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Free keywords:
General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE
Abstract:
We present three-dimensional simulations of the dynamical bar-mode
instability in magnetized and differentially rotating stars in full general
relativity. Our focus is on the effects that magnetic fields have on the
dynamics and the onset of the instability. In particular, we perform
ideal-magnetohydrodynamics simulations of neutron stars that are known to be
either stable or unstable against the purely hydrodynamical instability, but to
which a poloidal magnetic field in the range of $10^{14}$--$10^{16}$ G is
superimposed initially. As expected, the differential rotation is responsible
for the shearing of the poloidal field and the consequent linear growth in time
of the toroidal magnetic field. The latter rapidly exceeds in strength the
original poloidal one, leading to a magnetic-field amplification in the the
stars. Weak initial magnetic fields, i.e. $ \lesssim 10^{15}$ G, have
negligible effects on the development of the dynamical bar-mode instability,
simply braking the stellar configuration via magnetic-field shearing, and over
a timescale for which we derived a simple algebraic expression. On the other
hand, strong magnetic fields, i.e. $\gtrsim 10^{16}$ G, can suppress the
instability completely, with the precise threshold being dependent also on the
amount of rotation. As a result, it is unlikely that very highly magnetized
neutron stars can be considered as sources of gravitational waves via the
dynamical bar-mode instability.
