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Register a new userConstructing angular distributions of neutrinos in core collapse supernova from zero-th and first moments calibrated by full Boltzmann neutrino transport
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Two-moment neutrino transport methods have been widely used for developing theoretical models of core-collapse supernova (CCSN), since they substantially reduce the computational burden inherent in the multi-dimensional neutrino-radiation hydrodynamical simulations. The approximation, however, comes at a price; the detailed structure of angular distribution of neutrinos is sacrificed, that is the main drawback of this approach. In this paper, we develop a novel method by which to construct angular distributions of neutrinos from the zero-th and first angular moments. In our method, the angular distribution is expressed with two quadratic functions of the neutrino angle in a piecewise fashion. We determine the best parameters in the fitting function by comparing to the neutrino data in a spherically symmetric CCSN model with full Boltzmann neutrino transport. We demonstrate the capability of our method by using our recent 2D CCSN model. We find that the essential features of the angular distributions can be well reconstructed, whereas the angular distributions of incoming neutrinos tend to have large errors that increase with flux factor ($kappa$). This issue originates from the insensitiveness of incoming neutrinos to $kappa$, that is an intrinsic limitation in moment methods. Based on the results of the demonstration, we assess the reliability of ELN-crossing searches with two-moment neutrino transport. This analysis is complementary to our another paper that scrutinizes the limitation of crossing searches with a few moments. We find that the systematic errors of angular distributions for incoming neutrinos lead to misjudgements of the crossing at $kappa gtrsim 0.5$. This casts doubt on the results of ELN-crossing searches based on two-moment methods in some previous studies.
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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 codes capability to treat general relativistic effects, we conduct some tests: we first compute the free streaming of neutrinos in the Schwarzschild and Kerr spacetimes and compare the results with the geodesic curves; in the Schwarzschild case we deploy not only a 1-dimensional grid in space under spherical symmetry but also a 2-dimensional spatial mesh under axisymmetry in order to assess the capability of the code to compute the spatial advection of neutrinos; secondly, we calculate the neutrino transport in a fixed matter background, which is taken from a core-collapse supernova simulation with our general relativistic but spherically symmetric Boltzmann-hydrodynamics code, to obtain a steady neutrino distribution; the results are compared with those given by the latter code.
We present multi-dimensional core-collapse supernova simulations using the Isotropic Diffusion Source Approximation (IDSA) for the neutrino transport and a modified potential for general relativity in two different supernova codes: FLASH and ELEPHANT. Due to the complexity of the core-collapse supernova explosion mechanism, simulations require not only high-performance computers and the exploitation of GPUs, but also sophisticated approximations to capture the essential microphysics. We demonstrate that the IDSA is an elegant and efficient neutrino radiation transfer scheme, which is portable to multiple hydrodynamics codes and fast enough to investigate long-term evolutions in two and three dimensions. Simulations with a 40 solar mass progenitor are presented in both FLASH (1D and 2D) and ELEPHANT (3D) as an extreme test condition. It is found that the black hole formation time is delayed in multiple dimensions and we argue that the strong standing accretion shock instability before black hole formation will lead to strong gravitational waves.
We present a comprehensive study of neutrino shock acceleration in core-collapse supernova (CCSN). The leading players are heavy leptonic neutrinos, $ u_{mu}$ and $ u_{tau}$; the former and latter potentially gain the energy up to $sim 100$ MeV and $sim 200$ MeV, respectively, through the shock acceleration. Demonstrating the neutrino shock acceleration by Monte Carlo neutrino transport, we make a statement that it commonly occurs in the early post bounce phase ($lesssim 50$ ms after bounce) for all massive stellar collapse experiencing nuclear bounce and would reoccur in the late phase ($gtrsim 100$ ms) for failed CCSNe. This opens up a new possibility to detect high energy neutrinos by terrestrial detectors from Galactic CCSNe; hence, we estimate the event counts for Hyper(Super)-Kamiokande, DUNE, and JUNO. We find that the event count with the energy of $gtrsim 80$ MeV is a few orders of magnitude higher than that of the thermal neutrinos regardless of the detectors, and muon production may also happen in these detectors by $ u_{mu}$ with the energy of $gtrsim 100$ MeV. The neutrino signals provide a precious information on deciphering the inner dynamics of CCSN and placing a constraint on the physics of neutrino oscillation; indeed, the detection of the high energy neutrinos through charged current reaction channels will be a smoking gun evidence of neutrino flavor conversion.
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.
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