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 $10^2-10^6$ 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 $ν$, $\dot ν$ and $\ddot ν$ of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between $\ddot ν$ and $\dot ν$ for both $\ddotν> 0$ and $\ddotν< 0$, as well as between $ν$ and $\dotν$. We interpret these dependencies as evolutionary ones due to $\dotν$ being nearly proportional to the pulsars' age. The derived statistical relations as well as "anomalous" values of $\ddotν$ are well described by assuming the long-time variations of the spin-down rate. The pulsar frequency evolution, therefore, consists of secular change of $ν_{ev}(t)$, $\dotν_{ev}(t)$ and $\ddotν_{ev}(t)$ according to the power law with $n \approx 5$, the irregularities, observed within a timespan as a timing noise, and the variations on the timescale larger than that timespan -- several tens of years.