Understanding the residual patterns of timing solutions of radio pulsars with a model of magnetic field oscillation

We explain some phenomena existing generally in the timing residuals: amplitude and sign of the second derivative of a pulsar's spin-frequency ((nu) over double dot), some sophisticated residual patterns, which also change with the time span of data segments. The sample is taken from Hobbs et al., in which the pulsar's spin-frequency and its first derivative have been subtracted from the timing solution fitting. We first classify the timing residual patterns into different types based on the sign of (nu) over double dot. Then we use the magnetic field oscillation model developed in our group to fit successfully the different kinds of timing residuals with the Markov Chain Monte Carlo method. Finally, we simulate the spin evolution over 20 years for a pulsar with typical parameters and analyse the data with the conventional timing solution fitting. By choosing different segments of the simulated data, we find that most of the observed residual patterns can be reproduced successfully. This is the first time that the observed residual patterns are fitted by a model and reproduced by simulations with very few parameters. From the distribution of the different residual patterns in the P-(P) over dot diagram, we argue that (1) a single magnetic field oscillation mode exists commonly in all pulsars throughout their lifetimes; (2) there may be a transition period over the lifetimes of pulsars, in which multiple magnetic field oscillation modes exist.