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Neutrinos are believed to have a key role in the explosion mechanism of core-collapse supernovae as they carry most of the energy released by the gravitational collapse of a massive star. If their flavor is converted fast inside the neutrino sphere, the supernova explosion may be influenced. This paper is reporting the results of the extended work of our previous paper. We perform a thorough survey of the ELN crossing in one of our self-consistent, realistic Boltzmann simulations in two spatial dimensions under axisymmetry for the existence of the crossings between $\nu_e$ and $\bar\nu_e$ angular distributions, or the electron lepton number (ELN) crossing. We report for the first time the positive detections deep inside the core of the massive star in the vicinity of neutrino sphere at $r$ $\approx$ 16 - 21 km. We find that low values of the electron fraction $Y_e$ produced by convective motions together with the appearance of light elements are critically important to give rise to the ELN crossing by enhancing the chemical potential difference between proton and neutron, and hence by mitigating the Fermi-degeneracy of $\nu_e$. Since the region of positive detection are sustained and, in fact, expanding with time, it may have an impact on the explosion of core-collapse supernovae, observational neutrino astronomy and nucleosynthesis of heavy nuclei., Comment: 12 pages, 12 figures, accepted for publication in PRD

Recent theoretical work indicates that the neutrino radiation in core-collapse supernovae may be susceptible to flavor instabilities that set in far behind the shock, grow extremely rapidly, and have the potential to profoundly affect supernova dynamics and composition. Here we analyze the nonlinear collective oscillations that are prefigured by these instabilities. We demonstrate that a zero-crossing in $n_{\nu_e} - n_{\bar{\nu}_e}$ as a function of propagation angle is not sufficient to generate instability. Our analysis accounts for this fact and allows us to formulate complementary criteria. Using Fornax simulation data, we show that fast collective oscillations qualitatively depend on how forward-peaked the neutrino angular distributions are., Comment: 7 pages, 3 figures

We present a linear stability analysis of the fast-pairwise neutrino flavor conversion based on a result of our latest axisymmetric core-collapse supernova (CCSN) simulation with full Boltzmann neutrino transport. In the CCSN simulation, coherent asymmetric neutrino emissions of electron-type neutrinos ($\nu_{\rm e}$) and their anti-particles ($\bar{\nu}_{\rm e}$), in which the asymmetry of $\nu_{\rm e}$ and $\bar{\nu}_{\rm e}$ is anti-correlated with each other, occur at almost the same time as the onset of aspherical shock expansion. We find that the asymmetric neutrino emissions play a crucial role on occurrences of fast flavor conversions. The linear analysis shows that unstable modes appear in both pre- and post-shock flows; for the latter they appear only in the hemisphere of higher $\bar{\nu}_{\rm e}$ emissions (the same hemisphere with stronger shock expansion). We analyze in depth the characteristics of electron-lepton-number (ELN) crossing by closely inspecting the angular distributions of neutrinos in momentum space. The ELN crossing happens in various ways, and the property depends on the radius: in the vicinity of neutron star, $\bar{\nu}_{\rm e}$ ($\nu_{\rm e}$) dominates over $\nu_{\rm e}$ ($\bar{\nu}_{\rm e}$) in the forward (backward) direction: at the larger radius the ELN crossing occurs in the opposite way. We also find that the non-radial ELN crossing occurs at the boundary between no ELN crossing and the radial one, which is an effect of genuine multi-D transport. Our findings indicate that the collective neutrino oscillation may occur more commonly in CCSNe and suggest that the CCSN community needs to accommodate these oscillations self-consistently in the modelling of CCSNe., Comment: Accepted to ApJ

We make a strong case that the fast neutrino-flavor conversion, one of the collective flavor oscillation modes, commonly occurs in core-collapse supernovae (CCSNe). It is confirmed in the numerical data obtained in realistic simulations of CCSNe but the argument is much more generic and applicable universally: the coherent neutrino-nucleus scattering makes the electron lepton number (ELN) change signs at some inward direction and trigger the flavor conversion in the outward direction in the pre-shock region. Although the ELN crossing is tiny and that is why it has eluded recognition so far, it is still large enough to induce the flavor conversion. Our findings will have an important observational consequences for CCSNe neutrinos.

