10% of the speed of light is also shown as a notable aspect caused by rarefaction waves. The conversion efficiency of bulk kinetic energy to internal energy is numerically evaluated. The time evolutions of the efficiency show deviations from the widely used inelastic two-point mass-collision model.

Neutrinos are considered to be one of the most important ingredients of collapse-driven supernovae. In the last couple of years, we have seen major progress in both numerical modelling and microphysical understanding of supernova neutrinos. The successful explosion, however, is still elusive. In the former half of this article, we give a brief overview on the current status of the theoretical understanding of the supernova mechanism. In the latter half, we present some new results on multi-dimensional aspects such as rapid rotations, strong magnetic fields and resultant anisotropic neutrino heating, to which our group is currently paying particular attention as an important element for successful explosions. We employ both statical and dynamical approaches. The gravitational waves obtained in the dynamical computations are summarized in an appendix.

We study the stress tensor of electron in strong magnetic fields which are greater than the critical value B-c similar or equal to 4.4 x 10(13) G. We claim that such a strong magnetic field induces the anisotropic kinetic pressure term of electron in magnetohydrodynamic equations and can generate entropy in collisional quantum plasmas. We discuss its consequence to the neutrino-driven wind in core-collapse supernovae and argue that it can produce large entropy per baryon, S similar to 400k(B). This mechanism might successfully account for the production of the heavy nuclei with mass numbers A = 80-250 through the r-process nucleosynthesis. (C) 2004 Elsevier B.V. All rights reserved.

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 (1.8-5.8) X 10(12) 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 x 10(-3) to 5.8 x 10(-4) rad s(-1) and 2.3 X 10(15) to 5.6 x 10(16) 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.

We perform a series of two-dimensional, axisymmetric, magnetohydrodynamic simulations of the rotational collapse of a supernova core. In order to calculate the waveforms of the gravitational wave, we derive the quadrupole formula including the contributions from the electromagnetic fields. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than those of the poloidal ones at the presupernova stage. Thus we systematically investigate the effects of the toroidal magnetic fields on the amplitudes and waveforms of the gravitational wave. Furthermore, we employ two kinds of the realistic equation of states which are often used in supernova simulations. Then, we investigate the effects of the equation of states on the gravitational wave signals. As for microphysics, we take into account the electron capture and neutrino transport by the so-called leakage scheme. With these computations, we find that the peak amplitudes of the gravitational wave are lowered by an order of 10% for models with the strongest toroidal magnetic fields. However, the peak amplitudes are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we point out that the amplitudes of second peaks are still within the detection limit of the first LIGO for the source, although the characteristics of second peaks are reduced by the magnetic fields. We stress the importance of the detection, since it will give us information about the angular momentum distribution of massive evolved stars. When we compare the gravitational waves from the two realistic equations of state, significant differences are not found, except that the typical frequencies of the gravitational wave become slightly higher for the softer equation of state.

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.

We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of the gravitational collapse of a magnetized rotating massive star as a model of gamma-ray bursts (GRBs). The current calculation focuses on general relativistic MHD with simplified microphysics ( we ignore neutrino cooling, physical equation of state, and photodisintegration). Initially, we assume that the core collapse has failed in this star. A few M(.) black hole is inserted by hand into the calculation. The simulations presented in the paper follow the accretion of gas into a black hole that is assumed to have formed before the calculation begins. The simulation results show the formation of a disklike structure and the generation of a jetlike outflow inside the shock wave launched at the core bounce. We have found that the jet is accelerated by the magnetic pressure and the centrifugal force and is collimated by the pinching force of the toroidal magnetic field amplified by the rotation and the effect of geometry of the poloidal magnetic field. The maximum velocity of the jet is mildly relativistic (similar to0.3c). The velocity of the jet becomes larger as the initial rotational velocity of stellar matter gets faster. On the other hand, the dependence on the initial magnetic field strength is a bit more complicated: the velocity of the jet increases with the initial field strength in the weak field regime, then is saturated at some intermediate field strength, and decreases beyond the critical field strength. These results are related to the stored magnetic energy determined by the balance between the propagation time of the Alfven wave and the rotation time of the disk ( or twisting time).

