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  1. Abstract

    We analyze the slow periodicities identified in burst sequences from FRB 121102 and FRB 180916 with periods of about 16 and 160 days, respectively, while also addressing the absence of any fast periodicity that might be associated with the spin of an underlying compact object. Both phenomena can be accounted for by a young, highly magnetized, precessing neutron star that emits beamed radiation with significant imposed phase jitter. Sporadic narrow-beam emission into an overall wide solid angle can account for the necessary phase jitter, but the slow periodicities with 25%–55% duty cycles constrain beam traversals to be significantly smaller. Instead, phase jitter may result from variable emission altitudes that yield large retardation and aberration delays. A detailed arrival time analysis for triaxial precession includes wobble of the radio beam and the likely larger, cyclical torque resulting from the changes in the spin–magnetic moment angle. These effects will confound identification of the fast periodicity in sparse data sets longer than about a quarter of a precession cycle unless fitted for and removed as with orbital fitting. Stochastic spin noise, likely to be much larger than in radio pulsars, may hinder detection of any fast periodicity in data spans longer than a few days. These decoherence effects will dissipate as sources of fast radio bursts age, so they may evolve into objects with properties similar to Galactic magnetars.

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  2. Abstract

    The repeating fast radio bursts (FRBs) 180916.J0158 and 121102 are visible during periodically occurring windows in time. We consider the constraints on internal magnetic fields and geometries if the cyclical behavior observed for FRB 180916.J0158 and FRB 121102 is due to the precession of magnetars. In order to frustrate vortex line pinning we argue that internal magnetic fields must be stronger than about 1016G, which is large enough to prevent superconductivity in the core and destroy the crustal lattice structure. We conjecture that the magnetic field inside precessing magnetars has three components: (1) a dipole component with characteristic strength ∼ 1014G; (2) a toroidal component with characteristic strength ∼ 1015–1016G that only occupies a modest fraction of the stellar volume; and (3) a disordered field with characteristic strength ∼ 1016G. The disordered field is primarily responsible for permitting precession, which stops once this field component decays away, which we conjecture happens after ∼1000 yr. Conceivably, as the disordered component damps bursting activity diminishes and eventually ceases. We model the quadrupolar magnetic distortion of the star, which is due to its ordered components primarily, as triaxial and very likely prolate. We address the question of whether the spin frequency ought to be detectable for precessing, bursting magnetars by constructing a specific model in which bursts happen randomly in time with random directions distributed in or between cones relative to a single symmetry axis. Within the context of these specific models, we find that there are precession geometries for which detecting the spin frequency is very unlikely.

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