Long-term Monte Carlo-based neutrino-radiation hydrodynamics simulations for a black hole-torus system

We present our new general relativistic Monte Carlo (MC)-based neutrino radiation hydrodynamics code designed to solve axisymmetric systems with several improvements. The main improvements are as follows: (i) the development of an extended version of the implicit MC method for multi-species radiation fields; (ii) modeling of neutrino pair process rates based on a new numerically efficient and asymptotically correct fitting function for the kernel function; (iii) the implementation of new numerical limiters on the radiation-matter interaction to ensure a stable and physically correct evolution of the system. We apply our code to a black hole (BH)-torus system with a BH mass of $3\,M_\odot$, BH dimmensionless spin of 0.8, and a torus mass of $0.1\,M_\odot$, which mimics a post-merger remnant of a binary neutron star merger in the case that the massive neutron star collapses to a BH within a short time scale ($\sim10\,{\rm ms}$). We follow the evolution of the BH-torus system up to more than $1\,{\rm s}$ with our MC-based radiation viscous-hydrodynamics code that dynamically takes into account non-thermal pair annihilation. We find that the system evolution and the various key quantities, such as neutrino luminosity, ejecta mass, torus $Y_e$, and pair annihilation luminosity, are broadly in agreement with the results of the previous studies. We also find that the $\nu_e{\bar \nu}_e$ pair annihilation can launch a relativistic outflow for a time scale of $\sim 0.1\,{\rm s}$, and it can be energetic enough to explain some of short-hard gamma-ray bursts and the precursors. Finally, we calculate the indicators of the fast flavor instability directly from the obtained neutrino distribution functions, which indicate that the instability can occur particularly near the equatorial region of the torus.