A Detailed Comparison of Multi-Dimensional Boltzmann Neutrino Transport Methods in Core-Collapse Supernovae

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/MCvsD

Neutrino Radiation Transport and Other Topics in High Energy Density Astrophysics

Neutron star mergers and the collapse of massive stars result in some of the universe’s most violet explosions. However, the detailed mechanisms behind all of these astrophysical explosions remain elusive. Their strongly nonlinear and complicated nature makes them difficult and expensive to simulate, and the properties of matter in these extreme conditions are poorly constrained. I use a variety of computational tools to understand the detailed mechanisms behind both types of events. I describe my relativistic time-independent multidimensional Monte Carlo neutrino radiation transport code Sedonu that provides an accurate account of the neutrino radiation fields and the interaction with neutrinos and background fluid. Though Sedonu calculations are time-independent, I demonstrate their utility in dynamical general relativistic variable Eddington tensor radiation hydrodynamics simulations. I apply Sedonu to simulations of accretion disks following neutron star mergers to demonstrate that more realistic disk cooling and neutrino-driven mass ejection rates are larger than is predicted using approximate transport methods. I also reinforce that neutrino pair annihilation from these disk configurations is unlikely to be able to energize a gamma-ray burst jet. I subject Sedonu to the first thorough comparison of Boltzmann neutrino radiation transport methods in multiple spatial dimensions in the context of core-collapse supernovae. The comparisons with the other highly accurate discrete ordinates-based transport scheme show remarkably similar results, verifying the accuracy of both methods and underscoring the importance of numerical fidelity. I perform the first broad parameter study on how different descriptions of dense nuclear matter and star rotation rates influence the dynamics of, and hence gravitational waves from, the bounce and early post-bounce phase of rapidly rotating core collapse supernovae. Using the results of 1824 two-dimensional general relativistic core-collapse simulations, I demonstrate that the equation of state is unlikely to be constrained by LIGO observations. I show that the effect of the equation of state on the gravitational wave frequency can be described by a single universal relation. Finally, I use results of three-dimensional general relativistic magnetohydrodynamics simulations of rapidly rotating core collapse to demonstrate that the polar magnetic structures that form are destroyed by a magnetohydrodynamic kink instability.</p

The Fast Flavor Instability in Hypermassive Neutron Star Disk Outflows

We examine the effect of neutrino flavor transformation by the fast flavor instability (FFI) on long-term mass ejection from accretion disks formed after neutron star mergers. Neutrino emission and absorption in the disk set the composition of the disk ejecta, which subsequently undergoes $r$-process nucleosynthesis upon expansion and cooling. Here we perform 28 time-dependent, axisymmetric, viscous-hydrodynamic simulations of accretion disks around hypermassive neutron stars (HMNSs) of variable lifetime, using a 3-species neutrino leakage scheme for emission and an annular-lightbulb scheme for absorption. We include neutrino flavor transformation due the FFI in a parametric way, by modifying the absorbed neutrino fluxes and temperatures, allowing for flavor mixing at various levels of flavor equilibration, and also in a way that aims to respect the lepton-number preserving symmetry of the neutrino self-interaction Hamiltonian. We find that for a promptly-formed black hole (BH), the FFI lowers the average electron fraction of the disk outflow due to a decrease in neutrino absorption, driven primarily by a drop in electron neutrino/antineutrino flux upon flavor mixing. For a long-lived HMNS, the disk emits more heavy lepton neutrinos and reabsorbs more electron neutrinos than for a BH, with a smaller drop in flux compensated by a higher neutrino temperature upon flavor mixing. The resulting outflow has a broader electron fraction distribution, a more proton-rich peak, and undergoes stronger radiative driving. Disks with intermediate HMNS lifetimes show results that fall in between these two limits. In most cases, the impact of the FFI on the outflow is moderate, with changes in mass ejection, average velocity, and average electron fraction of order $\sim 10\%$, and changes in the lanthanide/actinide mass fraction of up to a factor $\sim 2$.Comment: submitted to PR

