Neutrino Transport Research Articles

Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations

We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.

ASCERTAINING THE CORE COLLAPSE SUPERNOVA MECHANISM: The State of the Art and the Road Ahead

▪ Abstract More than four decades have elapsed since modeling of the core collapse supernova mechanism began in earnest. To date, the mechanism remains elusive, at least in detail, although significant progress has been made in understanding these multiscale, multiphysics events. One-, two-, and three-dimensional simulations of or relevant to core collapse supernovae have shown that (a) neutrino transport, (b) fluid instabilities, (c) rotation, and (d) magnetic fields, together with proper treatments of (e) the sub- and super- nuclear density stellar core equation of state, (f) the neutrino interactions, and (g) gravity are all important. The importance of these ingredients applies to both the explosion mechanism and to phenomena directly associated with the mechanism, such as neutron star kicks, supernova neutrino and gravitational wave emission, and supernova spectropolarimetry. Not surprisingly, current two- and three-dimensional models have yet to include (a)–(d) with sufficient realism. One-dimensional spherically symmetric models have achieved a significant level of sophistication but, by definition, cannot incorporate (b)–(d), except phenomenologically. Fully general relativistic spherically symmetric simulations with Boltzmann neutrino transport do not yield explosions, demonstrating that some combination of (b), (c), and (d) is required to achieve this. Systematic layering of the dimensionality and the physics will be needed to achieve a complete understanding of the supernova mechanism and phenomenology. The past modeling efforts alluded to above have illuminated that core collapse supernovae may be neutrino driven, magnetohydrodynamically (MHD) driven, or both, but uncertainties in the current models prevent us from being able to answer even this most basic question. And it may be that more than one possibility is realized in nature. Nonetheless, if a supernova is neutrino driven, magnetic fields will likely have an impact on the dynamics of the explosion. Similarly, if a supernova is MHD driven, the neutrino transport will dictate the dynamics of stellar core collapse, bounce, and the postbounce evolution, which in turn will create the environment in which an MHD-driven explosion would occur. Thus, although reduction will allow us to sort out the roles of each of the major physics components listed above, we will not obtain a quantitative, and perhaps even qualitative, understanding of core collapse supernovae until all components and their coupling are included in the models with sufficient realism.

A Simple Parameterization of the Consequences of Deleptonization for Simulations of Stellar Core Collapse

A simple and computationally efficient parameterization of the deleptonization, the entropy changes, and the neutrino stress is presented for numerical simulations of stellar core collapse. The parameterization of the neutrino physics is based on a bounce profile of the electron fraction as it results from state-of-the-art collapse simulations with multigroup Boltzmann neutrino transport in spherical symmetry. Two additional parameters include an average neutrino escape energy and a neutrino trapping density. The parameterized simulations reproduce the consequences of the delicate neutrino thermalization-diffusion process during the collapse phase and provide a by far more realistic alternative to the adiabatic approximation, which has often been used in the investigation of the emission of gravitational waves, of multidimensional general relativistic effects, of the evolution of magnetic fields, or even of the nucleosynthesis in simulations of core collapse and bounce. For supernova codes that are specifically designed for the postbounce phase, the parameterization builds a convenient bridge between the point where the applicability of a stellar evolution code ends and the point where the postbounce evolution begins.

Core‐Collapse Supernovae with Nonuniform Magnetic Fields

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 β 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.

Conservative special relativistic radiative transfer for multidimensional astrophysical simulations: Motivation and elaboration

Many astrophysical phenomena exhibit relativistic radiative flows. While velocities in excess of $v \sim 0.1c$ can occur in these systems, it has been common practice to approximate radiative transfer to $\cO(v/c)$. In the case of neutrino transport in core-collapse supernovae, this approximation gives rise to an inconsistency between the lepton number transfer and lab frame energy transfer, which have different $\cO(v/c)$ limits. A solution used in spherically symmetric $\cO(v/c)$ simulations has been to retain, for energy accounting purposes, the $\cO(v^2/c^2)$ terms in the lab frame energy transfer equation that arise from the $\cO(v/c)$ neutrino number transport equation. Avoiding the proliferation of such ``extra'' $\cO(v^2/c^2)$ terms in the absence of spherical symmetry motivates a special relativistic formalism, which we exhibit in coordinates sufficiently general to encompass Cartesian, spherical, and cylindrical coordinate systems.

