The majority of my research focus during my Ph.D. was on investigating the role of neutrino flavor transformation on the neutrino-driven supernova mechanism. In order to complete this investigation, I had to develop a method to self-consistently couple the effects of neutrino oscillation into the neutrino transport and hydrodynamic evolution of a supernova simulation.
Supernova simulations have traditionally relied upon classical neutrino transport. A neutrino that is created in one flavor remains that flavor for the entirety of its existence. This was believed to be a justified assumption due to the extreme matter densities in the cores of supernovae which would suppress any neutrino flavor transformation. However, new understandings of neutrino interactions in these dense regions challenged this assumption. There were also significant implications to this as it is the neutrinos that drive the supernova explosion. Therefore changes in their flavor composition could lead to significant changes in the explosion dynamics, as well as in the explosive nucleosynthesis that occurs in the expelled outer layers of the star.
The problem with incorporating neutrino flavor transformation into supernova simulations however is the computation required. State-of-the-art supernova simulations are complex and require hundreds of hours on powerful supercomputers in order to complete even a few seconds of evolution. Similarly neutrino oscillation codes, evaluating on a static slice of a supernova simulation can require hours of cpu time to accurately evaluate the neutrino evolution. Including this at every time step of a supernova simulation would therefore quickly eclipse the computational capabilities of any machine it was running on.
In order to achieve my goal, I had to make several simplifications in order to limit the computational demand of my final simulation. One of the first simplifications was to go back to a spherically symmetric model of CCSNe. While it is understood that spherically symmetric models lack important multi-dimensional physics essential for supernova explosions to occur — physics that can only be accurately captured in full 3D — these 1D simulations are still capable of providing valuable insights on supernovae for a fraction of the computational demands of a full 3D simulation. Restrictions were also placed on when and where in the domain of the simulation the neutrino oscillation effects would be computed, further limiting the impact these calculations would have on the run-time of the final simulation.
My final simulation code combined the SQA neutrino oscillation code developed by Dr. Kneller with the 1D Supernova code Agile-BOLTZTRAN. The combined ABS code utilizes a method I developed to self-consistently apply the oscillation calculations to the neutrino transport providing the ability to examine the effects of neutrino oscillation on the neutrino heating and shock evolution for the first time.
This hybrid (quantum-classical) transport scheme is achieved by introducing an oscillation source term into the equations for classical neutrino transport. This simulates the effect of oscillation by driving additional absorption and emission of neutrinos. Neutrino number is conserved by coupling the absorption of one neutrino flavor from this oscillation opacity directly to the emission of the other neutrino flavor (the version of BOLTZTRAN I used only included 2 neutrino flavors). The effective rate of absorption in the source term is determined based on the transition probabilities from the oscillation calculations.
The results obtained from this ABS code was published as a Rapid Communication in Physical Review D. The results we obtained indicate that the inclusion of neutrino flavor change may have a negative impact on neutrino heating, resulting in the supernova explosion becoming more difficult to achieve. We found that while the oscillations did increase the average energy of the electron (anti)neutrinos — which are primarily responsible for driving the explosion — due to the higher average energies of the heavy lepton (anti)neutrinos emitted, this was offset by an overall decrease in the number of electron neutrinos within the gain region.
Charles J. Stapleford 