General relativistic hydrodynamics with viscosity: Contraction, catastrophic collapse, and disk formation in hypermassive neutron stars

Abstract

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 allows 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 often 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, especially when viscous heating is substantial. The stabilizing influences of viscous heating, which generates enhanced thermal pressure, and centrifugal support prevent collapse in some cases, at least until the star cools. 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.

Relativistic outflows from remnants of compact object mergers and their viability for short gamma-ray bursts

“…The size and the exact density profile of the halo can strongly depend on, e.g., the physical parameters of the merging progenitors, the details of the merger dynamics, the time delay of the black hole formation, and the neutrino-driven baryonic outflow from a transient, massive, hot post-merging neutron star. A high density halo would have to be expected if, for example, the collapse to a black hole were delayed due to the effects of very rapid (differential) rotation or viscous heating (e.g., Duez et al 2004;Morrison et al 2004), in which case the hot neutron star would radiate neutrinos and a neutrino-driven wind (e.g., Duncan et al 1986) would lead to a dense, expanding baryonic cloud around the merger site. It may also be possible to find situations where the accretion torus is surrounded by a thin, dilute halo, in particular, if the BH forms during the merger or within a few dynamical timescales afterwards (e.g., Shibata & Uryū 2000;Shibata et al 2003;Oechslin et al 2004).…”

Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity

“…Rapidly and differentially rotating neutron stars may be subject to bar and/or one-armed spiral mode instabilities which could affect the dynamics (though star A was shown in [7,12] to be stable against such instabilities, at least on dynamical timescales). Additionally, the development of the MRI in 2D differs from the 3D case [45].…”

“…Following previous papers (e.g, [7,12,28,30]), we choose the initial rotation law u 0 u ϕ = A 2 (Ω c − Ω), where u µ is the four-velocity, Ω c is the angular velocity along the rotational axis, and Ω ≡ u ϕ /u 0 is the angular velocity. In the Newtonian limit, this rotation law becomes…”

“…tively. (In [12], which considered evolution with shear viscosity, star A was referred to as "star I" and star B1 was referred to as "star V"). The rest mass of star A exceeds the supramassive limit by 46%, while the rest masses of stars B1 and B2 are below the supramassive limit.…”

“…Several processes can act to transport angular momentum and drive the HMNS to collapse. Previous calculations in full general relativity have modeled the evolution of HMNS driven by viscous angular momentum transport [12] and by angular momentum loss due to gravitational radiation [10]. In both cases, the core of the HMNS eventually collapses to a black hole.…”