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Evolution of the long-period pulsar GLEAM-X J162759.5-523504.3

The long-period ($P = 1091$ s) of the recently discovered pulsar GLEAM-X J162759.5-523504.3 can be attained by neutron stars evolving with fallback discs and magnetic dipole moments of a few $10^{30}$ G cm$^3$ at ages greater than $\sim 2 \times 10^5$ yr consistently with the observational upper limits to the period derivative, $\dot{P}$, and the X-ray luminosity, $L_X$, of the source. The current upper limits for $\dot{P}$ allow two alternative present states: (1) The disc is still active with ongoing accretion at a low rate such that the accretion luminosity is much less than the neutron star's cooling luminosity, which in turn is below the upper limit for $L_X$. In this scenario the spin-down will continue at $\dot{P} \sim 10^{-10}$ s s$^{-1}$ until the disc becomes inactive; the final period will be $P \sim$ a few $10^3$ s. (2) The disc is already inactive, there is no accretion. In this case the period evolution has leveled off to the observed value in the final period range. The remaining, very weak, dipole torque sustaining asymptotic spin-down at $\dot{P} \sim 4 \times 10^{-18}$ s s$^{-1}$. Long periods $P \sim$ a few $10^3$ s were predicted for the final states of soft gamma repeaters and anomalous X-ray pulsars with relatively strong dipole fields in earlier work with the fallback disc model.