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 θ-component reaches ~10% of the dominant rr-component and, more importantly, it dictates the evolution of lateral neutrino fluxes, dominating over the θθ-component, in the semi-transparent region. These data will be useful to further test and possibly improve the prescriptions used in the approximate methods.
We report on the core-collapse supernova simulation we conducted for a 11.2 M progenitor model in three-dimensional space up to 20 ms after bounce, using a radiation hydrodynamics code with full Boltzmann neutrino transport. We solve the six-dimensional Boltzmann equations for three neutrino species and the three-dimensional compressible Euler equations with Furusawa and Togashi's nuclear equation of state. We focus on the prompt convection at 10 ms after bounce and investigate how neutrinos are transported in the convective matter. We apply a new analysis based on the eigenvalues and eigenvec…
We investigate r-process nucleosynthesis in three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucl…
We investigated the impacts of magnetorotational instability (MRI) on the dynamics of weakly magnetized, rapidly rotating core-collapse by conducting high resolution MHD simulations in axisymmetry 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 higher to lower latitudes, which causes the expansion of the heating region at low…
We develop a neutrino transfer code for core-collapse simulations, that directly solves the multidimensional Boltzmann equations in full general relativity. We employ the discrete ordinate method, which discretizes the six dimensional phase space. The code is an extension of our special relativistic code coupled to a Newtonian hydrodynamics code, which is currently employed for core-collapse supernova simulations. In order to demonstrate our code's capability to treat general relativistic effects, we conduct some tests: we first compute the free streaming of neutrinos in the Schwarzschild and …
We investigate the protoneutron star (PNS) convection using our newly developed general relativistic Boltzmann neutrino radiation-hydrodynamics code. This is a pilot study for more comprehensive investigations later. As such, we take a snapshot of a PNS at 2.3 seconds after bounce from a 1D PNS cooling calculation and run our simulation for $\sim160\,\mathrm{ms}$ in 2D under axisymmetry. The original PNS cooling calculation neglected convection entirely and the initial condition is linearly unstable to convection. We find in our 2D simulation that convection is instigated there indeed and expa…
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 agreeme…
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 $ν_e$ and $\barν_e$ angular …
We present results of new three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. These simulations are the first of their kind and include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae are fundamentally different from what was anticipated on the basis of previous simulations in axisymmetry (2D). A strong bipol…
We present the gravitational wave signatures for a suite of axisymmetric core collapse supernova models with progenitors masses between 12 and 25 solar masses. These models are distinguished by the fact they explode and contain essential physics (in particular, multi-frequency neutrino transport and general relativity) needed for a more realistic description. Thus, we are able to compute complete waveforms (i.e., through explosion) based on non-parameterized, first-principles models. This is essential if the waveform amplitudes and time scales are to be computed more precisely. Fourier decompo…
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 possi…
We introduce a new discrete-ordinate scheme for solving the general relativistic Boltzmann transport equation in the context of core-collapse supernovae. Our algorithm avoids the need to spell out the complicated advection terms in energy and angle that arise when the transport equation is formulated in spherical polar coordinates, in the comoving frame, or in a general relativistic spacetime. We instead approach the problem by calculating the advection of neutrinos across momentum space using an intuitive particle-like approach that has excellent conservation properties and fully accounts for…
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 (6D) phase space. Adopting representative snapshots of the post-bounce core from other supernova simulations in three dimensions, we solve the temporal evolutions to stationary states of neutrino distribution functions by 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 dimensiona…
Using the Boltzmann-radiation-hydrodynamics code, which solves the Boltzmann equation for neutrino transport, we present the results of the simulations with the nuclear equations of state (EOSs) of Lattimer and Swesty (LS) and Furusawa and Shen (FS). We extend the simulation time of the LS model and conduct thorough investigations, though our previous paper briefly reported some of the results. Only the LS model shows the shock revival. This seems to originate from the nuclear composition: the different nuclear composition results in the different energy loss by photodissociation and hence the…
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…