Equation of State Effects on Gravitational Waves from Rotating Core Collapse

Gravitational waves (GWs) generated by axisymmetric rotating collapse, bounce, and early postbounce phases of a galactic core-collapse supernova are detectable by current-generation gravitational wave observatories. Since these GWs are emitted from the quadrupole-deformed nuclear-density core, they may encode information on the uncertain nuclear equation of state (EOS). We examine the effects of the nuclear EOS on GWs from rotating core collapse and carry out 1824 axisymmetric general-relativistic hydrodynamic simulations that cover a parameter space of 98 different rotation profiles and 18 different EOS. We show that the bounce GW signal is largely independent of the EOS and sensitive primarily to the ratio of rotational to gravitational energy, T/|W|, and at high rotation rates, to the degree of differential rotation. The GW frequency (f_(peak)∼600–1000  Hz) of postbounce core oscillations shows stronger EOS dependence that can be parametrized by the core’s EOS-dependent dynamical frequency √Gρc. We find that the ratio of the peak frequency to the dynamical frequency f_(peak)/√Gρc follows a universal trend that is obeyed by all EOS and rotation profiles and that indicates that the nature of the core oscillations changes when the rotation rate exceeds the dynamical frequency. We find that differences in the treatments of low-density nonuniform nuclear matter, of the transition from nonuniform to uniform nuclear matter, and in the description of nuclear matter up to around twice saturation density can mildly affect the GW signal. More exotic, higher-density physics is not probed by GWs from rotating core collapse. We furthermore test the sensitivity of the GW signal to variations in the treatment of nuclear electron capture during collapse. We find that approximations and uncertainties in electron capture rates can lead to variations in the GW signal that are of comparable magnitude to those due to different nuclear EOS. This emphasizes the need for reliable experimental and/or theoretical nuclear electron capture rates and for self-consistent multidimensional neutrino radiation-hydrodynamic simulations of rotating core collapse

Chaos in Neutrino Fast Flavor Instability

Neutrinos play a crucial role in explosive stellar events. In core collapse supernovae (CCSN), neutrinos produced thermally in the proto-neutron star drive the CCSN dynamics, reviving the shock wave that causes the explosion. In neutron star mergers (NSM), neutrinos can significantly affect the ratio of neutrons to protons in the ejected mass via charged-current reactions, having a big impact on the production of heavy elements. Simulations have revealed that in those systems neutrinos undergo substantial fast flavor instabilities that make it challenging to fully understand the neutrino non-linear many-body dynamics, mainly because of the large number of neutrinos involved and the small spatial scale of the neutrino flavor oscillation in comparison with the CCSN and NSM spatial scale. In simplified neutrino models (bipolar oscillations), the presence of chaos in the flavor evolution has been proposed. Since chaotic systems are very sensitive to initial conditions, i.e., trajectories of slightly different initial conditions diverge exponentially, our ability to predict the neutrino flavor behavior in CCSN and NSM could be limited. To clarify this problem, we approximate the behavior of neutrinos inside NSM by simulating neutrino fast flavor instabilities in a domain a few centimeters wide. Our goal is to analyze the dynamics of nearby flavor states in the presence of neutrino fast flavor instabilities. We solve the neutrino quantum kinetic equation numerically including the neutrino self-interaction term in the flavor Hamiltonian, using the particle-in-cell code EMU under the mean field approximation. We conclude that solutions with nearby initial states diverge exponentially in the non-linear regime of the neutrino flavor evolution, demonstrating the presence of chaos. This produces a huge uncertainty in both the spatial flavor neutrino distributions and the density matrix of the individual computational particles. However, the domain-averaged neutrino density matrix component is not highly affected by chaos (1% maximum uncertainty) and could be used as a key variable in global neutrino simulations of CCSN and NSM

Comparing treatments of weak reactions with nuclei in simulations of core-collapse supernovae

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 ApJ