We investigate the dynamics and morphology of jets propagating into the interstellar medium using two-dimensional relativistic hydrodynamic simulations. The calculations are performed assuming axisymmetric geometry and follow jet propagation over a long distance. The jets are assumed to be "light,'' with the density ratio between the beam to the ambient gas much less than unity. We examine the mechanism for the appearance of vortices at the head of jets in the hot spot. Such vortices are known as a trigger of a deceleration phase, which appears after a short phase in which the jet propagation follows the results from one-dimensional analysis. We find that an oblique shock at the boundary rim near the end of the beam strongly affects the flow structure in and around the hot spot. Weakly shocked gas passes through this oblique shock and becomes a trigger for the generation of vortices. We also find the parameter dependence of these effects for the propagation and dynamics of the jets. The jet with slower propagation velocity is weakly pinched, has large vortices, and shows very complex structure at the head of the jets and extended synchrotron emissivity.

We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of collapsars as a model of gamma ray bursts (GRBs). This simulation showed the formation of a disk-like structure and the generation of a mildly relativistic jet (～0.3c). We have found the jet is accelerated by the magnetic pressure and the centrifugal force and is collimated by the pinching force of the toroidal magnetic field amplified by the rotation.

We calculate the time dependent line and recombination spectrum of non-equilibrium plasma heated by strong radiation as a test model of X-ray line emission of GRB afterglows. Our calculation shows that the non-equilibrium effect of the plasma is complex and important in the time evolution of the spectrum. The origin of these lines is puzzling us, but it is essential to understand the nature of GRBs and their circumstellar matter.

We perform a series of two-dimensional, axisymmetric, magnetohydrodynamic simulations of the rotational collapse of a supernova core. In order to calculate the waveforms of the gravitational wave, we derive the quadrupole formula including the contributions from the electromagnetic fields. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than those of the poloidal ones at the presupernova stage. Thus we systematically investigate the effects of the toroidal magnetic fields on the amplitudes and waveforms of the gravitational wave. Furthermore, we employ two kinds of the realistic equation of states which are often used in supernova simulations. Then, we investigate the effects of the equation of states on the gravitational wave signals. As for microphysics, we take into account the electron capture and neutrino transport by the so-called leakage scheme. With these computations, we find that the peak amplitudes of the gravitational wave are lowered by an order of 10% for models with the strongest toroidal magnetic fields. However, the peak amplitudes are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we point out that the amplitudes of second peaks are still within the detection limit of the first LIGO for the source, although the characteristics of second peaks are reduced by the magnetic fields. We stress the importance of the detection, since it will give us information about the angular momentum distribution of massive evolved stars. When we compare the gravitational waves from the two realistic equations of state, significant differences are not found, except that the typical frequencies of the gravitational wave become slightly higher for the softer equation of state. © 2004 The American Physical Society.

We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of the gravitational collapse of a magnetized rotating massive star as a model of gamma ray bursts (GRBs). This simulation showed the formation of a disk-like structure and the generation of a jet-like outflow inside the shock wave launched at the core bounce. We have found the jet is accelerated by the magnetic pressure and the centrifugal force and is collimated by the pinching force of the toroidal magnetic field amplified by the rotation and the effect of geometry of the poloidal magnetic field. The maximum velocity of the jet is mildly relativistic (similar to 0.3 c).

We study characteristics of the relativistic equation of state (EOS) for collapse-driven supernovae, which is derived by relativistic nuclear many body theory. Recently the relativistic EOS table has become available as a new complete set of physical EOS for numerical simulations of supernova explosion. We examine this EOS table by using general relativistic hydrodynamics of the gravitational collapse and bounce of supernova cores. In order to study dense matter in dynamical situation, we perform simplified calculations of core collapse and bounce by following adiabatic collapse with the fixed electron fraction for a series of progenitor models. This is intended to give us "approximate models" of prompt explosion. We investigate the profiles of thermodynamical quantities and the compositions during collapse and bounce. We also perform the calculations with the Lattimer-Swesty EOS to compare the properties of dense matter. As a measure of the stiffness of the EOS, we examine the explosion energy of the prompt explosion with electron capture totally suppressed. We study the derivative of the thermodynamical quantities obtained by the relativistic EOS to discuss the convective condition in neutron-rich environment, which may be important in the delayed explosion. (C) 2003 Elsevier B.V. All rights reserved.