We have conducted nineteen state-of-the-art 3D core-collapse supernova simulations spanning a broad range of progenitor masses. This is the largest collection of sophisticated 3D supernova simulations ever performed. We have found that while the majority of these models explode, not all do, and that even models in the middle of the available progenitor mass range may be less explodable. This does not mean that those models for which we did not witness explosion would not explode in Nature, but that they are less prone to explosion than others. One consequence is that the "compactness" measure is not a metric for explodability. We find that lower-mass massive star progenitors likely experience lower-energy explosions, while the higher-mass massive stars likely experience higher-energy explosions. Moreover, most 3D explosions have a dominant dipole morphology, have a pinched, wasp-waist structure, and experience simultaneous accretion and explosion. We reproduce the general range of residual neutron-star masses inferred for the galactic neutron-star population. The most massive progenitor models, however, in particular vis \`a vis explosion energy, need to be continued for longer physical times to asymptote to their final states. We find that while the majority of the inner ejecta have Y$_e = 0.5$, there is a substantial proton-rich tail. This result has important implications for the nucleosynthetic yields as a function of progenitor. Finally, we find that the non-exploding models eventually evolve into compact inner configurations that experience a quasi-periodic spiral SASI mode. We otherwise see little evidence of the SASI in the exploding models., Comment: Accepted to Monthly Notices of the Royal Astronomical Society

In this {\it Letter}, we present the result of an axisymmetric CCSN simulation conducted with appropriate treatments of neutrino transport and proper motions of proto-neutron star (PNS), in which a remarkable PNS acceleration is observed in association with asymmetric neutrino emissions by the time of $300$ms after bounce. We find that these asymmetric neutrino emissions play important roles in the acceleration of PNS in this phase. The correlation between the PNS proper motion and the asymmetric ejecta is similar to that in the neutron star (NS) kick of hydrodynamic origin. Both electron-type neutrinos ($\nu_{\rm e}$) and their anti-particles ($\bar{\nu}_{\rm e}$) have $\sim 10\%$ level of asymmetry between the northern and southern hemispheres, while other heavy-leptonic neutrinos ($\nu_x$) have much smaller asymmetry of $\sim 1 \%$. The emissions of $\bar{\nu}_{\rm e}$ and $\nu_x$ are higher in the hemisphere of stronger shock expansion whereas the $\nu_{\rm e}$ emission is enhanced in the opposite hemisphere: in total the neutrinos carry some linear momentum to the hemisphere of the stronger shock expansion. The asymmetry is attributed to the non-spherical distribution of electron-fraction ($Y_e$) in the envelope of PNS. Although it is similar to LESA (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 symmetry of the matter distribution there, which are 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 the later evolution., Comment: Accepted to ApJL

We present a new method for neutrino-matter coupling in multi-dimensional radiation-hydrodynamic simulations of core-collapse supernova (CCSN) with the full Boltzmann neutrino transport. The development is motivated by the fact that the accurate conservation of momentum is required for reliable numerical modelings of CCSN dynamics including a recoil of proto-neutron star (PNS). The new method is built on a hybrid approach, in which we use the energy-momentum tensor of neutrinos to compute the momentum feedback from neutrino to matter in the optically thick region while we employ the collision term in the optically thin region. In this method we utilize a general relativistic description of radiation-hydrodynamics with angular moments, which allows us to evaluate the momentum feedback from neutrino to matter without inconsistency with our Boltzmann solver. We demonstrate that the new method substantially improves the accuracy of linear momentum conservation in our CCSN simulations under reasonable angular resolutions in momentum space, alleviating the difficulty in giving the diffusion limit precisely with the discrete ordinate (Sn) method. It is the first-ever demonstration that the PNS kick can be handled directly and properly in multi-dimensional radiation-hydrodynamic simulations with the full Boltzmann neutrino transport., Comment: Accepted to ApJS

