Evidence of longterm cyclic evolution of radio pulsar periods

Abstract

The measurements of pulsar frequency second derivatives have shown that they are 1e2...1e6 times larger than expected for standard pulsar spin-down law. Moreover, the second derivatives as well as braking indices are even negative for about half the pulsars. We explain these paradoxical results on the basis of the statistical analysis of the rotational parameters f0, f1 and f2 of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between f2 and f1 for both f2 > 0 (correlation coefficient r ~ 0.9) and f2 < 0 (r ~ 0.85), as well as between f0 and f1 (r ~ 0.6...0.7). We interpret these dependencies as evolutionary ones due to f1 being nearly proportional to the pulsars' age. The derived statistical relations as well as "anomalous" values of f2 are well described by assuming the existence of long-time variations of the spin-down rate. The pulsar frequency evolution, therefore, consists of secular change of f0_{ev}(t), f1_{ev}(t) and f2_{ev}(t) according to the power law with n ~ 5, the irregularities, observed within the timespan as timing noise, and the non-monotonous variations on the timescale of several tens of years, which is larger than that of the timespan. It is possible that the nature of long-term variations is similar to that of short-term ones. The idea of non-constant secular pulsars' braking index n is also analysed.