2D Multi-Angle, Multi-Group Neutrino Radiation-Hydrodynamic Simulations of Postbounce Supernova Cores

We perform axisymmetric (2D) multi-angle, multi-group neutrino radiation-hydrodynamic calculations of the postbounce phase of core-collapse supernovae using a genuinely 2D discrete-ordinate (S_n) method. We follow the long-term postbounce evolution of the cores of one nonrotating and one rapidly-rotating 20-solar-mass stellar model for ~400 milliseconds from 160 ms to ~550 ms after bounce. We present a multi-D analysis of the multi-angle neutrino radiation fields and compare in detail with counterpart simulations carried out in the 2D multi-group flux-limited diffusion (MGFLD) approximation to neutrino transport. We find that 2D multi-angle transport is superior in capturing the global and local radiation-field variations associated with rotation-induced and SASI-induced aspherical hydrodynamic configurations. In the rotating model, multi-angle transport predicts much larger asymptotic neutrino flux asymmetries with pole to equator ratios of up to ~2.5, while MGFLD tends to sphericize the radiation fields already in the optically semi-transparent postshock regions. Along the poles, the multi-angle calculation predicts a dramatic enhancement of the neutrino heating by up to a factor of 3, which alters the postbounce evolution and results in greater polar shock radii and an earlier onset of the initially rotationally weakened SASI. In the nonrotating model, differences between multi-angle and MGFLD calculations remain small at early times when the postshock region does not depart significantly from spherical symmetry. At later times, however, the growing SASI leads to large-scale asymmetries and the multi-angle calculation predicts up to 30% higher average integral neutrino energy deposition rates than MGFLD.Comment: 20 pages, 21 figures. Minor revisions. Accepted for publication in ApJ. A version with high-resolution figures may be obtained from http://www.stellarcollapse.org/papers/Ott_et_al2008_multi_angle.pd

Global Anisotropy Versus Small-Scale Fluctuations in Neutrino Flux in Core-Collapse Supernova Explosions

Effects of small-scale fluctuations in the neutrino radiation on core-collapse supernova explosions are examined. Through a parameter study with a fixed radiation field of neutrinos, we find substantial differences between the results of globally anisotropic neutrino radiation and those with fluctuations. As the number of modes of fluctuations increases, the shock positions, entropy distributions, and explosion energies approach those of spherical explosion. We conclude that global anisotropy of the neutrino radiation is the most effective mechanism of increasing the explosion energy when the total neutrino luminosity is given. This supports the previous statement on the explosion mechanism by Shimizu and coworkers.Comment: 14 pages, including 12 figures. To be published in the Astrophysical Journa

Monte Carlo Study of Supernova Neutrino Spectra Formation

The neutrino flux and spectra formation in a supernova core is studied by using a Monte Carlo code. The dominant opacity contribution for nu_mu and nu_tau is elastic scattering on nucleons. In addition we switch on or off a variety of processes which allow for the exchange of energy or the creation and destruction of neutrino pairs, notably nucleon bremsstrahlung, the e^+ e^- pair annihilation process and nu_e-bar nu_e -> nu_{mu,tau} nu_{mu,tau}-bar, recoil and weak magnetism in elastic nucleon scattering, elastic scattering on electrons and positrons and elastic scattering on electron neutrinos and anti-neutrinos. The least important processes are neutrino-neutrino scattering and e^+ e^- annihilation. The formation of the spectra and fluxes of nu_mu is dominated by the nucleonic processes, i.e. bremsstrahlung and elastic scattering with recoil, but also nu_e nu_e-bar annihilation and nu_mu e^\pm scattering contribute significantly. When all processes are included, the spectral shape of the emitted neutrino flux is always ``pinched,'' i.e. the width of the spectrum is smaller than that of a thermal spectrum with the same average energy. In all of our cases we find that the average nu_mu-bar energy exceeds the average nu_e-bar energy by only a small amount, 10% being a typical number. Weak magnetism effects cause the opacity of nu_mu to differ slightly from that of nu_mu-bar, translating into differences of the luminosities and average energies of a few percent. Depending on the density, temperature, and composition profile, the flavor-dependent luminosities L_{nu_e}$, L_{nu_e-bar}, and L_{nu_mu} can mutually differ from each other by up to a factor of two in either direction.Comment: 33 pages, 16 eps-figs, submitted to ApJ. Sections added: weak magnetism, discussion of different analytic fits to the spectra and detailed spectral shap

Testing Approximations of Thermal Effects in Neutron Star Merger Simulations

We perform three-dimensional relativistic hydrodynamical calculations of neutron star mergers to assess the reliability of an approximate treatment of thermal effects in such simulations by combining an ideal-gas component with zero-temperature, micro-physical equations of state. To this end we compare the results of simulations that make this approximation to the outcome of models with a consistent treatment of thermal effects in the equation of state. In particular we focus on the implications for observable consequences of merger events like the gravitational-wave signal. It is found that the characteristic gravitational-wave oscillation frequencies of the post-merger remnant differ by about 50 to 250 Hz (corresponding to frequency shifts of 2 to 8 per cent) depending on the equation of state and the choice of the characteristic index of the ideal-gas component. In addition, the delay time to black hole collapse of the merger remnant as well as the amount of matter remaining outside the black hole after its formation are sensitive to the description of thermal effects.Comment: 10 pages, 6 figures, 9 eps files; revised with minor additions due to referee comments; accepted by Phys.Rev.