We investigate the impact of asymmetric neutrino emissions on the explosive nucleosynthesis in neutrino-driven core-collapse supernovae (CCSNe). We find that the asymmetric emissions tend to yield larger amounts of proton-rich ejecta (electron fraction, $Y_e > 0.51$) in the hemisphere of the higher $\nu_{\rm e}$ emissions, meanwhile neutron-rich matter ($Y_e < 0.49$) are ejected in the opposite hemisphere of the higher ${\bar \nu}_{\rm e}$ emissions. For larger asymmetric cases with $\ge 30\%$, the neutron-rich ejecta is abundantly produced, in which there are too much elements heavier than Zn compared to the solar abundances. This may place an upper limit of the asymmetric neutrino emissions in CCSNe. The characteristic features are also observed in elemental distribution; (1) abundances lighter than Ca are insensitive to the asymmetric neutrino emissions: (2) the production of Zn and Ge is larger in the neutron-rich ejecta even for smaller asymmetric cases with $\le 10\%$. We discuss these observational consequences, which may account for the (anti-)correlations among asymmetries of heavy elements and neutron star kicks in supernova remnants (SNRs). Future SNR observations of the direct measurement for the mass and spatial distributions of $\alpha$ elements, Fe, Zn and Ge will provide us the information on the asymmetric degree of neutrino emissions., Comment: Accepted for publication in MNRAS, 5 pages, 5 figures

Using our new state-of-the-art core-collapse supernova (CCSN) code Fornax, we explore the dependence upon spatial resolution of the outcome and character of three-dimensional (3D) supernova simulations. For the same 19-M$_{\odot}$ progenitor star, energy and radial binning, neutrino microphysics, and nuclear equation of state, changing only the number of angular bins in the $\theta$ and $\phi$ directions, we witness that our lowest resolution 3D simulation does not explode. However, when jumping progressively up in resolution by factors of two in each angular direction on our spherical-polar grid, models then explode, and explode slightly more vigorously with increasing resolution. This suggests that there can be a qualitative dependence of the outcome of 3D CCSN simulations upon spatial resolution. The critical aspect of higher spatial resolution is the adequate capturing of the physics of neutrino-driven turbulence, in particular its Reynolds stress. The greater numerical viscosity of lower-resolution simulations results in greater drag on the turbulent eddies that embody turbulent stress, and, hence, in a diminution of their vigor. Turbulent stress not only pushes the temporarily stalled shock further out, but bootstraps a concomitant increase in the deposited neutrino power. Both effects together lie at the core of the resolution dependence we observe., Comment: Accepted to MNRAS

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 (NS) and black holes (BH). 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 post-process 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., Comment: 25 pages, 25 figures, Accepted for publication in PRD

We perform an extensive study of the influence of nuclear weak interactions on core-collapse supernovae (CCSNe), paying particular attention to consistency between nuclear abundances in the equation of state (EOS) and nuclear weak interactions. We compute properties of uniform matter based on the variational method. For inhomogeneous nuclear matter, we take a full ensemble of nuclei into account with various finite-density and thermal effects and directly use the nuclear abundances to compute nuclear weak interaction rates. To quantify the impact of a consistent treatment of nuclear abundances on CCSN dynamics, we carry out spherically symmetric CCSN simulations with full Boltzmann neutrino transport, systematically changing the treatment of weak interactions, EOSs, and progenitor models. We find that the inconsistent treatment of nuclear abundances between the EOS and weak interaction rates weakens the EOS dependence of both the dynamics and neutrino signals. We also test the validity of two artificial prescriptions for weak interactions of light nuclei and find that both prescriptions affect the dynamics. Furthermore, there are differences in neutrino luminosities by ~10% and in average neutrino energies by 0.25-1 MeV from those of the fiducial model. We also find that the neutronization burst neutrino signal depends on the progenitor more strongly than on the EOS, preventing a detection of this signal from constraining the EOS., Comment: Accepted to ApJS

We study the gravitational wave signal from eight new 3D core-collapse supernova simulations. We show that the signal is dominated by $f$- and $g$-mode oscillations of the protoneutron star and its frequency evolution encodes the contraction rate of the latter, which, in turn, is known to depend on the star's mass, on the equation of state, and on transport properties in warm nuclear matter. A lower-frequency component of the signal, associated with the standing accretion shock instability, is found in only one of our models. Finally, we show that the energy radiated in gravitational waves is proportional to the amount of turbulent energy accreted by the protoneutron star., Comment: 9 pages, 5 figures; version accepted to ApJ Letters

