Bruenn, Stephen W.

Core-Collapse Supernovae (CCSNe) are some of the most powerful events in the universe liberating an astonishing 3×1053 ergs of the gravitational binding energy released by the collapse of the stellar core to a nascent neutron star (PNS) that is formed in these events. The visible display is capable of outshining the entire galaxy where it inhabits. Most of this energy, ~ 99%, is carried away by neutrinos of all flavors, however.
According to the favored theory of CCSNe, the production and transport of neutrinos from the dense core through the less dense mantle is believed to deposit energy in the mantle and thereby initiate the supernova explosion. Numerically modeling these events realistically to validate the model therefore requires an accurate neutrino transport algorithm coupled to sophisticated neutrino microphysics to compute the emission, transport, and energy deposition of neutrinos.
The CHIMERA code is a radiation-hydrodynamics code that has been developed to numerically model CCSNe in multiple spatial dimensions. The neutrino transport algorithm currently incorporated in CHIMERA is based upon the Multigroup Flux-Limited Diffusion (MGFLD) method. This current method basically uses only the zeroth angular moment of the Boltzmann equation and closes the system with terms dropped from the first angular moment to produce a diffusion-like equation. A flux-limiter is added to interpolate between the diffusive and free-streaming regimes, and to prevent the algorithm from computing acausal, i.e., faster than light transport, in regions where the neutrino mean free paths are large.

Steady state solutions to the Boltzmann transport equation were obtained
for the transport of neutrinos across a finite, plane parallel slab
using discrete ordinate methods. Semi-analytic solutions were obtained
in the case of isoenergetic, isotropic scattering for one energy group
and in the restricted case of isoenergetic and nonisoenergetic (Compton),
isotropic scattering between two energy groups where the isoenergetic
and the Compton scattering rates are the same for the two groups. For
these two cases solutions were obtained for total optical thicknesses
of 0.2, 2, and 20. When the Compton scattering rates of the two energy
groups are allowed to be different, the transport equation becomes nonlinear
due to the exclusion principle. For this case a numerical scheme
was developed which yielded solutions for slabs having optical thicknesses
up to unity.

This thesis considers the neutrino-driven wind that arises from a proto-neutron star following a supernova explosion as a possible site for the synthesis of the heavy elements by the r-process. We first review the conditions necessary to obtain an r-process, the constraints on the r-process yields for each event, and show the neutrino-driven winds from proto-neutron stars are suitable for an r-process. We next discuss some of the modifications of the supernova code that were necessary in order to numerically simulate the neutrino-driven winds and steps necessary to initiate these conditions. Three important parameters of the wind characterizing the nucleosynthesis are the net electron fraction, the entropy per baryon, and the expansion time-scale. We derive approximate analytic expressions for the neutrino luminosities and mean energies, and the final entropy and net electron fraction of the wind, and compare those against a numerical simulation. We finally present the results of a numerical simulation of the first several seconds of the wind phase, and conclude with an assessment of whether or not an r-process will occur at this time.

We examine the effects of general relativity on neutrino transport during the critical shock reheating phase of core collapse supernovae. We derive the equations for general relativistic, static, multi-group, flux-limited diffusion (MGFLD), and use these to modify a Newtonian MGFLD code. The steady-state neutrino distributions calculated by the revised code for several post-collapse stellar cores are compared to those computed with the original Newtonian MGFLD code. The general relativistic transport calculations display the expected reductions in neutrino rms energy and luminosity arising from redshift and curvature effects. Although the effects of general relativity on neutrino transport work against the shock revival, firm conclusions cannot be drawn at this time because of other important general relativistic effects on the structure of the core. Nevertheless, it is clear that modeling with Newtonian transport has little connection to reality.

We use a semianalytical approach to derive criteria for the presence of doubly diffusive instabilities in postcollapsed stellar matter believed to be essential for producing a supernova explosion. Critical stability equations are obtained from both Boltzmann Equation Moment formalism and Single Particle Eigenvalue approach. Computer experiments are performed to numerically evaluate the key equilibration timescales contained in these equations. Contrary to the widely accepted view, we find that the core, if unstable, is unstable to semiconvection, rather than to neutron fingers. We also find for a given density and entropy there is a critical value for the lepton fraction Y1, below which the stellar core is completely stable to doubly diffusive instabilities of either kind. A considerable fraction of the core proves to lie below the critical Y1, immediately following shock propagation. As the core evolves this fraction quickly encompasses the entire core. We conclude that doubly diffusive instabilities of any kind are unlikely to play a role in the supernova explosion mechanism.

