3-Dimensional Simulations of the Reorganization of a Quark Star's Magnetic Field as Induced by the Meissner Effect

Abstract

In a previous paper (Ouyed et al. 2004) we presented a new model for soft gamma-ray repeaters (SGR), based on the onset of colour superconductivity in quark stars. In this model, the bursts result from the reorganization of the exterior magnetic field following the formation of vortices that confine the internal magnetic field (the \mz effect). Here we extend the model by presenting full 3-dimensional simulations of the evolution of the inclined exterior magnetic field immediately following vortex formation. The simulations capture the violent reconnection events in the entangled surface magnetic field as it evolves into a smooth, more stable, configuration which consists of a dipole field aligned with the star's rotation axis. The total magnetic energy dissipated in this process is found to be of the order of $10^{44} \mathrm{erg}$ and, if it is emitted as synchrotron radiation, peaks typically at $280 \mathrm{keV}$. The intensity decays temporally in a way resembling SGRs and AXPs (anomalous X-ray pulsars), with a tail lasting from a few to a few hundred times the rotation period of the star, depending on the initial inclination between the rotation and dipole axis. One of the obvious consequences of our model's final state (aligned rotator) is the suppression of radio-emission in SGRs and AXPs following their bursting era. We suggest that magnetar-like magnetic field strength alone cannot be responsible for the properties of SGRs and AXPs, while a quark star entering the ``Meissner phase'' is compatible with the observational facts. We compare our model to observations and highlight our predictions.