The progenitor stars of core-collapse supernovae (CCSNe) are asymmetrically fluctuating due to turbulent convections in the late stages of their lives. The progenitor asymmetry at the pre-supernova stage has recently caught the attention as a new ingredient to facilitate shock revival in the delayed neutrino-heating mechanism. In this paper, we investigate the importance of the progenitor asymmetries to shock revival with a semi-analytical approach. Free parameters were chosen such that the time evolution of shock radii and mass accretion rates are compatible with the results of detailed numerical simulations of CCSNe in spherical symmetry. We first estimate the amplitude of asymmetries required for the shock revival by the impulsive change of pre-shock flows in the context of neutrino heating mechanism, and then convert the amplitude to the corresponding amplitude in the pre-supernova phase by taking into account the growth of asymmetries during infall. We apply our model to various types of progenitors and find that the requisite amplitude of pre-supernova asymmetry is roughly three times larger than the prediction by current stellar evolution models unless other additional physical ingredients such as multi-dimensional fluid instabilities and turbulent convections in post-shock flows aid shock revival. We thus conclude that progenitor asymmetries can not trigger the shock revival by the impulsive way but rather play a supplementary role in reality., Comment: Accepted to MNRAS

With the Boltzmann-radiation-hydrodynamics code, which we have developed to solve numerically the Boltzmann equations for neutrino transfer, the Newtonian hydrodynamics equations, and the Newtonian self-gravity simultaneously and consistently, we simulate the collapse of a rotating core of the progenitor with a zero-age-main-sequence mass of $11.2\,M_\odot$ and a shelluler rotation of $1\,{\rm rad\,s^{-1}}$ at the center. We pay particular attention in this paper to the neutrino distribution in phase space, which is affected by the rotation. By solving the Boltzmann equations directly, we can assess the rotation-induced distortion of the angular distribution in momentum space, which gives rise to the rotational component of the neutrino flux. We compare the Eddington tensors calculated both from the raw data and from the M1-closure approximation. We demonstrate that the Eddington tensor is determined by complicated interplays of the fluid velocity and the neutrino interactions and that the M1-closure, which assumes that the Eddington factor is determined by the flux factor, fails to fully capture this aspect, especially in the vicinity of the shock. We find that the error in the Eddington factor reaches $\sim 20\%$ in our simulation. This is due not to the resolution but to the different dependence of the Eddington and flux factors on the angular profile of the neutrino distribution function, and hence modification to the closure relation is needed., Comment: 24 pages, 23 figures, 0 explosion, published in ApJ

We propose a new class of method for solving nonlinear systems of equations, which, among other things,has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extention to the Newton-Raphson(NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method., Comment: 17 pages, 7 figures

We developed a three-dimensional radiative transfer code for an ultra-relativistic background flow-field by using the Monte Carlo (MC) method in the context of gamma-ray burst (GRB) emission. For obtaining reliable simulation results in the coupled computation of MC radiation transport with relativistic hydrodynamics which can reproduce GRB emission, we validated radiative transfer computation in the ultra-relativistic regime and assessed the appropriate simulation conditions. The radiative transfer code was validated through two test calculations: (1) computing in different inertial frames and (2) computing in flow-fields with discontinuous and smeared shock fronts. The simulation results of the angular distribution and spectrum were compared among three different inertial frames and in good agreement with each other. If the time duration for updating the flow-field was sufficiently small to resolve a mean free path of a photon into ten steps, the results were thoroughly converged. The spectrum computed in the flow-field with a discontinuous shock front obeyed a power-law in frequency whose index was positive in the range from 1 to 10 MeV. The number of photons in the high-energy side decreased with the smeared shock front because the photons were less scattered immediately behind the shock wave due to the small electron number density. The large optical depth near the shock front was needed for obtaining high-energy photons through bulk Compton scattering. Even one-dimensional structure of the shock wave could affect the results of radiation transport computation., Comment: 19 pages, 26 figures, accepted to Journal of Computational Physics

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 sub-dominant 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 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 Monte Carlo random walk approximation., Comment: Accepted to ApJS. 24 pages, 19 figures. Key simulation results and codes are available at https://stellarcollapse.org/MCvsDO

