On the peculiarities in the rotational frequency evolution of isolated neutron stars

Abstract The measurements of pulsar frequency second derivatives have shown that they are 102−106 times larger than expected for standard pulsar spin-down law, and are even negative for about half of pulsars. We explain these paradoxical results on the basis of the statistical analysis of the rotational parameters ν, $\dot{\nu}$ and $\ddot{\nu}$ of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between $\ddot{\nu}$ and $\dot{\nu}$ for both $\ddot{\nu}>0$ and $\ddot{\nu}<0$ , as well as between ν and $\dot{\nu}$ . We interpret these dependencies as evolutionary ones due to $\dot{\nu}$ being nearly proportional to the pulsars’ age. The derived statistical relations as well as “anomalous” values of $\ddot{\nu}$ are well described by assuming the long-time variations of the spin-down rate. The pulsar frequency evolution, therefore, consists of secular change of νev(t), $\dot{\nu}_{\mathrm{ev}}(t)$ and $\ddot{\nu}_{\mathrm{ev}}(t)$ according to the power law with n≈5, the irregularities, observed within a timespan as a timing noise, and the variations on the timescale larger than that—several decades.