# General relativistic viscous hydrodynamics of differentially rotating neutron stars

## TL;DR

This study uses a simplified relativistic viscous hydrodynamics model to simulate differentially rotating neutron stars, revealing potential for long-term stable simulations and viscous-driven outflows that could explain neutron-rich ejecta post-merger.

## Contribution

It introduces a stable, long-term simulation approach for relativistic viscous hydrodynamics in neutron stars using a simplified Israel-Stewart formalism, highlighting viscous effects on ejecta.

## Key findings

- Viscous angular momentum transport is effective.
- Outflows driven by high shear viscosity can eject >0.01 solar masses.
- Neutron-rich ejecta could originate from viscous effects in merger remnants.

## Abstract

Employing a simplified version of the Israel-Stewart formalism for general-relativistic shear-viscous hydrodynamics, we perform axisymmetric general-relativistic simulations for a rotating neutron star surrounded by a massive torus, which can be formed from differentially rotating stars. We show that with our choice of a shear-viscous hydrodynamics formalism, the simulations can be stably performed for a long time scale. We also demonstrate that with a possibly high shear-viscous coefficient, not only viscous angular momentum transport works but also an outflow could be driven from a hot envelope around the neutron star for a time scale $\gtrsim 100\,$ms with the ejecta mass $\gtrsim 10^{-2}M_\odot$ which is comparable to the typical mass for dynamical ejecta of binary neutron star mergers. This suggests that massive neutron stars surrounded by a massive torus, which are typical outcomes formed after the merger of binary neutron stars, could be the dominant source for providing neutron-rich ejecta, if the effective shear viscosity is sufficiently high, i.e., if the viscous $\alpha$ parameter is $\gtrsim 10^{-2}$. The present numerical result indicates the importance of a future high-resolution magnetohydrodynamics simulation that is the unique approach to clarify the viscous effect in the merger remnants of binary neutron stars by the first-principle manner.