We present a new subgrid model for neutrino quantum kinetics, which is
primarily designed to incorporate effects of collective neutrino oscillations
into neutrino-radiation-hydrodynamic simulations for core-collapse supernovae
and mergers of compact objects. We approximate the neutrino oscillation term in
quantum kinetic equation by Bhatnagar-Gross-Krook (BGK) relaxation-time
prescription, and the transport equation is directly applicable for classical
neutrino transport schemes. The BGK model is motivated by recent theoretical
indications that non-linear phases of collective neutrino oscillations settle
into quasi-steady structures. We explicitly provide basic equations of the BGK
subgrid model for both multi-angle and moment-based neutrino transport to
facilitate the implementation of the subgrid model in the existing neutrino
transport schemes. We also show the capability of our BGK subgrid model by
comparing to fully quantum kinetic simulations for fast neutrino-flavor
conversion. We find that the overall properties can be well reproduced in the
subgrid model; the error of angular-averaged survival probability of neutrinos
is within $sim 20 %$. By identifying the source of error, we also discuss
perspectives to improve the accuracy of the subgrid model.
Introduction
In this article, we present a new subgrid model for neutrino quantum kinetics. The model is designed to incorporate the effects of collective neutrino oscillations into neutrino-radiation-hydrodynamic simulations for core-collapse supernovae and mergers of compact objects.
Neutrino Oscillation Term
We approximate the neutrino oscillation term in the quantum kinetic equation using the Bhatnagar-Gross-Krook (BGK) relaxation-time prescription. This approximation allows the transport equation to be directly applicable for classical neutrino transport schemes. The BGK model is motivated by recent theoretical indications that non-linear phases of collective neutrino oscillations settle into quasi-steady structures.
Basic Equations of the BGK Subgrid Model
We explicitly provide the basic equations of the BGK subgrid model for both multi-angle and moment-based neutrino transport. This will facilitate the implementation of the subgrid model in existing neutrino transport schemes.
Validation of the BGK Subgrid Model
We demonstrate the capability of our BGK subgrid model by comparing it to fully quantum kinetic simulations for fast neutrino-flavor conversion. We find that the overall properties can be well reproduced in the subgrid model, with an error of the angular-averaged survival probability of neutrinos within approximately 20%.
Potential Challenges
- Improving accuracy: Although our subgrid model already shows promising results, there is room for improvement to reduce the error in the survival probability of neutrinos. Future research should focus on identifying the sources of error and finding ways to enhance the accuracy of the model.
- Complex implementation: Implementing the subgrid model in existing neutrino transport schemes may be challenging due to the complexity of the equations and the need for computational resources. This requires collaboration between scientists and developers to ensure a seamless integration.
Opportunities on the Horizon
- Advancements in simulation technology: As computational power continues to improve, simulations incorporating the BGK subgrid model can be performed with higher resolution and accuracy. This opens up new possibilities for studying core-collapse supernovae and compact object mergers.
- Further understanding of neutrino oscillations: Continued research into the behavior of collective neutrino oscillations will provide insights into the dynamics that can be incorporated into the subgrid model. This will lead to more accurate simulations and a deeper understanding of astrophysical phenomena.
Conclusion
The introduction of our BGK subgrid model for neutrino quantum kinetics provides a valuable tool for enhancing the realism of neutrino-radiation-hydrodynamic simulations. While there are still challenges to overcome and opportunities to explore, this model represents a significant step forward in our ability to study core-collapse supernovae and compact object mergers. By improving the accuracy of the subgrid model and leveraging advancements in simulation technology and our understanding of neutrino oscillations, we can unlock new insights into these fascinating astrophysical phenomena.