Supernovae

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.

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.

The evolution of the carbon-oxygen cores of intermediate mass stars
immediately prior to and following carbon ignition is described. The
thermal consequences of the convectively driven URCA process are considered
in detail and applied to these cores following carbon ignition
to determine their thermal. We found, as did Paczynski and Ergma, and
Couch and Arnett, that a global thermal balance and stability is possible for some models. Unlike the previous investigators, however, we found that some models were possibly unstable due to local heating at
the edge of the convective region. The implications for intermediate mass stars burning carbon are potentially serious, as these stars naturally evolve into the region occupied by these unstable models.

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 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.

Core-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of the prime sources of gravitational waves for interferometric detectors. Gravitational waves can give us access to the electromagnetically hidden compact inner core of supernovae. They will provide valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. Detection of GW signals and analysis of the observations will require realistic signal predi ctions from the non-parameterized relativistic numerical simulations of CCSN. This dissertation presents the gravitational wave signature of core-collapse v supernovae. Previous studies have considered either parametric models or nonexploding models of CCSN. This work presents complete waveforms, through the explosion phase, based on first-principles models for the first time. We performed 2D simulations of CCSN using the CHIMERA code for 12, 15, and 25M non-rotating progenitors. CHIMERA incorporates most of the criteria for realistic core-collapse modeling, such as multi-frequency neutrino transport coupled with relativistic hydrodynamics, eective GR potential, nuclear reaction network, and an industry-standard equation of state.

A Shock wave as represented by the Riemann problem and a Point-blast explosion are two key phenomena involved in a supernova explosion. Any hydrocode used to simulate supernovae should be subjected to tests consisting of the Riemann problem and the Point-blast explosion. L. I. Sedov's solution of Point-blast explosion and Gary A. Sod's solution of a Riemann problem have been re-derived here from one dimensional fluid dynamics equations . Both these problems have been solved by using the idea of Self-similarity and Dimensional analysis. The main focus of my research was to subject the CHIMERA supernova code to these two hydrodynamic tests. Results of CHIMERA code for both the blast wave and Riemann problem have then been tested by comparing with the results of the analytic solution.