We perform two-dimensional relativistic hydrodynamic simulations in the context of collapsar model. Calculations of explosive nucleosynthesis are also accomplished. We investigate the influence of the structure of the progenitor and energy deposition rate on the resulting explosive nucleosynthesis, assuming that Ni-56 is mainly synthesized in the jet launched by the neutrino heating. We show that the amount of Ni-56 is very sensitive to the energy deposition rate. Thus, we conclude that it is quite natural to detect no underlying supernova in some X-ray afterglows, such as GRB 010921. We also point out the possibility that the relative abundance of the elements with an intermediate mass number, such as Si and S, in the X-ray afterglow of GRB 011211 may be naturally explained if the energy deposition rate at the central engine is relatively long because little Ni-56 should be synthesized under such an environment. If this discussion is true, there should be a correlation between the line features in the X-ray afterglow and the duration of the gamma-ray burst. It should be noted that the duration of GRB 011211 is 270 s,making it the longest burst ever observed by BeppoSAX, although it suffers from the effect of redshift (z(host)=2.14), and supporting our conclusion. Our results also suggest that the type I collapsar model, in which the energy deposition rate is relatively low ((E)over dot similar to 10(51) ergs s(-1)), might have difficulty in reproducing the observed amount of Ni-56 in a hypernova such as SN 1998bw. This means that models of the mechanism of the central engine of a hypernova-accompanying gamma-ray burst may be constrained by the requirements of explosive nucleosynthesis.

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.

We perform a series of two-dimensional hydrodynamic simulations of the rotational collapse of a supernova core in axisymmetry. We employ a realistic equation of state (EOS) and take into account electron capture and neutrino transport by the so-called leakage scheme. It is an important step to apply the realistic EOS coupled with microphysics to 2D simulations for computing gravitational radiation in rotational core collapse. We use the quadrupole formula to calculate the amplitudes and the waveforms of the gravitational wave assuming Newtonian gravity. With these computations, we extend the conventional category of the gravitational waveforms. Our results show that the peak amplitudes of the gravitational wave are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we find that the amplitudes of the second peaks are within the detection limit of the first LIGO for the source, and first point out the importance of the detection, since it will give us information as to the angular momentum distribution of evolved massive stars.

In this study, the effect of the rotation on the gravitational collapse is investigated by two-dimensional numerical simulation. Although most simulations for rotational collapse so far have been performed by employing the simplified equation of state for numerical simplicity, we employed more realistic equation of state by Shen et al. The initial angular momentum distribution is based on the recent calculation by Heger et al. The results obtained are quantitatively consistent with the previous work by Muller et al. In addition, we find it possible to realize the anisotropic neutrino radiation, which supports the scenario, in which explosion is induced by the anisotropic radiation from oblate core by rotation (Shimizu et al.).

Using a new numerical EOS (equation of state) table calculated by Shen et al., we performed numerical simulations of protoneutron star cooling. The EOS is based on the relativistic mean field theory, and the parameters in its Lagrangian have been chosen to reproduce the experimental properties of both stable and unstable nuclei. Furthermore, the numerical table covers such a wide range of thermodynamical quantities (temperature, 0 similar to 100MeV; electron fraction, 0 similar to 0.56; density, 10(5.1) similar to 10(15.4) g/cc) that cooling simulations even for 50 seconds could be done without troubles. The quasistatic evolution of protoneutron stars was investigated in detail with a numerical code including neutrino transfer (MGFLD scheme). Dependencies both on EOS and on initial models and implications to the SN1987A constraint on neutrino oscillation models are discussed.

Physics of the inertial fusion is based on a variety of elements such as compressible hydrodynamics, radiation transport, non-ideal equation of state, non-LTE atomic process, and laser plasma interaction. In addition, implosion process is not in stationary state and fluid dynamics, energy transport and instabilities should be solved simultaneously. In order to study such complex physics, an integrated implosion code including all physics important in the implosion process should be developed. Before starting this work, an integrated code based on Hirt's ALE method had been developed. But it needed sophisticated rezoning/remapping algorithm and less dissipative ALE method in hardly distorted mesh. In this work, we have developed 2-D integrated implosion code based on CIP method which was described in ALE formation. In the IFE research, the fast ignition scheme is one of the epoch making new scheme. In the scheme, the formation of the high density core plasma is one of the problem to be solved. In this paper non-spherical implosion for fast ignition is solved using the integrated code.

Nonlocal transport becomes important in a variety of situations in physics. We briefly review under what conditions it appears to be important in modeling energy transport by neutral gas, neutrons, charged particles, photons, and neutrinos. In the cases of these last three, the cross-sections strongly depend upon particle energies. In such cases, nonlocal transport becomes important even when each mean free path is much shorter than the length of the change of its energy density. We mainly review the research that has been done on nonlocal electron energy transport in relation to laser-produced plasmas and the way in which precise calculation of neutrino transport changes the properties of a shock wave, which is used as a driver to explode a massive star such as a supernova, by solving Boltzmann-type equations for neutrinos and anti-neutrinos.

