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Evolution of the long-period pulsar PSR J0901-4046

The fallback disc model predicted that anomalous X-ray pulsars (AXPs) and soft-gamma repeaters (SGRs) will evolve to isolated long period pulsars before the discovery of the first two long-period pulsars (LPPs) this year. Unlike normal radio pulsars, LPPs show transient pulsed-radio epochs with unusual and variable pulse shapes, similar to the radio behaviour of the few radio emitting AXP/SGRs. We show that the present properties of the recently discovered second LPP, PSR J0901-4046 ($P \simeq 76$ s), are obtained as a result of evolution in interaction with a fallback disc, as we had already shown for the first discovered LPP, GLEAM-X J162759.5-523504.3 ($P \simeq 1091$ s). While there is only an upper limit to the period derivative, $\dot{P}$, of GLEAM-X J162759.5-523504.3, the $\dot{P}$ of the PSR J0901-4046 has already been measured, providing better constraints for the evolutionary models. The model can produce the source properties with a dipole moment $μ\simeq 10^{30}$ G cm$^3$. The results are not sensitive to the initial pulsar period. Our results indicate that PSR J0901-4046 went through an AXP/SGR epoch at an age of a few $10^4$ yr, and is $\sim (6 - 8) \times 10^5$ yr old at present.