Dynamical bar-mode instability in magnetized relativistic stars

Abstract

We present accurate 3D simulations in full general relativity of magnetized and differentially rotating relativistic star models, focusing on the effects that magnetic fields have on the dynamics of bar-stable models and on the onset of the dynamical bar-mode instability in bar-unstable models. In particular, we evolve initial matter equilibrium configurations that are already known to be stable or unstable against this kind of instability in the unmagnetized case, super-imposing a purely poloidal magnetic field, all confined inside the star, with different strength values in the range $10^{11}$-$10^{16}$ Gauss. Low magnetic fields have negligible effetcs on the dynamics of bar-stable models. On the contrary, for very strong magnetic fields, i.e., above $10^{15}$ Gauss, these models are braked considerably in their rotation and evolve into configurations that have uniformly rotating extended cores with large rest-mass densities models. Regarding the effects on the dynamical bar-mode instability, we find that magnetic fields seem to have very low effects on the $m=2$ deformation for field strengths of order $10^{15}$ Gauss or less, only reducing the growth rate of the instability and the maximum distortion of the bar deformation. Magnetic fields greater than some units in $10^{15}$ or $10^{16}$ Gauss (the treshold being different for the different unstable models) are indeed able to completely suppress the purely hydrodinamical instability, making the distorsion of the stars negligible with consequent negative effect on them as possible gravitational wave sources. For all models we observe a sudden formation and linear growth of a toroidal magnetic field component that rapidly overcomes the original poloidal one as a consequence of the winding of the magnetic field lines dragged by differential rotation, and hence an amplification of the total magnetic energy inside the stars of about two orders of magnitude. Later in the evolution, bar-unstable models exhibit and rapid exponential growth of the toroidal magnetic field component. The nature of this growth has been studied by performing additional simulations at finer resolutions, since a possible explanation for this behavior is the onset of the magnetorotational instability, whose charateristic modes require a very high resolution in order to be fully resolved. Due to computational limitations, we could only observe a few features that seem to support our hypothesis, without providing a firm evidence.