In this paper we present a numerical study of plasma jets produced by intense laser matter interactions. Through this study we hope to better understand astrophysical jets and their recent experimental simulations in the laboratory. We paid special attention to radiation cooling and the interaction of the jet with ambient gas. Four cases are presented in this paper: two of them deal with the propagation of jets in the vacuum, while in the other two the propagation takes place in the ambient gas. Available experimental results are reproduced to good accuracy in the vacuum case. For jets in ambient gas, we find that the existence of the surrounding gas confines the jet into a narrow cylindrical shape so that both the density and temperature of the jet remain high enough for effective radiation cooling. As a result, a collimated plasma jet is formed in these cases. The dimensionless parameters characterizing the laboratory jets and protostellar jets have overlapping domains. We also discuss the cooling lengths for our model and compare them with the corresponding values in the astrophysical jets. A plasma jet in the ambient gas experiment is proposed which is within the reach of present-day technology and can be relevant to astrophysical phenomena.

In this short article, significant issues related to the calculations of the opacity of partially ionized atoms are explained in detail. We will mainly pay attention to the treatment of the detailed level structure of low and intermediate Z atoms, based on which the authors are currently developing the opacity code. Some recent advanced treatments of high Z atoms as well as major projects in the world are also briefly reviewed.

We reanalyze r-process nucleosynthesis in the neutron-rich ejecta from a prompt supernova explosion of a low-mass (11 M.) progenitor. Although it has not yet been established that a prompt explosion can occur, it is not yet ruled out as a possibility for low-mass supernova progenitors. Moreover, there is mounting evidence that a new r-process site may be required. Hence, we assume that a prompt explosion can occur and make a study of r-process nucleosynthesis in the supernova ejecta. To achieve a prompt explosion we have performed a general relativistic hydrodynamic simulation of adiabatic collapse and bounce using a relativistic nuclear-matter equation of state. The electron fraction Y-e during the collapse was fixed at the initial-model value. The size of the inner collapsing core was then large enough to enable a prompt explosion to occur in the hydrodynamic calculation. Adopting the calculated trajectories of promptly ejected material, we explicitly computed the burst of neutronization due to electron captures on free protons in the photodissociated ejecta after the passage of the shock. The thermal and compositional evolution of the resulting neutron-rich ejecta originating from near the surface of the proto-neutron star was obtained. These were used in nuclear reaction network calculations to evaluate the products of r-process nucleosynthesis. We find that, unlike earlier studies of nucleosynthesis in prompt supernovae, the amount of r-process material ejected per supernova is quite consistent with observed Galactic r-process abundances. Furthermore, the computed r-process abundances are in good agreement with solar abundances of r-process elements for A &gt; 100. This suggests that prompt supernovae are still viable r-process sites. Such events may be responsible for the abundances of the heaviest r-process nuclei.

We study the equation of state of electron in strong magnetic fields which
are greater than the critical value $B_c \simeq 4.4 \times 10^{13}$ Gauss. We
find that such a strong magnetic field induces the anisotropic pressure of
electron. We apply the result to the neutrino-driven wind in core-collapse
supernovae and find that it can produce large entropy per baryon, $S \sim 400
k_B$. This mechanism might successfully account for the production of the heavy
nuclei with mass numbers A = 80 -- 250 through the r-process nucleosynthesis.

We study supernova explosions and the associated r-process using a nuclear-matter equation of state (EOS) which has been constrained by the experimental data of unstable nuclei. This EOS table has been recently derived from relativistic many-body theory. We have applied it to numerical simulations of supernovae and the r-process. We find that a successful r-process is indeed possible in hydrodynamical simulations of the nu -driven wind from the nascent proto-neutron star as long as the expansion time scale is short.

Since SN 1987A, many observations have indicated that supernova explosions are not spherical. The cause of the asymmetric explosion is still controversial (e.g., asymmetry in the envelope, the convective engine in the central core or in the proto-neutron star). In our previous study, anisotropic neutrino radiation has been proposed as an explanation for this asymmetry. In this paper we carried out a series of systematic multidimensional numerical simulations in order to investigate the effect of anisotropic neutrino radiation itself on the supernova explosion energy. The neutrino luminosity and the degree of anisotropy in neutrino radiation were assumed as input parameters, and the numerical results for various parameters were compared with each other. It was found that only a few percent of anisotropy in the neutrino emission distribution is sufficient to increase the explosion energy by a large factor. The explosion energy calculated so far in many supernova models has tended to be too short to explain the observation. Anisotropy of 10% in neutrino radiation roughly corresponds to an enhancement of 4% in total neutrino luminosity as far as the explosion energy is concerned. The increase in the explosion energy due to anisotropic neutrino radiation can be explained as follows. Anisotropically emitted neutrinos locally heat the supernova matter and revive a stalled shock wave in the direction of enhanced radiation. The expansion of the gas by the shock propagation results in a decrease in the neutrino cooling (emission) rate that rapidly decreases with the matter temperature. It is this suppression of energy loss that contributes largely to the increase in explosion energy. The efficiency of neutrino heating (absorption) itself is almost unchanged between anisotropic and spherical models with available energy fixed for neutrinos. In order for a stalled shock wave to revive, enhancement of the local intensity in the neutrino flux is of great importance, rather than that of the total neutrino luminosity over all the solid angle. It is first pointed out that such local neutrino heating is capable of triggering a supernova explosion. Anisotropic neutrino radiation is considered to be a plausible mechanism for a "successful" explosion other than the so far suggested "convective trigger."

