Magnetar birth: rotation rates and gravitational-wave emission

Understanding the evolution of the angle $\chi$ between a magnetar's rotation and magnetic axes sheds light on the star's birth properties. This evolution is coupled with that of the stellar rotation $\Omega$, and depends on the competing effects of internal viscous dissipation and external torques. We study this coupled evolution for a model magnetar with a strong internal toroidal field, extending previous work by modelling -- for the first time in this context -- the strong proto-magnetar wind acting shortly after birth. We also account for the effect of buoyancy forces on viscous dissipation at late times. Typically we find that $\chi\to 90^\circ$ shortly after birth, then decreases towards $0^\circ$ over hundreds of years. From observational indications that magnetars typically have small $\chi$, we infer that these stars are subject to a stronger average exterior torque than radio pulsars, and that they were born spinning faster than $\sim 100-300$ Hz. Our results allow us to make quantitative predictions for the gravitational and electromagnetic signals from a newborn rotating magnetar. We also comment briefly on the possible connection with periodic Fast Radio Burst sources.