Abstract
We show that magnetic fields stronger than about 1015 G are able to suppress the development of the hydrodynamical bar-mode instability in relativistic stars. The suppression is due to a change in the rest-mass density and angular velocity profiles due to the formation and to the linear growth of a toroidal component that rapidly overcomes the original poloidal one, leading to an amplification of the total magnetic energy. The study is carried out performing three-dimensional ideal-magnetohydrodynamics simulations in full general relativity, superimposing to the initial (matter) equilibrium configurations a purely poloidal magnetic field in the range 1014 −1016 G. When the seed field is a few parts in 1015 G or above, all the evolved models show the formation of a low-density envelope surrounding the star. For much weaker fields, no effect on the matter evolution is observed, while magnetic fields which are just below the suppression threshold are observed to slow down the growth-rate of the instability.
Highlights
Rotating neutron stars (NSs) are subject to the so-called m = 2 dynamical barmode instability for non-radial axial modes with azimuthal dependence eimφ (m = 1, 2, ...), when the instability parameter β ≡ T /|W | exceeds a critical value
We investigate if the presence of magnetic fields can affect the onset and development of this kind of instability in full general relativity, as well as the role played by the magnetic braking to possibly suppress the instability
For each unstable model (U3, U11 and U13) we have performed a number of simulations adding an initial purely poloidal magnetic field around the typical value of the field strengths expected for magnetars and, in the range from 1.0 × 1014 G to 1.0 × 1016 G
Summary
We choose to evolve different equilibrium relativistic stellar models that have already been studied in the non-magnetized case by Baiotti et al [3], so that their behavior against the bar-mode instability is already known and fully understood when no magnetic fields are present. To better find out the changes to the bar-mode dynamics induced by the presence of a magnetic field, we focused our attention on a sequence of models having a fixed constant amount of differential rotation A = 1 and a constant rest mass M0 1.5 M , which were already studied in the non-magnetized case in [3].
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