Magnetic Braking in Differentially Rotating, Relativistic Stars

Abstract

We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars. The remnant of a binary neutron star merger or supernova core collapse may produce such a "hypermassive" neutron star. Although a hypermassive neutron star may be stable on a dynamical timescale, magnetic braking and viscous damping of differential rotation will ultimately alter the equilibrium structure, possibly leading to delayed catastrophic collapse. Here we consider the slow-rotation, weak-magnetic field limit in which E_rot << E_mag << W, where E_rot is the rotational kinetic energy, E_mag is the magnetic energy, and W is the gravitational binding energy of the star. We assume the system to be axisymmetric and solve the MHD equations in both Newtonian gravitation and general relativity. Toroidal magnetic fields are generated whenever the angular velocity varies along the initial poloidal field lines. We find that the toroidal fields and angular velocities oscillate independently along each poloidal field line, which enables us to transform the original 2+1 equations into 1+1 form and solve them along each field line independently. The incoherent oscillations on different field lines stir up turbulent-like motion in tens of Alfven timescales ("phase mixing"). In the presence of viscosity, the stars eventually are driven to uniform rotation, with the energy contained in the initial differential rotation going into heat. Our evolution calculations serve as qualitative guides and benchmarks for future, more realistic MHD simulations in full 3+1 general relativity.

26 pages, 27 graphs, 1 table, accepted for publication by Phys. Rev. D

References in corpus (2)

• A very energetic supernova associated with the gamma-ray burst of 29 March 2003
• The Carnegie Observatories Astrophysics Series

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• Effect of Differential Rotation on the Maximum Mass of Neutron Stars: Realistic Nuclear Equations of State
• Relativistic Hydrodynamic Evolutions with Black Hole Excision
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• Mergers of Irrotational Neutron Star Binaries in Conformally Flat Gravity
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• General Relativistic Simulations of Slowly and Differentially Rotating Magnetized Neutron Stars
• Nonradial oscillations of slowly and differentially rotating compact stars
• Collapse of Uniformly Rotating Stars to Black Holes and the Formation of Disks
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• Gravitational Wave Astronomy
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• Four-Hair Relations for Differentially Rotating Neutron Stars in the Weak-Field Limit