With a view of applications to the simulations of supernova explosions and protoneutron star cooling, we derive the Boltzmann equations for the neutrino transport with flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy while the collision terms are obtained in the Born approximation. The resulting equations take the familiar form of the Boltzmann equation with corrections due to mixing both in the advection part and in the collision part. These corrections are essentially the same as those derived by Sirera et al. for the advection terms and those by Raffelt et al. for the collision terms, respectively, though the formalism employed here is different from theirs. The derived equations will be easily implemented in numerical codes employed in the simulations of supernova explosions and protoneutron star cooling.

We discuss the neutrino-driven wind from a proto-neutron star based on general-relativistic hydrodynamical simulations. We examine the properties of the neutrino-driven wind to explore the possibility of r-process nucleosynthesis. Numerical simulations involving neutrino heating and cooling processes were performed with the assumption of a constant neutrino luminosity by using realistic profiles of the proto-neutron star (PNS) as well as simplified models. The dependence on the mass of PNS and the neutrino luminosity is presented systematically. Comparisons with analytic treatments in the previous studies are also given. In the cases with the realistic PNS, we have found that the entropy per baryon and the expansion time scale are neither high nor short enough for the r-process within the current assumptions. On the other hand, we have also found that the expansion time scale obtained by hydrodynamical simulations is systematically shorter than that in the analytic solutions due to our proper treatment of the equation of state. This fact might lead to an increase in the neutron-to-seed ratio, which is suitable for the r-process in a neutrino-driven wind. Indeed, in the case of massive and compact proto-neutron stars with high neutrino luminosities, the expansion time scale is found to be sufficiently short in hydrodynamical simulations, and the r-process elements up to A similar to 200 are produced in the r-process network calculation.

We calculate neutrino reaction rates with nucleons via the neutral and charged currents in the supernova core in the relativistic random phase approximation (RPA) and study their effects on the opacity of the supernova core. The formulation is based on the Lagrangian employed in the calculation of the nuclear equation of stale (EOS) in the relativistic mean field theory (RMF). The nonlinear meson terms are treated appropriately so that the consistency of the density correlation derived in RPA with the thermodynamic derivative obtained from the EOS by the RMF is satisfied in the static and long wavelength limit. We employ pion and rho meson exchange interactions together with the phenomenological Landau-Migdal parameters for the isospin-dependent nuclear interactions. We find that both the charged and neutral current reaction rates are suppressed from Bruenn's standard approximate formula considerably in the high density regime (rho(b) greater than or similar to 10(14) g/cm(3) with rho(b) the baryonic density). In the low density regime (rho(b) less than or similar to 10(14) g/cm(3)), on the other hand, the vector current contribution to the neutrino-nucleon scattering rate is enhanced in the vicinity of the boundary of the liquid-gas phase transition, while the other contributions are moderately suppressed there also. In the high temperature regime (T greater than or similar to 40 MeV with T the temperature) or in the regime where electrons have a large chemical potential, the latter of which is important only for the electron capture process and its inverse process, the recoil of nucleons cannot he neglected and further reduces the reaction rates with respect to the standard approximate formula which discards any energy transfer in the processes. These issues could have a great impact on the neutrino heating mechanism of collapse-driven supernovae.

We studied possible modifications of the neutrino-nucleon scattering rate due to the nucleon-nucleon collisions in the hot dense matter which we find in the supernova core. We show that the finite width of the nucleon spectral function induced by the nucleon collisions leads to a broadening of the dynamical spin structure function of the nucleon, resulting in a reduction of the rate of neutrino-nucleon scattering via the axial vector current and making the energy exchange between neutrinos and nucleons easier. The reduction rate is relatively large, similar to 0.6, even at density similar to 10(13)g/cm(3) and could have a significant impact on the dynamics of the collapse-driven supernova as well as the cooling of the proto neutron star. (C) 2000 Elsevier Science B.V. All rights reserved.

