# Three-Dimensional Boltzmann-Hydro Code for core-collapse in massive stars III. A New method for momentum feedback from neutrino to matter

## TL;DR

This paper introduces a novel hybrid neutrino-matter coupling method in multi-dimensional supernova simulations, significantly improving momentum conservation accuracy and enabling direct modeling of proto-neutron star kicks.

## Contribution

A new hybrid approach for neutrino-matter coupling that enhances momentum conservation in core-collapse supernova simulations with full Boltzmann neutrino transport.

## Key findings

- Improved momentum conservation accuracy in simulations.
- First direct modeling of proto-neutron star kicks.
- Effective handling of diffusion limit with discrete ordinate method.

## Abstract

We present a new method for neutrino-matter coupling in multi-dimensional radiation-hydrodynamic simulations of core-collapse supernova (CCSN) with the full Boltzmann neutrino transport. The development is motivated by the fact that the accurate conservation of momentum is required for reliable numerical modelings of CCSN dynamics including a recoil of proto-neutron star (PNS). The new method is built on a hybrid approach, in which we use the energy-momentum tensor of neutrinos to compute the momentum feedback from neutrino to matter in the optically thick region while we employ the collision term in the optically thin region. In this method we utilize a general relativistic description of radiation-hydrodynamics with angular moments, which allows us to evaluate the momentum feedback from neutrino to matter without inconsistency with our Boltzmann solver. We demonstrate that the new method substantially improves the accuracy of linear momentum conservation in our CCSN simulations under reasonable angular resolutions in momentum space, alleviating the difficulty in giving the diffusion limit precisely with the discrete ordinate (Sn) method. It is the first-ever demonstration that the PNS kick can be handled directly and properly in multi-dimensional radiation-hydrodynamic simulations with the full Boltzmann neutrino transport.