A realistic equation of state is essential for accurate modeling of stellar core collapse. In this thesis, we present a derivation of the equation of state for stellar matter up to nuclear density. We begin with the lepton contribution to the equation of state. The thermodynamic equations of state for the leptons are derived from the grand potential. Two approximations for the lepton equations of state which obtain in different regimes are presented. A discussion of the computer programs that were developed to calculate the solutions to these equations is included, and the results are compared with those of similar programs. A formalism is introduced for treating the nuclear component of the equation of state. The energy per baryon of nuclei at zero temperature is derived using a compressible liquid drop model. Finite temperature effects are incorporated by (1) including the thermal excitation energy, and (2) by introducing a second phase (the drip phase) of like particles (neutrons, protons, and $\alpha$-particles) that coexist with the nuclei. Equilibrium conditions for the two phases and the nuclear mass number A are derived. Expressions for the nuclear thermodynamic quantities of interest are presented.

The models of exploding stars--supernovae--do not explode. This dissertation investigates the transfer of energy from the interior to the outer layers in such stars to try to understand what is missing in these models that would solve the supernova problem. Hydrodynamic instabilities and aspects in the microphysics of the neutrino transport in postcollapsed stellar matter are considered. In Chapter II we derive criteria for the presence of doubly diffusive instabilities believed to be essential for producing a supernova explosion. Contrary to the widely accepted view, we find that the core, if unstable, is unstable to semiconvection, rather than to neutron fingers. A critical value for the lepton fraction, Y1, is found for a given density and entropy, below which the stellar core is completely stable to instabilities. A considerable fraction of the stellar core is found to lie below the critical Y1. As the core evolves this fraction quickly encompasses the entire core. Thus doubly diffusive instabilities of any kind are unlikely to play a role in the supernova explosion mechanism. A strong magnetic field may modify the neutrino-nucleon absorption rates which are critical for shock reheating. In Chapter III we derive the cross section of neutrino absorption on neutrons in the presence of a strong magnetic field. We calculate values for the neutrino inverse mean free path and numerically compare them to the values in the non magnetic case. We find that they exhibit an oscillatory behavior, with huge peaks present due to discontinuities in the density of state. We conclude that the presence of a strong magnetic field does not yield a dramatic reduction in the inverse mean free paths which would be necessary to substantially increase the neutrino luminosity and revive the shock. Neutrino-neutrino scattering in the vicinity of the neutrino sphere may modify the neutrino luminosities and therefore affect shock reheating. In the last Chapter we calculate the neutrino-neutrino scattering cross sections, incorporating them into the source term of the Boltzmann equation for subsequent numerical computation. Inclusion of these scattering rates in transport codes will increase the accuracy of neutrino transport calculations.

This work is a simulation of the Accretion-Induced Collapse of a 1.37 solar mass white dwarf into a neutron star and the subsequent generation of a neutrino-driven wind, with an examination as to whether the event is a candidate for r-process nucleosynthesis. The simulation utilizes a new radiation hydrodynamic code, RadHyd, to model the AIC event. We examine the process of Accretion-Induced Collapse utilizing two sets of neutrino-scattering and absorption rates: The first, and simpler of the two has been in use since they were first introduced in 1985. The second includes a more accurate implementation of neutrino-nucleon scattering and nucleon bremsstrahlung. The improved nue - nue-nucleon scattering rate now permits energy to be exchanged between neutrinos and matter by this process, and is therefore important for the numu's and nutau's, as their only channels for exchanging energy in the standard rates was by the relatively weak NES and pair processes. Neutrino-nucleon bremmsstrahlung is also important for numu's and nutau's as this opens another channel (beside pair process) for their production. Both simulations show a neutrino-driven wind being generated after core bounce and shock propagation. We examine the conditions in these winds to ascertain whether the requisite conditions are attained for an r-process. In neither case are these achieved during the time of the simulations (i.e. 2 seconds). However, these simulations need to be carried out at least an order of magnitude longer before firm conclusions can be drawn about the applicability of this site for the r-process.

This work is a simulation of a 15 solar mass star from initial core collapse through the formation of the neutrino-driven wind with an eye towards a possible site for the r-process. We use a new radiation hydrodynamics code known as RadHyd, which is a merger of EVH-1 and MGFLD. The EVH-1 code is a piecewise parabolic method, or PPM, Godunov solver with Newtonian gravitation and MGFLD is a sophisticated multi-group, flux-limited diffusion radiation transport code. Core collapse is initiated from a progenitor model S15s7b of Weaver and Woosley. A maximum radius of 2.0 x 10^11 cm is chosen to retain the shock on the grid for the desired duration of the simulation. The stagnated shock is revived after 300 ms by increasing the internal energy between the shock and the gain radius over a period of 50 ms. Boundary conditions provided by the outward moving shock yield a subsonic wind. The progenitor model is evolved with two different explosion energies (1.5 and 2.5 foes) and two sets of neutrino reaction rates. The first set is the standard set from Bruenn [5], whereas the second contains neutrino-nucleon elastic scattering with nucleon recoil and blocking and nucleon bremsstrahlung. In the analysis, we compare the structure differences caused by the different neutrino rates in the time from bounce to 300 ms after bounce, when the energy addition will take place. Finally, we discuss the further evolution of the model and characterize properties of the neutrino-driven wind for the two sets of rates and explosion energies.