We have coded a Boltzmann solver based on a finite difference scheme (SN method) aiming at calculations of neutrino transport in type TT supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been made for realistic atmospheres of post bounce core models under the assumption of a static background. We have also investigated in detail the dependence of the results on the numbers of radial, angular, and energy grid points and the way to discretize the spatial advection term which is used in the Boltzmann solver. A general relativistic calculation has been done for one of the models. We find good overall agreement between the two methods. This gives credibility to both methods which are based on completely different formulations. In particular, the number and energy fluxes and the mean energies of the neutrinos show remarkably good agreement, because these quantities are determined in a region where the angular distribution of the neutrinos is nearly isotropic and they are essentially frozen in later on. On the other hand, because of a relatively small number of angular grid points (which is inevitable due to limitations of the computation time) the Boltzmann solver tends to slightly underestimate the flux factor and the Eddington factor outside the (mean) "neutrinosphere" where the angular distribution of the neutrinos becomes highly anisotropic. As a result, the neutrino number (and energy) density is somewhat overestimated in this region. This fact suggests that the Boltzmann solver should be applied to calculations of the neutrino heating in the hot-bubble region with some caution because then might be a tendency to overestimate the energy deposition rate in disadvantageous situations. A comparison shows that this trend is opposite to the results obtained with a multi-group flux-limited diffusion approximation of neutrino transport. Employing three different flux limiters, we find that all of them lead to a significant underestimation of the neutrino energy density in the semitransparent regime, and thus must yield too low values for the net neutrino heating (heating minus cooling) in the hot-bubble region. The accuracy of the Boltzmann solver can be improved by using a variable angular mesh to increase the angular resolution in the region where the neutrino distribution becomes anisotropic.

First results of numerical simulations are presented which compute the dynamical evolution of a neutron star with a mass slightly below the minimum stable mass by means of a new implicit (general relativistic) hydrodynamic code. We show that such a star first undergoes a phase of quasi-static expansion, caused by slow nuclear beta-decays, lasting for about 20 seconds, but then explodes violently. The kinetic energy of the explosion is around 10(49) erg, the peak luminosity in electron anti-neutrinos is of order 10(52) erg/s, and the thermodynamic conditions of the expanding matter are favorable for r-process nucleosynthesis. These results are obtained for the Harrison-Wheeler equation of state and a simple and, possibly, unrealistic treatment of beta-decay rates and nuclear fission, which were adopted for comparison with previous works. However, we do not expect that the outcome will change qualitatively if more recent nuclear input physics is used.
Although our study does not rely on a specific scenario of how a neutron star starting from a bigger (and stable) mass can reach the dynamical phase, we implicitly assume that the final mass-loss event happens on a very short time scale, i.e., on a time scale shorter than a sound-crossing time, by removing a certain amount of mass as an initial perturbation. This assumption implies that the star has no time to adjust its nuclear composition to the new mass through a sequence of quasi-equilibria. In the latter case, however, there exists no stable configuration below the minimum mass, because the equation of state of fully catalyzed matter is too soft. Therefore, the dynamics of the explosion will not be too different from what we have obtained if different initial perturbations are assumed.

We have performed 1-dimensional calculations for explosive nucleosynthesis in collapse-driven supernova and investigated its sensitivity to the initial form of the shock wave. We have found the tendency that the peak temperature becomes higher around the mass cut if the input energy is injected more in the form of kinetic energy rather than internal energy. Then, the mass cut becomes larger, and, as a result, neutron-rich matter is less included in the ejecta; this is favorable for producing the observational data compared with a previous model. Our results imply that the standard method to treat various processes for stellar evolution, such as convection and electron capture during the silicon burning stage, is still compatible with the calculation of explosive nucleosynthesis.