Flavor changing supersymmetry interactions in a supernova

We consider for the first time flavor changing neutral currents (FCNC’s) in the infall stage of stellar collapse. We take as an example R-Parity violating interactions of the minimal standard supersymmetric model involving neutrinos and quarks. However, our considerations extend to other kinds of flavor changing neutrino reactions as well. We examine non-forward neutrino scattering processes on heavy nuclei and free nucleons in the supernova core. This investigation has led to four principal original discoveries/products: (1) first calculation of neutrino flavor changing cross sections for spin 1/2 (e.g., free nucleon) and spin 0 nuclear targets; (2) discovery of nuclear mass number squared ( A 2) coherent amplification of neutrino-quark FCNC’s; (3) analysis of FCNC-induced alteration of electron capture and weak/nuclear equilibrium in the collapsing core; and (4) generalization of the calculated cross sections (mentioned in 1) for the case of hot heavy nuclei to be used in collapse/supernova and neutrino transport simulations. The scattering processes that we consider allow electron neutrinos to change flavor during core collapse, thereby opening holes in the ν e sea, which allows electron capture to proceed and results in a lower core electron fraction Y e. A lower Y e implies a lower homologous core mass, a lower shock energy, and a greater nuclear photo-disintegration burden for the shock. In addition, unlike the standard supernova model, the core now could have net muon and/or tau lepton numbers. These effects could be significant even for supersymmetric couplings below current experimental bounds.

Approaching the dynamics of hot nucleons in supernovae

All recent numerical simulations agree that stars in the main sequence mass range of 9 — 40 M ⊙ do not produce a prompt hydrodynamic ejection of the outer layers after core collapse and bounce. Rather they suggest that stellar core collapse and supernova explosion are dynamically distinct astrophysical events, separated by an unspectacular accretion phase of at least ∼ 40 ms duration. As long as the neutrinospheres remain convectively stable, the explosion dynamics is determined by the neutrons, protons, electrons and neutrinos in the layer of impact-heated matter piling up on the protoneutron star. The crucial role of neutrino transport in this regime has been emphasized in many previous investigations. Here, we search for efficient means to address the role of magnetic fields and fluid instabilities in stellar core collapse and the postbounce phase.

Generalized Boltzmann formalism for oscillating neutrinos

In the standard approaches to neutrino transport in the simulation of core-collapse supernovae, one will often start from the classical Boltzmann equation for the neutrino's spatial, temporal, and spectral evolution. For each neutrino species, and its anti-particle, the classical density in phase space, or the associated specific intensity, will be calculated as a function of time. The neutrino radiation is coupled to matter by source and sink terms on the "right-hand-side" of the transport equation and together with the equations of hydrodynamics this set of coupled partial differential equations for classical densities describes, in principle, the evolution of core collapse and explosion. However, with the possibility of neutrino oscillations between species, a purely quantum-physical effect, how to generalize this set of Boltzmann equations for classical quantities to reflect oscillation physics has not been clear. To date, the formalisms developed have retained the character of quantum operator physics involving complex quantities and have not been suitable for easy incorporation into standard supernova codes. In this paper, we derive generalized Boltzmann equations for quasi-classical, real-valued phase-space densities that retain all the standard oscillation phenomenology, including resonant flavor conversion (the MSW effect), neutrino self-interactions, and the interplay between decohering matter coupling and flavor oscillations. With this formalism, any code(s) that can now handle the solution of the classical Boltzmann or transport equation can easily be generalized to include neutrino oscillations in a quantum-physically consistent fashion.

