The evolution of the magnetic inclination angle as an explanation of the long term red timing-noise of pulsars

We study the possibility that the long term red timing-noise in pulsars originates from the evolution of the magnetic inclination angle chi. The braking torque under consideration is a combination of the dipole radiation and the current loss. We find that the evolution of chi can give rise to extra cubic and fourth-order polynomial terms in the timing residuals. These two terms are determined by the efficiency of the dipole radiation, the relative electric-current density in the pulsar tube and chi. The following observation facts can be explained with this model: (a) young pulsars have positive <(nu)double over dot>; (b) old pulsars can have both positive and negative <(nu)double over dot>; (c) the absolute values of <(nu)double over dot> are proportional to -<(nu)over dot>; (d) the absolute values of the braking indices are proportional to the characteristic ages of pulsars. If the evolution of chi is purely due to rotation kinematics, then it cannot explain the pulsars with braking index less than 3, and thus the intrinsic change of the magnetic field is needed in this case. Comparing the model with observations, we conclude that the drift direction of chi might oscillate many times during the lifetime of a pulsar. The evolution of chi is not sufficient to explain the rotation behaviour of the Crab pulsar, because the observed chi and <(chi)over dot> are inconsistent with the values indicated from the timing residuals using this model.