Nucleosynthesis in supernovae is reviewed considering the recent development. There is a consensus that supernovae have two distinct origins. One is the explosion of white dwarfs which we call SNIa. The other is the explosion of massive stars of M-ms greater than or similar to 10M. which we call SNII (M-ms is the stellar mass in the main-sequence stage). However, the mechanism of the explosion for both supernovae is now in debate. SNIa is the result of the mass accretion onto a white dwarf from a companion star. The deflagration model which has been believed as the standard model of SNIa may be modified because many different types of SNIa have been observed recently. Furthermore, multi-dimensional hy drodynamical calculations suggest a slow deflagration model rather than a fast deflagration model like W7. On the other hand, to explain new types of SNIa, delayed or late detonation model has been proposed. For SNII, there does not still exist the reliable calculations from the core collapse to the explosion after a bounce; the present delayed explosion calculation cannot explain the observed explosion energy of SN1987A. Though these calculations are limited to the spherical cases, from the observation and multi-dimensional calculations, asymmetric explosion is suggested. Therefore, we must explore possible explosion models of supernovae for both SNIa and SNII. Recently, developed are two-dimensional hydrodynamical calculations to simulate an asymmetric explosive nucleosynthesis; we have found significant differences compared with the spherical explosive nucleosynthesis. For SNIa, new models of delayed detonation and results of the explosive nucleosynthesis was proposed by [9]. These new models are expected to compensate the previous models in many observational points.

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) Ti-44 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) Ni-57 and Ni-58 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 shack 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, Ca-44, 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.

An implicit Lagrangian hydrodynamics code for general relativistic spherical collapse is presented. This scheme is based on an approximate linearized Riemann solver (Roe-type scheme) and needs no artificial viscosity. This code is aimed especially at the calculation of the late phase of collapse-driven supernovae and the nascent neutron star, where there is a remarkable contrast between the dynamical timescale of the proto-neutron star and the diffusion timescale of neutrinos, without such severe limitation of the Courant condition at the center of the neutron star. Several standard test calculations have been done, and their results show the following: (1) This code captures the shock wave accurately, although some erroneous jumps of specific internal energy are found at the contact discontinuity in the shock tube problems. (2) The scheme shows no instability even if we choose the Courant number larger than 1. (3) However, the Courant number should be kept below similar to 0.2 at the shock position, so that the shock can be resolved with a few meshes. (4) The scheme reproduces the well-known analytic solutions to the point blast explosion, the gravitational collapse of the uniform gas with gamma = 4/3, and the general relativistic collapse of uniform dust. In addition, what is more important, calculations of hydrostatic configurations and the onset of radial instability, a preliminary neutrino transport in a proto-neutron star, and adiabatic collapses of a stellar core have also been done in order to show the performance of the code in the context of the collapse-driven supernovae. It is found that the time step can be extended far beyond the Courant limitation at the center of the neutron star, which fact is crucially significant for the purpose of this project. The details of the scheme and the results of these test calculations are discussed.

As is well known, massive stars, which would be the progenitor of type II supernovae, are rapid rotators. It is obviously necessary to investigate the effects of rotation on gravitational collapse of stellar cores and supernova explosions. We review (i) rotational core collapse, (ii) jet-like explosion induced by rotation and asymmetric neutrino emission from proto-neutron-stars, and (iii) explosive nucleosynthesis when an asymmetric jet-like explosion occurs, based on our recent work.

We have numerically calculated amplitudes and wave forms of gravitational radiation emitted from a central core in an axisymmetric supernova. The rotational core collapse has been systematically simulated under the assumption that the dynamical system is axisymmetric, and the complex microphysics such as nuclear equation of state and electron capture are approximated by a phenomenological equation of state. We have utilized the quadrupole formula to calculate the amplitudes and the wave forms of gravitational wave, and we have also assumed the Newtonian evolution of hydrodynamics. From these computations we have obtained burst-type wave forms. It is found from the comparison with results by Muller et al. or by Finn that the peak amplitude is sensitive to the stiffness of equation of state around the core bounce. Our results also show that the duration of the first burst is simply determined from the mean density of the inner core at the core bounce. Since the mean density of the inner core at the core bounce is dependent upon the angular momentum of the inner core and the stiffness of matter, we find it possible to obtain the information as to the angular momentum of a stellar core and the equation of state of high-density matter from the combined data of amplitude and duration of the burst from axisymmetric supernova explosion.

Recent theoretical development of collapse-driven supernova explosion is reviewed. In particular, we discuss in detail i) convection in the hot bubble region above the protoneutron star as the source of the large amplitude velocity fluctuations which is necessary to explain large scale mixing in SN1987A, and ii) jet-like explosion induced by axisymmetric neutrino emission from a rotating oblate proto-neutron star, which might account for asymmetry of expanding envelope of SN1987A.