An ADI-Like Preconditioner for Boltzmann Transport

Numerical modeling of radiation transport and fluid dynamics are central to many fields of science. This paper studies the application of preconditioned iterative methods to time-dependent coupled hydrodynamics and radiation (Boltzmann) transport. In particular, we focus on the solution of Jacobian matrices in full Newton iterations in the modeling of neutrino (radiation) transport in core collapse supernovae. This is a demanding radiation hydrodynamics application, requiring accurate time-dependent neutrino transport coupled to hydrodynamics driven by this transport. Given a fully implicit finite differencing of the transport equations, the Jacobian matrices have a special block tridiagonal structure. The off-diagonal blocks are exactly diagonal and correspond to the spatial transport of neutrinos and the coupling of adjacent spatial zones owing to this transport. The dense diagonal blocks, on the other hand, arise from the coupling between the neutrino direction cosines and energy, as a result of neutrino emission, absorption, and scattering, in the multiple species multiple energy group discrete ordinates formulation for solving the Boltzmann transport equations. We consider an effective alternating direct implicit (ADI)-like preconditioner where we alternately sweep along the one-dimensional spatial direction and separately handle the coupling among multidirection multigroup variables within each spatial discretization cell. Numerical examples are given to illustrate the fast convergence and efficient parallel implementation. The results suggest that even simple fixed point iteration can achieve a similar convergence rate as {\tt GMRES} and {\tt BICGSTAB}.

North‐South Neutrino Heating Asymmetry in Strongly Magnetized and Rotating Stellar Cores

We perform a series of two-dimensional 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, the rotations law, the degree of differential rotation, and the profiles of the magnetic fields to construct the initial conditions. By so doing, we estimate how the rotation-induced anisotropic neutrino heating are affected by the strong magnetic fields through parity-violating effects and first investigate how the north-south asymmetry of the neutrino heating in a strongly magnetized supernova core could be. 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 the neutrino leakage scheme. With these computations, we find that the parity-violating corrections reduce $ \lesssim 0.5 %$ of the neutrino heating rate than that without the magnetic fields in the vicinity of the north pole of a star, on the other hand, enhance about $ \lesssim 0.5 %$ 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 time.

Toward 2-D and 3-D simulations of core-collapse supernovae with magnetic fields

We describe a code development and integration effort aimed at producing a numerical tool suitable for exploring the effects of stellar rotation and magnetic fields in a neutrino-driven core-collapse supernova environment. A one-dimensional, multi-energy group, flux-limited neutrino diffusion module (MGFLD) has been integrated with ZEUS-MP, a multidimensional, parallel gas hydrodynamics and magnetohydrodynamics code. With the neutrino diffusion module, ZEUS-MP can simulate the core-collapse, bounce, and explosion of a stellar progenitor in two and three space dimensions in which multidimensional hydrodynamics are coupled to 1-D neutrino transport in a ray-by-ray approximation. This paper describes the physics capabilities of the code and the technique for implementing the serial MGFLD module for parallel execution in a multi-dimensional simulation. Because the development and debugging of the integrated code is not yet complete, we provide a current status report of the effort and identify outstanding issues currently under investigation.

Transport equations in moving material Part I: Neutrons and photons

Transport equations are usually formulated against a static material background in transport applications for neutral (neutrons, photons, mesons) and charged (electrons, protons, ions) particles. When the background is moving, the equations need be modified and corrected. We discuss these modifications and corrections, in both relativistic and nonrelativistic regimes, and contrast equations across applications. Neutron, photon, electron, neutrino, and meson transport are treated in a two part series. This review collects, collates, and expands published and unpublished developments and equations for moving material transport in different particle arenas. Hopefully, such provides a useful reference and source for readers across disciplines, linking basic underlying dynamics and representations. Part I centers on neutrons and photons, and Part II deals with electrons and neutrinos, almost an historical split. While transport equations for these particles share much in common, there are fundamental differences between particles that interact pointwise versus continuously, particles of zero rest mass versus nonzero rest mass, particles with relativistic energy versus nonrelativistic energy, and particles with short range versus long range. Our focuses are the fundamental equations and underlying dynamics of transport in moving backgrounds.The impacts in applications, important and legion, are detailed in the literature as cited. Accordingly, and invoking topic closure, applications are not recounted. Also, numerical techniques, developed with the emergence of supercomputing, are not treated herein. Both applications and numerical techniques are probably subjects of a separate communication Some modern transport codes dealing with moving material issues, however, are cited for reader reference. Many codes have been in existence for 25+ years, undergoing continuous updating, modification, improvement, and physical extension. For Part I, the main points of discussion and development are seen in the following Table of Contents, divided into neutron and photon moving material transport. An attempt at coverage of moving material transport with brevity is sought, and hopefully references provide details minimized, or not recounted, herein.

