Nonlinear interglitch dynamics, the braking index of the Vela pulsar and the time to the next glitch

The interglitch timing of the Vela pulsar is characterized by a constant second derivative of the rotation rate. This takes over after the post-glitch exponential relaxation and is completed at about the time of the next glitch. The vortex creep model explains the second derivatives in terms of nonlinear response to the glitch. We present interglitch timing fits to the present sample covering 16 large glitches, taking into account the possibility that in some glitches part of the step in the spin-down rate may involve a `persistent shift', as observed in the Crab pulsar. Modifying the expression for the time between glitches with this hypothesis leads to better agreement with the observed interglitch time intervals. We extrapolate the interglitch model fits to obtain spin-down rates just prior to each glitch and use these to calculate the braking index n = 2.81 ± 0.12. The next glitch should occur around 2017 December 22, ±197 d if no persistent shift is involved, but could occur as early as 2016 July 27, ±152 d if the 2013 glitch gave rise to a typical Vela persistent shift. Note added: Literally while we were submitting the first version of this paper on 2016 December 12, we saw ATel #9847 announcing a Vela pulsar glitch which has arrived 138 d after our prediction with a persistent shift, within the 1σ uncertainty of 152 d.