This paper is a sequel to our previous one (Kato et al.2015), which calculated the luminosities and spectra of electron-type anti-neutrinos ($\bar{\nu}_e$'s) from the progenitors of core-collapse supernovae. Expecting that a capability to detect electron-type neutrinos ($\nu_e$'s) 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 an electron capture supernova (ECSN) and iron-core collapse supernovae (FeCCSNe). We find that the number luminosities reach $\sim10^{57} \mathrm{s^{-1}}$ and $\sim10^{53} \mathrm{s^{-1}}$ at maximum for $\nu_e$ and $\bar{\nu}_e$, 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 $\bar{\nu}_e$'s from the ECSN-progenitor will be undetected at almost all detectors, whereas we will be able to observe $\gtrsim$15900 $\nu_e$'s at DUNE for the inverted mass hierarchy. From the FeCCSN-progenitors, the number of $\bar{\nu}_e$ events will be largest for JUNO, 200-900 $\bar{\nu}_e$'s, depending on the mass hierarchy whereas the number of $\nu_e$ events at DUNE is $\gtrsim$2100 for the inverted mass hierarchy. These results imply that the detection of $\bar{\nu}_e$'s is useful to distinguish FeCCSN- from ECSN-progenitors, while $\nu_e$'s will provide us with detailed information on the collapse phase regardless of the type and mass of progenitor., Comment: 22 pages, 14 figures, 4 tables, accepted to ApJ

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

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 shell effects at high temperatures brings significant change to weak rates by smoothing the nuclear abundance distribution: the electron capture rate decreases by $\sim$20$\%$ in the early phase and increases by $\sim$40$\%$ in the late phase at most, while the cross section for neutrino-nucleus scattering is reduced by $\sim$15$\%$. 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 $\sim$80$\%$ in the early phase and by $\sim$5$\%$ 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., Comment: 28 pages 14 figures, accepted for publication in Phys. Rev. C

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., Comment: Accepted for publication in ApJS

A new computationally efficient method has been introduced to treat self-gravity in mesh based hydrodynamical simulations. It is applied simply by slightly modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method can not only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology., Comment: 7 pages, 6 figures, accepted for publication in PRD

We examine the bright radio synchrotron counterparts of low-luminosity gamma-ray bursts (llGRBs) and relativistic supernovae (SNe) and find that they can be powered by spherical hypernova (HN) explosions. Our results imply that radio-bright HNe are driven by relativistic jets that are choked deep inside the progenitor stars or quasi-spherical magnetized winds from fast-rotating magnetars. We also consider the optical synchrotron counterparts of radio-bright HNe and show that they can be observed as precursors several days before the SN peak with an r-band absolute magnitude of M_r ~ -14 mag. While previous studies suggested that additional trans-relativistic components are required to power the bright radio emission, we find that they overestimated the energy budget of the trans-relativistic component by overlooking some factors related to the minimum energy of non-thermal electrons. If an additional trans-relativistic component exists, then a much brighter optical precursor with M_r ~ -20 mag can be expected. Thus, the scenarios of radio-bright HNe can be distinguished by using optical precursors, which can be detectable from < 100 Mpc by current SN surveys like the Kiso SN Survey, Palomar Transient Factory, and Panoramic Survey Telescope & Rapid Response System., Comment: 7 pages, 3 figures, Published version in ApJ

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_{sun} 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., Comment: 25 pages, 22 figures, submitted to ApJ

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 to characterize 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 2D and 3D rotational models, it is found that m=!0 modes of neutrino-driven convection or SASI are important for shock revival around the critical surface., Comment: First revised version, submitted to ApJ, 14 pages, 13 figures, 2 tables

The observations of jet breaks in the afterglows of short gamma-ray bursts (SGRBs) indicate that the jet has a small opening angle of < 10{\deg}. The collimation mechanism of the jet is a longstanding theoretical problem. We numerically analyze the jet propagation in the material ejected by double neutron star merger, and demonstrate that if the ejecta mass is > 10^{-2} M_{sun}, the jet is well confined by the cocoon and emerges from the ejecta with the required collimation angle. Our results also suggest that there are some populations of choked (failed) SGRBs or low-luminous new types of event. By constructing a model for SGRB 130603B, which is associated with the first kilonova/macronova can- didate, we infer that the equation-of-state of neutron stars would be soft enough to provide sufficient ejecta to collimate the jet, if this event was associated with a double neutron star merger., Comment: 6 pages, 3 figures, accepted for publication in the Astrophysical Journal Letters

