A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics

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, while it is more accurate and consistent than the flux-limited diffusion method. The finite-volume discretization of the essentially hyperbolic system of moment equations employs methods well-known from hydrodynamics. For the time integration of the potentially stiff moment equations we employ a scheme in which only the local source terms are treated implicitly, while the advection terms are kept explicit, thereby allowing for an efficient computational parallelization of the algorithm. We investigate various problem setups in one and two dimensions to verify the implementation and to test the quality of the algebraic closure scheme. In our most detailed test, we compare a fully dynamic, one-dimensional core-collapse simulation with two published calculations performed with well-known Boltzmann-type neutrino-hydrodynamics codes and we find very satisfactory agreement.Comment: 30 pages, 12 figures. Revised version: several additional comments and explanations, results remain unchanged. Accepted for publication in MNRA

Three-Dimensional Core-Collapse Supernova Simulations with Multi-Dimensional Neutrino Transport Compared to the Ray-by-Ray-plus Approximation

Self-consistent, time-dependent supernova (SN) simulations in three spatial dimensions (3D) are conducted with the Aenus-Alcar code, comparing, for the first time, calculations with fully multi-dimensional (FMD) neutrino transport and the ray-by-ray-plus (RbR+) approximation, both based on a two-moment solver with algebraic M1 closure. We find good agreement between 3D results with FMD and RbR+ transport for both tested grid resolutions in the cases of a 20 solar-mass progenitor, which does not explode with the employed simplified set of neutrino opacities, and of an exploding 9 solar-mass model. This is in stark contrast to corresponding axisymmetric (2D) simulations, which confirm previous claims that the RbR+ approximation can foster explosions in 2D in particular in models with powerful axial sloshing of the stalled shock due to the standing accretion shock instability (SASI). However, while local and instantaneous variations of neutrino fluxes and heating rates can still be considerably higher with RbR+ transport in 3D, the time-averaged quantities are very similar to FMD results because of the absence of a fixed, artificial symmetry axis that channels the flow. Therefore, except for stochastic fluctuations, the neutrino signals and the post-bounce evolution of 3D simulations with FMD and RbR+ transport are also very similar, in particular for our calculations with the better grid resolution. Higher spatial resolution has clearly a more important impact than the differences by the two transport treatments. Our results back up the use of the RbR+ approximation for neutrino transport in 3D SN modeling.Comment: 25 pages, 16 figures; referee comments included, new appendix added; accepted by Ap

Effects of LESA in Three-Dimensional Supernova Simulations with Multi-Dimensional and Ray-by-Ray-plus Neutrino Transport

A set of eight self-consistent, time-dependent supernova (SN) simulations in three spatial dimensions (3D) for 9 solar-mass and 20 solar-mass progenitors is evaluated for the presence of dipolar asymmetries of the electron lepton-number emission as discovered by Tamborra et al. and termed lepton-number emission self-sustained asymmetry (LESA). The simulations were performed with the Aenus-Alcar neutrino/hydrodynamics code, which treats the energy- and velocity-dependent transport of neutrinos of all flavors by a two-moment scheme with algebraic M1 closure. For each of the progenitors, results with fully multi-dimensional (FMD) neutrino transport and with ray-by-ray-plus (RbR+) approximation are considered for two different grid resolutions. While the 9 solar-mass models develop explosions, the 20 solar-mass progenitor does not explode with the employed version of simplified neutrino opacities. In all 3D models we observe the growth of substantial dipole amplitudes of the lepton-number (electron neutrino minus antineutrino) flux with stable or slowly time-evolving direction and overall properties fully consistent with the LESA phenomenon. Models with RbR+ transport develop LESA dipoles somewhat faster and with temporarily higher amplitudes, but the FMD calculations exhibit cleaner hemispheric asymmetries with a far more dominant dipole. In contrast, the RbR+ results display much wider multipole spectra of the neutrino-emission anisotropies with significant power also in the quadrupole and higher-order modes. Our results disprove speculations that LESA is a numerical artifact of RbR+ transport. We also discuss LESA as consequence of a dipolar convection flow inside of the nascent neutron star and establish, tentatively, a connection to Chandrasekhar's linear theory of thermal instability in spherical shells.Comment: 20 pages, 9 figures; revised version accepted by ApJ; new Figs. 6,7, and new panels in Fig.8 added; Sects. 4,5,6 considerably extended in reply to referee question

Neutron-star merger ejecta as obstacles to neutrino-powered jets of gamma-ray bursts

