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Fluctuating neutron star magnetosphere: braking indices of eight pulsars, frequency second derivatives of 222 pulsars and 15 magnetars

Eight pulsars have low braking indices, which challenge the magnetic dipole braking of pulsars. 222 pulsars and 15 magnetars have abnormal distribution of frequency second derivatives, which also make contradiction with classical understanding. How neutron star magnetospheric activities affect these two phenomena are investigated by using the wind braking model of pulsars. It is based on the observational evidence that pulsar timing is correlated with emission and both aspects reflect the magnetospheric activities. Fluctuations are unavoidable for a physical neutron star magnetosphere. Young pulsars have meaningful braking indices, while old pulsars' and magnetars' fluctuation item dominates their frequency second derivatives. It can explain both the braking index and frequency second derivative of pulsars uniformly. The braking indices of eight pulsars are the combined effect of magnetic dipole radiation and particle wind. During the life time of a pulsar, its braking index will evolve from three to one. Pulsars with low braking index may put strong constraint on the particle acceleration process in the neutron star magnetosphere. The effect of pulsar death should be considered during the long term rotational evolution of pulsars. An equation like the Langevin equation for Brownian motion was derived for pulsar spin-down. The fluctuation in the neutron star magnetosphere can be either periodic or random, which result in anomalous frequency second derivative and they have similar results. The magnetospheric activities of magnetars are always stronger than those of normal pulsars.