Monotonic and cyclic components of radio pulsar spin-down

this article we revise the problem of anomalous values of pulsar braking indices nobs and frequency second derivatives v. arising in observations. The intrinsic evolutionary braking is buried deep under superimposed irregular processes, which prevent direct estimations of its parameters for the majority of pulsars. We re-analyse the distribution of 'ordinary' radio pulsars on v-v, v-v, v-v and n(obs)-tau(ch) diagrams assuming their spin-down to be the superposition of a 'true' monotonic term and a symmetric oscillatory term. We demonstrate that their effects may be clearly separated using simple ad hoc arguments. Using the maximum-likelihood estimator, we derive the parameters of both components. We find characteristic time-scales of such oscillations to be of the order of 10(3)-10(4) yr, while their 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, pulsar secular evolution is consistent with the classical magnetodipolar model with braking index n approximate to 3. Therefore, observed pulsar characteristic ages (and similar estimators that depend on the observed v) are also affected by long-term cyclic processes and differ up to 0.5-5 times from their monotonic values. This fact naturally resolves the discrepancy of characteristic and independently estimated physical ages of several objects, as well as explaining the very large, up to 10(8) yr, characteristic ages of some pulsars. We discuss the possible physical connection of long-term oscillation with complex neutron star rotation relative to its magnetic axis due to the influence of the near-field part of the magnetodipolar torque.