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 (SASI) 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., Comment: Accepted for publication in ApJ, 54 pages, 20 figures, 3 table

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 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 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 have different evolutions from those without it in the non-linear phase of SASI. This results is because matter in the gain region has a varying density and temperature and there appear sub-regions 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., Comment: 28 pages, 13 figures, 1 table, accepted for publication in ApJ. Made significant revision in response to the referee's comments

We numerically investigate the jet propagation through a rotating collapsing Wolf-Rayet star with detailed central engine physics constructed based on the neutrino-driven collapsar model. The collapsing star determines the evolution of mass accretion rate, black hole mass and spin, all of which are important ingredients for determining the jet luminosity. We reveal that neutrino-driven jets in rapidly spinning Wolf-Rayet stars are capable of breaking out from the stellar envelope, while those propagating in slower rotating progenitors fail to jet breakout due to insufficient kinetic power. For progenitor models with successful jet breakouts, the kinetic energy accumulated in the cocoon could be as large as ~1051erg and might significantly contribute to the luminosity of the afterglow emission or to the kinetic energy of the accompanying supernova if nickel production takes place. We further analyze the post breakout phase using a simple analytical prescription and conclude that the relativistic jet component could produce events with an isotropic-luminosity Lp(iso) ~1052erg/s and isotropic-energy Ej(iso) ~1054erg. Our findings support the idea of rapidly rotating Wolf-Rayet stars as plausible progenitors of GRBs, while slowly rotational ones could be responsible for low luminosity or failed GRBs., Comment: 7 pages, 5 figures, accepted for publication in ApJ

We perform some experimental simulations in 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 by hand up to the critical value, which is also de- termined by dynamical simulations. A 15M_{sun} 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 this 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 to the explosion energy in what proportions as well as their dependence 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 1D models studied in this paper cannot produce the appropriate explosion energy and nickel mass simultaneously, overproducing nickels, whereas this problem is resolved in 2D models if the shock is relaunched at 300-400ms after bounce., Comment: Accepted for publication in ApJ. A major bug fixed in the 2D simulations. The main conclusion unchanged qualitatively

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, on the other hand, we get rid of the steady-state condition and take into account shock wave motions instead. We have in mind the scenario that not the critical luminosity but the critical fluctuation generated by hydrodynamical instabilities such as SASI and neutrino-driven convection in the post-shock region 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 ~ 0.8 * (M_in/1.4M_sun) * {1- (rsh/10^8cm)}, in which fcrit denotes the critical pressure fluctuation normalized by the unperturbed post-shock value. Min and rsh 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 3D effects on shock revival, which is currently controversial in the supernova community., Comment: 15 pages, 10 figures, accepted for publication in ApJ

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 nonlinearly 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 an access to the most advanced numerical resources such as the "K computer". To tackle this problem, we have embarked on multi-front efforts. In particular we report in this paper our recent progresses in the treatments of multi-dimensional (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 comparisons will be made between 2D and 3D models quantitatively; 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 demonstrative test simulations. We will also address the perspectives of exa-scale computations on the next generation supercomputers., Comment: 41 pages, 21 figures, accepted by Progress of Theoretical and Experimental Physics

We investigate the propagation of accretion-powered jets in various types of massive stars such as Wolf-Rayet stars, light Population III (Pop III) stars, and massive Pop III stars, all of which are the progenitor candidates of Gamma-Ray Bursts (GRBs). We perform two dimensional axisymmetric simulations of relativistic hydrodynamics taking into account both the envelope collapse and the jet propagation (i.e., the negative feedback of the jet on the accretion). Based on our hydrodynamic simulations, we show for the first time that the accretion-powered jet can potentially break out relativistically from the outer layers of Pop III progenitors. In our simulations, the accretion rate is estimated by the mass flux going through the inner boundary, and the jet is injected with a fixed accretion-to-jet conversion efficiency $\eta$. By varying the efficiency $\eta$ and opening angle $\theta_{op}$ for more than 40 models, we find that the jet can make a relativistic breakout from all types of progenitors for GRBs if a simple condition $\eta \gtrsim 10^{-4} (\theta_{op}/8^{\circ})^2$ is satisfied, which is consistent with analytical estimates. Otherwise no explosion or some failed spherical explosions occur., Comment: 50 pages, 20 figures, accepted to ApJ