Toward five-dimensional core-collapse supernova simulations

The computational difficulty of six-dimensional neutrino radiation hydrodynamics has spawned a variety of approximations, provoking a long history of uncertainty in the corecollapse supernova explosion mechanism. Under the auspices of the Terascale Supernova Initiative, we are honoring the physical complexity of supernovae by meeting the computational challenge head-on, undertaking the development of a new adaptive mesh refinement code for self-gravitating, six-dimensional neutrino radiation magnetohydrodynamics. This code—called GenASiS, for General Astrophysical Simulation System—is designed for modularity and extensibility of the physics. Presently in use or under development are capabilities for Newtonian self-gravity, Newtonian and special relativistic magnetohydrodynamics (with ‘realistic’ equation of state), and special relativistic energy- and angle-dependent neutrino transport—including full treatment of the energy and angle dependence of scattering and pair interactions.

Core-Collapse Supernovae at the Threshold

SummaryRecent progress in modeling core-collapse supernovae is summarized and set in perspective. Two-dimensional simulations with state-of-the-art treatment of neutrino transport still fail to produce powerful explosions, but evidence is presented that they are very close to a success.

Core-collapse supernovae and gravitational waves

Core-collapse supernovae are dramatic events with a rich phenomenology, including gravitational radiation. Simulations of these events in multiple spatial dimensions with energy- and angle-dependent neutrino transport are still in their infancy. Core collapse and bounce in a supernova in our galaxy may well be visible by first-generation LIGO, but detailed understanding waits on improvements in modeling both stellar progenitors and the supernova process.

Neutrino scattering off pair-breaking and collective excitations in superfluid neutron matter and in color-flavor-locked quark matter

We calculate the correlation functions needed to describe the linear response of superfluid matter, and go on to calculate the differential cross section for neutral-current neutrino scattering in superfluid neutron matter and in color-flavor locked quark matter (CFL). We report the first calculation of scattering rates that includes neutrino interactions with both pair-breaking excitations and low-lying collective excitations (Goldstone modes). Our results apply both above and below the critical temperature, allowing use in simulations of neutrino transport in supernovae and neutron stars.

Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods

Accurate neutrino transport has been built into spherically symmetric simulations of stellar core collapse and postbounce evolution. The results of such simulations agree that spherically symmetric models with standard microphysical input fail to explode by the delayed, neutrino-driven mechanism. Independent groups implemented fundamentally different numerical methods to tackle the Boltzmann neutrino transport equation. Here we present a direct and detailed comparison of such neutrino radiation-hydrodynamical simulations for two codes, Agile-Boltztran of the Oak Ridge-Basel group and Vertex of the Garching group. The former solves the Boltzmann equation directly by an implicit, general relativistic discrete angle method on the adaptive grid of a conservative implicit hydrodynamics code with second-order TVD advection. In contrast, the latter couples a variable Eddington factor technique with an explicit, moving-grid, conservative high-order Riemann solver with important relativistic effects treated by an effective gravitational potential. The presented study is meant to test both neutrino radiation-hydrodynamics implementations and to provide a data basis for comparisons and verifications of supernova codes to be developed in the future. Results are discussed for simulations of the core collapse and post-bounce evolution of a 13 solar mass star with Newtonian gravity and a 15 solar mass star with relativistic gravity.

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

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

Neutrino Effects before, during, and after the Freezeout of ther‐Process

We study the effects of neutrino interactions before, during, and after the operation of the r-process in the context of a relativistic hydrodynamic neutrino-energized wind model that includes a Boltzmann solver for the dominant neutrino transport. We also employ newly available charged- and neutral-current interaction rates. Studies are made in a model with a short dynamical timescale that gives a fair reproduction of the solar system r-process abundance curve and hence could be a fair approximation to the true supernova environment. We confirm that charged- and neutral-current interactions can have specific unique effects on the final abundances. Early on, charged-current interactions determine the electron fraction, while later on, neutrino-induced neutron emission can continue to provide a slight neutron exposure even after the freezeout of the r-process. We propose two new potentially observable effects that derive from the use of a more realistic hydrodynamic model and/or new neutrino interaction rates. One is an enhanced odd-even effect in the final abundances, and the other is an enhancement of light A = 68-76 nuclei in the final abundances. These effects are consistent with some recent observations of r-process abundances in metal-poor halo stars and might help to identify the neutrino fluxes present near the freezeout of the r-process.

Gravitational radiation from rotational core collapse: Effects of magnetic fields and realistic equations of state

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.