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

The inter-glitch 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 non-linear response to the glitch. We present inter-glitch timing fits to the present sample covering 16 large glitches, taking into account the possibility that in some glitches part of the step in 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 inter-glitch time intervals. We extrapolate the inter-glitch 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 Dec. 22, 2017 +/- 197 days if no persistent shift is involved, but could occur as early as July 27, 2016 +/- 152 days 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 Dec. 12, 2016, we saw ATel # 9847 announcing a Vela pulsar glitch which has arrived 138 days after our prediction with a persistent shift, within the 1 sigma uncertainty of 152 days.