Evolution of newborn rapidly rotating magnetars: Effects of R -mode and fall-back accretion

Abstract

In this paper we investigate effects of the r-mode instability on a newborn rapidly-rotating magnetar with fall-back accretion. Such a magnetar could usually occur in core-collapse supernovae and gamma-ray bursts. We find that the magnetar's spin and r-mode evolution are influenced by accretion. If the magnetar is sufficiently spun up to a few milliseconds, gravitational radiation leads to the growth of the r-mode amplitude significantly. The maximum r-mode amplitude reaches an order of ~0.001 when the damping due to the growth of a toroidal magnetic field balances the growth of the r-mode amplitude. If such a sufficiently spun-up magnetar was located at a distance less than 1 Mpc, then gravitational waves would be detectable by the Einstein Telescope but would have an extremely low event rate. However, if the spin-up is insufficient, the growth of the r-mode amplitude is mainly due to the accretion torque. In this case, the maximum r-mode amplitude is of the order of ~10-6-10-5.