Differential Rotation in Neutron Stars: Magnetic Braking and Viscous Damping

By Stuart L. Shapiro. 2000

136 citations recorded by the source corpus.

Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars, according to general relativity. The remnant of a binary neutron star merger may give rise to such a "hypermassive" object. While such a star may be dynamically stable against gravitational collapse and bar formation, the radial stabilization due to differential rotation is likely to be temporary. Magnetic braking and viscosity combine to drive the star to uniform rotation, even if the seed magnetic field and the viscosity are small. This process inevitably leads to delayed collapse, which will be accompanied by a delayed gravitational wave burst and, possibly, a gamma-ray burst. We provide a simple, Newtonian MHD calculation of the braking of differential rotation by magnetic fields and viscosity. The star is idealized as a differentially rotating, infinite cylinder consisting of a homogeneous, incompressible conducting gas. We solve analytically the simplest case in which the gas has no viscosity and the star resides in an exterior vacuum. We treat numerically cases in which the gas has internal viscosity and the star is embedded in an exterior, low-density, conducting medium. Our evolution calculations are presented to stimulate more realistic MHD simulations in full 3 + 1 general relativity. They serve to identify some of the key physical and numerical parameters, scaling behavior, and competing timescales that characterize this important process.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/c0b2f7699b3231742574898aa6c4b334363d1db4

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In Astronomy and Astrophysics

Citations in the corpus

Properties of the Binary Neutron Star Merger GW170817 (2018, background): “A hypermassive NS, whose mass exceeds the maximum mass of a uniformly rotating star but is supported by differential rotation and possibly thermal gradients [145], will survive for ≲1s, after which time the NS collapses into a black hole [147,148].”
Approximate Universal Relations for Neutron Stars and Quark Stars (2016, background): “One could then also apply such universal relations for differentially rotating stars to hypermassive neutron stars formed after the merger of neutron star binaries [148, 179, 180].”
The birth of black holes: neutron star collapse times, gamma-ray bursts and fast radio bursts (2014, methodology): “Differential rotation within the equilibrium configuration will be suppressed on the Alfvén time-scale (Baumgarte, Shapiro & Shibata 2000; Shapiro 2000), which is approximated as tAlfven ≈ 0.15 ( Bp 1015 G ) ( Mp M )1/2 ( R 10 km )−1/2 s. (1) For the protomagnetar model of SGRBs under…”
THE NEUTRON STAR MASS DISTRIBUTION (2010, background): “While differential rotation provides excess radial stability against collapse, even for modest magnetic fields, magnetic braking and viscous forces will inevitably bring differentially rotating objects into uniform rotation (Shapiro 2000).”