Monotonic and cyclic components of radio pulsars spin-down

In this article we revise the problem of anomalous values of pulsars’ braking indices n_{obs} and frequency second derivatives F2 arising in observations. The intrinsic evolutionary braking is buried deep under superimposed irregular processes, that prevent direct estimations of its parameters for the majority of pulsars. We re-analyze the distribution of “ordinary” radio pulsars on a F2-F1, F2-F0, F1-F0 and n_{obs}-tau_{ch} diagrams assuming their spin-down to be the superposition of a “true” monotonous term and a symmetric oscillatory term. We demonstrate that their effects may be clearly separated using simple ad hoc arguments. Using maximum likelihood estimator we derive the parameters of both components. We find characteristic timescales of such oscillations to be of the order of 1e3-1e4 years, while its amplitudes are large enough to modulate the observed spin-down rate up to 0.5-5 times and completely dominate the second frequency derivatives. On the other hand, pulsars’ secular evolution is consistent with classical magnetodipolar model with braking index n ~ 3. So, observed pulsars’ characteristic ages (and similar estimators that depend on the observed F1) are also affected by long term cyclic process and differ up to 0.5-5 times from their monotonous values. This fact naturally resolves the discrepancy of characteristic and independently estimated physical ages of several objects, as well as explains very large, up to 1e8 years, characteristic ages of some pulsars. We discuss the possible physical connection of long term oscillation with a complex neutron star rotation relative its magnetic axis due to influence of the near-field part of magnetodipolar torque.