General Relativistic Hydrodynamics with Viscosity: Contraction, Catastrophic Collapse, and Disk Formation in Hypermassive Neutron Stars

         Matthew D. Duez
         Yuk Tung Liu
         Stuart L. Shapiro
         Branson C. Stephens

University of Illinois at Urbana-Champaign


Viscosity and magnetic fields drive differentially rotating stars toward uniform rotation, and this process has important consequences in many astrophysical contexts. For example, merging binary neutron stars can form a hypermassive remnant, i.e. a differentially rotating star with a mass greater than would be possible for a uniformly rotating star. The removal of the centrifugal support provided by differential rotation can lead to delayed collapse of the remnant to a black hole, accompanied by a delayed burst of gravitational radiation. Both magnetic fields and viscosity alter the structure of differentially rotating stars on secular timescales, and tracking this evolution presents a strenuous challenge to numerical hydrodynamic codes. Here, we present the first evolutions of rapidly rotating stars with shear viscosity in full general relativity. We self-consistently include viscosity in our relativistic hydrodynamic code by solving the fully relativistic Navier-Stokes equations. We perform these calculations both in axisymmetry and in full 3+1 dimensions. In axisymmetry, the resulting reduction in computational costs allow us to follow secular evolution with high resolution over dozens of rotation periods (thousands of M). We find that viscosity operating in a hypermassive star generically leads to the formation of a compact, uniformly rotating core surrounded by a low-density disk. These uniformly rotating cores are typically unstable to gravitational collapse. We follow the collapse in such cases and determine the mass and the spin of the final black hole and ambient disk. However, viscous braking of differential rotation in hypermassive neutron stars does not always lead to catastrophic collapse by the time our integrations terminate, especially when viscous heating is substantial. The stabilizing influences of viscous heating, which generates enhanced thermal pressure, and centrifugal support prevent, or postpone, collapse in some cases, at least until more matter from the disk accretes onto the core. In all cases studied, the rest mass of the resulting disk is found to be 10-20% of the original star, whether surrounding a uniformly rotating core or a rotating black hole. This study represents an important step toward understanding secular effects in relativistic stars and foreshadows more detailed, future simulations, including those involving magnetic fields.

Phys.Rev. D69 (2004) 104030, astro-ph/0402502

Hierarchy of Timescales

Initial Stellar Model

Star I (J/M2=1.0, M0/M0,sup=1.47)

Star II (J/M2=0.85, M0/M0,sup=1.21)

Star III (J/M2=1.0, M0/M0,sup=1.21)

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