General relativistic viscous hydrodynamics of differentially rotating neutron stars

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 $\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{ms}$ with the ejecta mass $\ensuremath{\gtrsim}{10}^{\ensuremath{-}2}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, 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 $\ensuremath{\alpha}$ parameter is $\ensuremath{\gtrsim}{10}^{\ensuremath{-}2}$. 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.