Modeling pulsar time noise with long term power law decay modulated by short term oscillations of the magnetic fields of neutron stars

We model the evolution of the magnetic fields of neutron stars as consisting of a long term power-law decay modulated by short term small amplitude oscillations. Our model predictions on the timing noise $\ddotν$ of neutron stars agree well with the observed statistical properties and correlations of normal radio pulsars. Fitting the model predictions to the observed data, we found that their initial parameter implies their initial surface magnetic dipole magnetic field strength ~ 5E14 G at ~0.4 year old and that the oscillations have amplitude between E-8 to E-5 and period on the order of years. For individual pulsars our model can effectively reduce their timing residuals, thus offering the potential of more sensitive detections of gravitational waves with pulsar timing arrays. Finally our model can also re-produce their observed correlation and oscillations of the second derivative of spin frequency, as well as the "slow glitch" phenomenon.

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