We present the first special relativistic, axisymmetric hydrodynamic simulations of black hole-torus systems (approximating general relativistic gravity) as remnants of binary-neutron star (NS-NS) and neutron star-black hole (NS-BH) mergers, in which the viscously driven evolution of the accretion torus is followed with self-consistent energy-dependent neutrino transport and the interaction with the cloud of dynamical ejecta expelled during the NS-NS merging is taken into account. The modeled torus masses, BH masses and spins, and the ejecta masses, velocities, and spatial distributions are adopted from relativistic merger simulations. We find that energy deposition by neutrino annihilation can accelerate outflows with initially high Lorentz factors along polar low-density funnels, but only in mergers with extremely low baryon pollution in the polar regions. NS-BH mergers, where polar mass ejection during the merging phase is absent, provide sufficiently baryon-poor environments to enable neutrino-powered, ultrarelativistic jets with terminal Lorentz factors above 100 and considerable dynamical collimation, favoring short gamma-ray bursts (sGRBs), although their typical energies and durations might be too small to explain the majority of events. In the case of NS-NS mergers, however, neutrino emission of the accreting and viscously spreading torus is too short and too weak to yield enough energy for the outflows to break out from the surrounding ejecta shell as highly relativistic jets. We conclude that neutrino annihilation alone cannot power sGRBs from NS-NS mergers.Comment: 7 pages, 4 figures, minor revisions compared to original version, accepted for publication in ApJ Letter

Nucleosynthesis in dynamical and torus ejecta of compact binary mergers

We present a comprehensive study of r-process element nucleosynthesis in the ejecta of compact binary mergers (CBMs) and their relic black-hole (BH)-torus systems. The evolution of the BH-accretion tori is simulated for seconds with a Newtonian hydrodynamics code including viscosity effects, pseudo-Newtonian gravity for rotating BHs, and an energy-dependent two-moment closure scheme for the transport of electron neutrinos and antineutrinos. The investigated cases are guided by relativistic double neutron star (NS-NS) and NS-BH merger models, producing ~3-6 Msun BHs with rotation parameters of A~0.8 and tori of 0.03-0.3 Msun. Our nucleosynthesis analysis includes the dynamical (prompt) ejecta expelled during the CBM phase and the neutrino and viscously driven outflows of the relic BH-torus systems. While typically ~20-25% of the initial accretion-torus mass are lost by viscously driven outflows, neutrino-powered winds contribute at most another ~1%, but neutrino heating enhances the viscous ejecta significantly. Since BH-torus ejecta possess a wide distribution of electron fractions (0.1-0.6) and entropies, they produce heavy elements from A~80 up to the actinides, with relative contributions of A>130 nuclei being subdominant and sensitively dependent on BH and torus masses and the exact treatment of shear viscosity. The combined ejecta of CBM and BH-torus phases can reproduce the solar abundances amazingly well for A>90. Varying contributions of the torus ejecta might account for observed variations of lighter elements with 40<Z<56 relative to heavier ones, and a considerable reduction of the prompt ejecta compared to the torus ejecta, e.g. in highly asymmetric NS-BH mergers, might explain the composition of heavy-element deficient stars.Comment: 7 pages, 4 figures, only changed title compared to previous version, accepted for publication in Proceedings of Science (Nuclei in the Cosmos XIII, Debrecen

Comprehensive nucleosynthesis analysis for ejecta of compact binary mergers

We present the first comprehensive study of r-process element nucleosynthesis in the ejecta of compact binary mergers (CBMs) and their relic black-hole (BH)-torus systems. The evolution of the BH-accretion tori is simulated for seconds with a Newtonian hydrodynamics code including viscosity effects, pseudo-Newtonian gravity for rotating BHs, and an energy-dependent two-moment closure scheme for the transport of electron neutrinos and antineutrinos. The investigated cases are guided by relativistic double neutron star (NS-NS) and NS-BH merger models, producing ~3-6 Msun BHs with rotation parameters of A~0.8 and tori of 0.03-0.3 Msun. Our nucleosynthesis analysis includes the dynamical (prompt) ejecta expelled during the CBM phase and the neutrino and viscously driven outflows of the relic BH-torus systems. While typically ~20-25% of the initial accretion-torus mass are lost by viscously driven outflows, neutrino-powered winds contribute at most another ~1%, but neutrino heating enhances the viscous ejecta significantly. Since BH-torus ejecta possess a wide distribution of electron fractions (0.1-0.6) and entropies, they produce heavy elements from A~80 up to the actinides, with relative contributions of A>130 nuclei being subdominant and sensitively dependent on BH and torus masses and the exact treatment of shear viscosity. The combined ejecta of CBM and BH-torus phases can reproduce the solar abundances amazingly well for A>90. Varying contributions of the torus ejecta might account for observed variations of lighter elements with 40<Z<56 relative to heavier ones, and a considerable reduction of the prompt ejecta compared to the torus ejecta, e.g. in highly asymmetric NS-BH mergers, might explain the composition of heavy-element deficient stars.Comment: 30 pages, 22 figures; revised version, accepted by MNRAS; appendix added with test results for neutrino transpor

Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) $H_{q}$ relevant to the fluctuation spectrum and poles of the order-$q$ power spectrum is proposed. The ``partition function'' is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.Comment: CYCLER Paper 93mar00