We investigate 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) accompanying photospheric emissions. We find that if the envelope rotates uniformly almost at the mass shedding limit, its outer part stops contracting eventually when the centrifugal force becomes large enough. Then another shock wave is formed, propagates outwards and breaks out of the envelope into the stellar wind. Which breaks out earlier, the jet or the centrifugal bounce-induced shock, 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 temperature 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 some non-thermal processes are operating to boost photon energies., Comment: Accepted for publication ApJ

We present a new formula to numerically construct configurations in rotational equilibrium, which consist 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., Comment: To appear on APJ, high-resolution figures are available in the published version.

Dissipations, e.g. heat flow and bulk and shear viscosities, cause the transport of energy, momentum and angular momentum, which is the essence of accretion of matters onto celestial objects. Dissipations are usually described by the Fourier and Navier-Stokes laws ("classic laws" of dissipations). However the classic laws result in an infinitely fast propagation of dissipations. In relativistic formulation, the classic laws of dissipations violate the causality, and hence no relativistic theory of accretion flow onto celestial object is formulated. In this short report, we summarize the causal dissipative hydrodynamics, so-called "Extended Irreversible Thermodynamics" (EIT), with a supplemental comment of which the original works of EIT are not aware, and then show two theorems about relativistic dissipative flows around a Schwarzschild black hole. By these theorems, a significant property of EIT in contrast with classic laws of dissipations is clarified, and a dissipative instability of an exact solution of relativistic perfect fluid flow is also obtained., Comment: 4 pages. Theorem 1 was mistaken, and it is replaced by a correct one. Based on a talk in JGRG19 (19th Workshop on General Relativity and Cosmology, Japan)

We show for the first time the direct time variable radio images in the context of shocked accretion flows around a black hole under the general relativistic treatment of both hydrodynamics and radiation transfer. Time variability around a black hole can be induced by the non-axisymmetric standing accretion shock instability (namely Black Hole SASI). Since the spiral arm shock waves generate the density and temperature waves at the post shock region, they cause time variability in the black hole vicinity. Based on our dynamical simulations, we discuss a possibility of detection for the time variable radio images of M87 by the future space telescope VSOP2/ASTRO-G satellite. The most luminous part of the images is predicted to be near 15 Schwarzschild radii for some snapshots. We show that our results are consistent with existing observational data such as timeaveraged radio spectra, VLBA images and variability timescale for M87. We also discuss observations of M87 with millimeter and sub-millimeter interferometers., Comment: 17 pages, 5 figures, Accepted to publication for ApJ

We report two different types of backflow from jets by performing 2D special relativistic hydrodynamical simulations. One is anti-parallel and quasi-straight to the main jet (quasi-straight backflow), and the other is bent path of the backflow (bent backflow). We find that the former appears when the head advance speed is comparable to or higher than the local sound speed at the hotspot while the latter appears when the head advance speed is slower than the sound speed bat the hotspot. Bent backflow collides with the unshocked jet and laterally squeezes the jet. At the same time, a pair of new oblique shocks are formed at the tip of the jet and new bent fast backflows are generated via these oblique shocks. The hysteresis of backflow collisions is thus imprinted in the jet as a node and anti-node structure. This process also promotes broadening of the jet cross sectional area and it also causes a decrease in the head advance velocity. This hydrodynamic process may be tested by observations of compact young jets., Comment: 9 pages, 5 figures, accepted for publication in ApJL

This paper is a sequel to our previous work for accretion onto a Schwarzschild black hole and the so-called standing accretion shock instability (SASI), in this paper we investigate non-axisymmetric perturbations for a Kerr black hole. The linear and non-linear phases for the shock evolution are analyzed in detail by both 2D 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 is also evident. Interestingly, the oscillation periods of the fundamental unstable modes are dependent only on the shock radius irrespective of the injection parameters., Comment: 27 pages, 12 figures, accepted in ApJ