Using full Boltzmann neutrino transport, we performed two-dimensional (2D) core-collapse supernova simulations in axisymmetry for two progenitor models with 11.2M and 15.0M both rotational and non-rotational. 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 d…
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 …
In this paper we study in detail the dynamics of flavor transformation for neutrinos propagating in the very dense environment of astrophysical compact objects as Type II supernova in post collapse phase and proto-neutron stars. The analysis is based on the formalism by Strack and Burrows, who introduced the generalized Boltzmann equation for Wigner phase space density. In appropriate limits the formalism reduces to the usual evolution equations for the wave functions or for density matrix elements of Liouville equation. We incorporate the most important aspects of neutrino propagation physics…
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-dimensi…
In this paper we study the dynamics of flavor transformation for neutrinos propagating in the very dense environment of astrophysical compact objects as Type II supernova in post collapse phase and proto-neutron stars. The analysis is based on the generalized Boltzmann equation, which incorporates the neutrinoneutrino interaction. We focus the analysis on the possible collective flavor dynamics, which can displays bipolar and synchronized flavor oscillations, and the associated transition from single-angle to multi-angle regime. To solve the kinetic equations we use an expansion in Legendre po…
We construct the chiral radiation transport equation for left-handed neutrinos in the context of radiation hydrodynamics for core-collapse supernovae. Based on the chiral kinetic theory incorporating quantum corrections due to the chirality of fermions, we derive a general relativistic form of the chiral transfer equation with collisions. We show that such quantum corrections explicitly break the spherical symmetry and axisymmetry of the system. In the inertial frame, in particular, we find that the so-called side jump leads to quantum corrections in the collisions between neutrinos and matter…
We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric. The resulting transport equation is intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are lab frame coordinate basis spacetime position components and comoving frame curvilinear momentum space coordinates. With an eye towards astrophysical applications---such as core-collapse supernovae and compact object mergers---in which the fluid includes nuclei and/or nuclear matte…
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 …
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…
We present results from simulations of core-collapse supernovae in FLASH using a newly-implemented multidimensional neutrino transport scheme and a newly-implemented general relativistic (GR) treatment of gravity. We use a two-moment method with an analytic closure (so-called M1 transport) for the neutrino transport. This transport is multienergy, multispecies, velocity-dependent and truly multidimensional, i.e., we do not assume the commonly used "ray-by-ray" approximation. Our GR gravity is implemented in our Newtonian hydrodynamics simulations via an effective relativistic potential (GREP) …
There is mounting evidence that neutrinos undergo fast flavor conversion (FFC) in core-collapse supernova (CCSN). In this letter, we investigate the roles of stellar rotation on the occurrence of FFC by carrying out axisymmetric CCSN simulations with full Boltzmann neutrino transport. Our result suggests that electron neutrino lepton number (ELN) angular crossings, which are the necessary and sufficient condition to trigger FFC, preferably occur in the equatorial region for rotating CCSNe. By scrutinizing the neutrino--matter interaction and neutrino radiation field, we find some pieces of evi…
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…
Bifurcated Impact of Neutrino Fast Flavor Conversion on Core-collapse Supernovae Informed by Multi-angle Neutrino Radiation Hydrodynamics
Waseda University（早稻田大学）；National Astronomical Observatory of Japan（日本国立天文台）；Kanto Gakuin University（关东学院大学）；RIKEN（理化学研究所）；National Institute of Technology, Ibaraki College（茨城工业高等专门学校）；Aomori University（青森大学）；High Energy Accelerator Research Organization（高能加速器研究机构）；National Institute of Technology, Numazu College（沼津工业高等专门学校）
We present three-dimensional simulations of core-collapse supernovae using the FLASH code that follow the progression of the explosion to the stellar surface, starting from neutrino-radiation hydrodynamic simulations of the neutrino-driven phase performed with the CHIMERA code. We consider a 9.6-$M_{\odot}$ zero-metallicity progenitor starting from both 2D and 3D CHIMERA models, and a 10-$M_{\odot}$ solar-metallicity progenitor starting from a 2D CHIMERA model, all simulated until shock breakout in 3D while tracking 160 nuclear species. The relative velocity difference between the supernova sh…
We present the new code ALCAR developed to model multidimensional, multi energy-group neutrino transport in the context of supernovae and neutron-star mergers. The algorithm solves the evolution equations of the 0th- and 1st-order angular moments of the specific intensity, supplemented by an algebraic relation for the 2nd-moment tensor to close the system. The scheme takes into account frame-dependent effects of order O(v/c) as well as the most important types of neutrino interactions. The transport scheme is significantly more efficient than a multidimensional solver of the Boltzmann equation…
