Spinning-Down of Moving Magnetars in the Propeller Regime

We use axisymmetric magnetohydrodynamic simulations to investigate the spinning-down of magnetars rotating in the propeller regime and moving supersonically through the interstellar medium. The simulations indicate that magnetars spin-down rapidly due to this interaction, faster than for the case of a non-moving star. From many simulation runs we have derived an approximate scaling laws for the angular momentum loss rate, \dot{L} \propto \~\eta_m^{0.3}\mu^{0.6}\rho^{0.8}{\cal M}^{-0.4} \Omega_*^{1.5}, where \rho is the density of the interstellar medium, \cal M is Mach number, \mu is the star's magnetic moment, \Omega_* is its angular velocity, and \eta_m is magnetic diffusivity. A magnetar with a surface magnetic field of 10^{13} - 10^{15} G is found to spin-down to a period P > 10^5-10^6 s in \sim 10^4 - 10^5 years. There is however uncertainty about the value of the magnetic diffusivity so that the time-scale may be longer. We discuss this model in respect of Soft Gamma Repeaters (SGRs) and the isolated neutron star candidate RXJ1856.5-3754.