Two-dimensional, Time-dependent, Multi-group, Multi-angle Radiation Hydrodynamics Test Simulation in the Core-Collapse Supernova Context

We have developed a time-dependent, multi-energy-group, and multi-angle (S$_n$) Boltzmann transport scheme for radiation hydrodynamics simulations, in one and two spatial dimensions. The implicit transport is coupled to both 1D (spherically-symmetric) and 2D (axially-symmetric) versions of the explicit Newtonian hydrodynamics code VULCAN. The 2D variant, VULCAN/2D, can be operated in general structured or unstructured grids and though the code can address many problems in astrophysics it was constructed specifically to study the core-collapse supernova problem. Furthermore, VULCAN/2D can simulate the radiation/hydrodynamic evolution of differentially rotating bodies. We summarize the equations solved and methods incorporated into the algorithm and present results of a time-dependent 2D test calculation. A more complete description of the algorithm is postponed to another paper. We highlight a 2D test run that follows for 22 milliseconds the immediate post-bounce evolution of a collapsed core. We present the relationship between the anisotropies of the overturning matter field and the distribution of the corresponding flux vectors, as a function of energy group. This is the first 2D multi-group, multi-angle, time-dependent radiation/hydro calculation ever performed in core collapse studies. Though the transport module of the code is not gray and does not use flux limiters (however, there is a flux-limited variant of VULCAN/2D), it still does not include energy redistribution and most velocity-dependent terms.Comment: 19 pages, plus 13 figures in JPEG format. Submitted to the Astrophysical Journa

Neutrino Signal of Electron-Capture Supernovae from Core Collapse to Cooling

An 8.8 solar mass electron-capture supernova (SN) was simulated in spherical symmetry consistently from collapse through explosion to nearly complete deleptonization of the forming neutron star. The evolution time of about 9 s is short because of nucleon-nucleon correlations in the neutrino opacities. After a brief phase of accretion-enhanced luminosities (~200 ms), luminosity equipartition among all species becomes almost perfect and the spectra of electron antineutrinos and muon/tau antineutrinos very similar. We discuss consequences for the neutrino-driven wind as a nucleosynthesis site and for flavor oscillations of SN neutrinos.Comment: 4 pages, 4 eps figures; published as Physical Review Letters, vol. 104, Issue 25, id. 25110

Prompt merger collapse and the maximum mass of neutron stars

We perform hydrodynamical simulations of neutron-star mergers for a large sample of temperature-dependent, nuclear equations of state, and determine the threshold mass above which the merger remnant promptly collapses to form a black hole. We find that, depending on the equation of state, the threshold mass is larger than the maximum mass of a non-rotating star in isolation by between 30 and 70 per cent. Our simulations also show that the ratio between the threshold mass and maximum mass is tightly correlated with the compactness of the non-rotating maximum-mass configuration. We speculate on how this relation can be used to derive constraints on neutron-star properties from future observations.Comment: 6 pages, 3 figures, accepted for publication in Phys. Rev. Let

Revealing the high-density equation of state through binary neutron star mergers

We present a novel method for revealing the equation of state of high-density neutron star matter through gravitational waves emitted during the postmerger phase of a binary neutron star system. The method relies on a small number of detections of the peak frequency in the postmerger phase for binaries of different (relatively low) masses, in the most likely range of expected detections. From such observations, one can construct the derivative of the peak frequency versus the binary mass, in this mass range. Through a detailed study of binary neutron star mergers for a large sample of equations of state, we show that one can extrapolate the above information to the highest possible mass (the threshold mass for black hole formation in a binary neutron star merger). In turn, this allows for an empirical determination of the maximum mass of cold, nonrotating neutron stars to within 0.1 M_sun, while the corresponding radius is determined to within a few percent. Combining this with the determination of the radius of cold, nonrotating neutron stars of 1.6 M_sun (to within a few percent, as was demonstrated in Bauswein et al., PRD, 86, 063001, 2012), allows for a clear distinction of a particular candidate equation of state among a large set of other candidates. Our method is particularly appealing because it reveals simultaneously the moderate and very high-density parts of the equation of state, enabling the distinction of mass-radius relations even if they are similar at typical neutron star masses. Furthermore, our method also allows to deduce the maximum central energy density and maximum central rest-mass density of cold, nonrotating neutron stars with an accuracy of a few per cent.Comment: 14 pages, 12 figures, 2 tables, accepted for publication in Phys. Rev.

Growth of Perturbation in Gravitational Collapse and Accretion

When a self-gravitating spherical gas cloud collapses or accretes onto a central mass, the inner region of the cloud develops a density profile $\rho\propto r^{-3/2}$ and the velocity approaches free-fall. We show that in this region, nonspherical perturbations grow with decreasing radius. In the linear regime, the tangential velocity perturbation increases as $r^{-1}$, while the Lagrangian density perturbation, $\Delta\rho/\rho$, grows as $r^{-1/2}$. Faster growth occurs if the central collapsed object maintains a finite multiple moment, in which case $\Delta\rho/\rho$ increases as $r^{-l}$, where $l$ specifies the angular degree of the perturbation. These scaling relations are different from those obtained for the collapse of a homogeneous cloud. Our numerical calculations indicate that nonspherical perturbations are damped in the subsonic region, and that they grow and approach the asymptotic scalings in the supersonic region. The implications of our results to asymmetric supernova collapse and to black hole accretion are briefly discussed.Comment: 23 pages including 6 ps figures; Minor changes and update; To appear in ApJ, 200