We present an open-source update to the spherically-symmetric, general-relativistic hydrodynamics, core-collapse supernova (CCSN) code GR1D (O'Connor & Ott, 2010, CQG, 27, 114103). The source code is available at http://www.GR1Dcode.org. We extend its capabilities to include a general relativistic treatment of neutrino transport based on the moment formalisms of Shibata et al., 2011, PTP, 125, 1255 and Cardall et al., 2013, PRD, 87 103004. We pay special attention to implementing and testing numerical methods and approximations that lessen the computational demand of the transport scheme by re…
We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the wide…
We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively), separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrin…
We explore the dependence on spatial dimension of the viability of the neutrino heating mechanism of core-collapse supernova explosions. We find that the tendency to explode is a monotonically increasing function of dimension, with 3D requiring $\sim$40$-$50\% lower driving neutrino luminosity than 1D and $\sim$15$-$25\% lower driving neutrino luminosity than 2D. Moreover, we find that the delay to explosion for a given neutrino luminosity is always shorter in 3D than 2D, sometimes by many hundreds of milliseconds. The magnitude of this dimensional effect is much larger than the purported magn…
General relativistic radiation hydrodynamics simulations are necessary to accurately model a number of astrophysical systems involving black holes and neutron stars. Photon transport plays a crucial role in radiatively dominated accretion disks, while neutrino transport is critical to core-collapse supernovae and to the modeling of electromagnetic transients and nucleosynthesis in neutron star mergers. However, evolving the full Boltzmann equations of radiative transport is extremely expensive. Here, we describe the implementation in the general relativistic SpEC code of a cheaper radiation hy…
The dense neutrino medium in a core-collapse supernova or a neutron-star merger event can experience fast flavor conversions on time/distance scales that are much smaller than those of vacuum oscillations. It is believed that fast neutrino flavor transformation occurs in the region where the angular distributions of $ν_e$ and $\barν_e$ cross each other. We present the first study of this crossing phenomenon and the fast neutrino flavor conversions in multidimensional (multi-D) supernova models. We examine the neutrino distributions obtained by solving the Boltzmann transport equation for sever…
We have been working within the fundamental paradigm that core collapse supernovae (CCSNe) may be neutrino driven, since the first suggestion of this by Colgate and White nearly five decades ago. Computational models have become increasingly sophisticated, first in one spatial dimension assuming spherical symmetry, then in two spatial dimensions assuming axisymmetry, and now in three spatial dimensions with no imposed symmetries. The increase in the number of spatial dimensions has been accompanied by an increase in the physics included in the models, and an increase in the sophistication with…
Machine Learning Detection of Non-Axisymmetric Fast Flavor Instabilities in Compact Objects
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)（马克斯·普朗克物理研究所（维尔纳·海森堡研究所））；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理部）；Department of Physics & Astronomy, University of New Hampshire（新罕布什尔大学物理与天文学系）；GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）
We explore heavy element nucleosynthesis in the explosion of massive stars which are triggered by a quark-hadron phase transition during the early post bounce phase of core-collapse supernovae. The present study is based on general relativistic radiation hydrodynamics simulations with three-flavor Boltzmann neutrino transport in spherical symmetry, which utilize a quark-hadron hybrid equation of state based on the MIT bag model for strange quark matter. The quark-hadron phase transition inside the stellar core forms a shock wave propagating towards the surface of the proto-neutron star. The sh…
A dense neutrino gas, such as the one anticipated in the supernova environment, can experience fast neutrino flavor conversions on scales much shorter than those expected in vacuum probably provided that the angular distributions of $ν_e$ and $\barν_e$ cross each other. We perform a detailed investigation of the neutrino angular distributions obtained by solving the Boltzmann equations for fixed matter profiles of some representative snapshots during the post-bounce phase of core-collapse supernovae in multidimensional calculations of an $11.2\mathrm{M}_{\odot}$ and a $27\mathrm{M}_{\odot}$ pr…
We explore explosions of massive stars, which are triggered via the quark-hadron phase transition during the early post bounce phase of core-collapse supernovae. We construct a quark equation of state, based on the bag model for strange quark matter. The transition between the hadronic and the quark phases is constructed applying Gibbs conditions. The resulting quark-hadron hybrid equations of state are used in core-collapse supernova simulations, based on general relativistic radiation hydrodynamics and three flavor Boltzmann neutrino transport in spherical symmetry. The formation of a mixed …