Systematic numerical simulations have been carried out systematically in order to clarify the effect of rotation on the dynamics of core collapse in the supernova explosions. We have utilized a simple phenomenological equation of state with a polytropic form to approximate the complicated microphysics, and we have not solved neutrino transport, either. The infalling matter is found to be clearly divided into two parts, one of which is the inner core contracting subsonically, and the other is the outer core falling supersonically as in the spherically symmetric collapse. The inner core becomes more massive and deformed as the rotational energy increases or as the degree of the differential rotation becomes greater. On the other hand, it is also clear that the explosion energy monotonically decreases as the rotational energy increases or as the degree of differential rotation becomes greater. This is because the centrifugal force prevents the inner core from contracting sufficiently and less gravitational energy is available to push the outer core. This feature is insensitive to the degree of neutrino trapping. It is, therefore, concluded that in general rotation of the core has a negative effect on the prompt explosion mechanism.

Numerical simulations of convection in the supernova core were carried out in which axisymmetrically modified neutrino radiation from a rotating proto-neutron star was assumed. Since neutrinos heat up matter around the rotational axis more intensively than around the equatorial plane, powerful and global convection of matter between the shock front and the proto-neutron star is induced, and, moreover, jetlike motion along the axis pushes the shock front into the prolate form. It is found that the hot bubble is distorted as a result of this quadrupolar convective motion and consequently that turbulent instability occurs behind the shock wave. This instability is considered to provide the initial fluctuation of Rayleigh-Taylor instability in the envelope, the seed of matter mixing in SN 1987A. We also found that three outstanding problems, namely, the seed of matter mixing, the high-velocity component of mixed elements, and observed asymmetry in the envelopes, can be explained simultaneously by those effects. Based on these results, we propose a new, possible scenario for the explosion mechanism.

Convective Instability behind a stalled shock wave is studied by performing a series of two-dimensional numerical simulations. This instability is induced by negative entropy gradient which is commonly formed in so-called ''hot bubble'' behind a stalled shock where matters are nearly hydrostatic and in radiative equilibrium. It is shown that an initial velocity perturbation of 1 % of the sound velocity grows to be a nonlinear fluctuation in approximately 100 ms. It is possible that this bubble instability becomes a seed of the Rayleigh-Taylor instability in the stellar envelope if the shock revives. It is also shown, however, that in actual fact the convective instability does not power the shock enough to change the way of its propagation. Rotation (the centrifugal force is at most 5 % of the gravitational force) does not affect the way of growth of the instability seriously either no matter what the initial rotation law is.

We have carried out three-dimensional simulations of convection above the proto neutron star in supernova explosions; this convection is driven by a negative entropy gradient due to heating of shocked matter by high-energy neutrinos radiated from the proto neutron star. We compared the three-dimensional calculations with axisymmetric or spherical calculations by changing the initial perturbations. We found that the explosion energy is unchanged by convective motion, but that convection can explain the seed of matter mixing. We also found that three-dimensional motion has an advantage for the ejection of r-process nuclei synthesized in hot bubbles.

We have carried out three-dimensional simulations of convection above the proto neutron star in supernova explosions; this convection is driven by a negative entropy gradient due to heating of shocked matter by high-energy neutrinos radiated from the proto neutron star. We compared the three-dimensional calculations with axisymmetric or spherical calculations by changing the initial perturbations. We found that the explosion energy is unchanged by convective motion, but that convection can explain the seed of matter mixing. We also found that three-dimensional motion has an advantage for the ejection of r-process nuclei synthesized in hot bubbles.

Asymmetric explosion of SN 1987 A is investigated by a two-dimensional axisymmetric hydrodynamical code. Two possibilities for the seed of the asymmetry, jet-like explosion of the Fe core and shock propagation in a star distorted by its own rotation, are investigated. For the latter studies, we calculated the density structure of the presupernova star in rotational equilibrium by using SCF method, which makes our calculation more realistic than previous works. The main results are as follows. (1) Jet-like explosion is more likely than distortion of the pre-supernova star since it is almost impossible to deform a blue supergiant to the degree necessary for the asymmetric explosion. (2) The degree of asymmetry observed by speckle can be explained by the asymmetry in the element distribution, not by the asymmetry in the density structure of ejecta. (3) There exist mainly two phases in the expansion: the blastwave phase when the radial flow dominates the expansion, and the subsequent expansion phase when the density profile becomes spherical by the effect of theta-flow.

We studied matter mixing by Rayleigh-Taylor instability in the jetlike supernova explosion by numerical calculations of two-dimensional hydrodynamics. We found that (1) the asymmetric explosion with 5% initial perturbation causes the same degree of matter mixing as the spherical one with 30% perturbation, and that (2) 30% initial perturbation in the jetlike explosion is sufficient to explain the mixing in SN 1987A suggested by many observations without any subsequent instability such as nickel bubble formation.