Magnetic Deformation of Magnetars for the Giant Flares of the Soft Gamma-Ray Repeaters

Abstract

We present one possible mechanism for the giant flares of the Soft Gamma-Ray Repeaters (SGRs) within the framework of magnetar, i.e., superstrongly magnetized neutron star model, motivated by the positive period increase associated with the August 27 event from SGR 1900+14. From the second-order perturbation analysis of the equilibrium of the magnetic polytrope, we find that there exist different equilibrium states separated by the energy of the giant flares and the shift in the moment of inertia to cause the period increase. This suggests that, if we assume that the global reconfiguration of the internal magnetic field of $H\simg 10^{16}$ G suddenly occurs, the positive period increase $ΔP_t/P_t \sim 10^{-4}$ as well as the energy $\simg 10^{44}$ ergs of the giant flares may be explained. The moment of inertia can increase with a release of energy, because the star shape deformed by the magnetic field can be prolate rather than oblate. In this mechanism, since the oscillation of the neutron star will be excited, a pulsation of $\sim$ ms period in the burst profile and an emission of the gravitational waves are expected. The gravitational waves could be detected by the planned interferometers such as LIGO, VIRGO and LCGT.