Ages of radio pulsar: long-term magnetic field evolution

We use the Bayesian approach to write the posterior probability density for the three-dimensional velocity of a pulsar and for its kinematic age. As a prior, we use the bimodal velocity distribution found in a recent article by Verbunt, Igoshev & Cator (2017). When we compare the kinematic ages with spin-down ages, we find that in general, they agree with each other. In particular, maximum likelihood analysis sets the lower limit for the exponential magnetic field decay timescale at $8$ Myr with a slight preference of $t_\mathrm{dec} \approx 12$ Myr and compatible with no decay at all. One of the objects in the study, pulsar B0950+08 has kinematic and cooling ages $\approx 2$ Myr which is in strong contradiction with its spin-down age $\tau\approx 17$ Myr. The 68 per cent credible range for the kinematic age is 1.2--8.0 Myr. We conclude that the most probable explanation for this contradiction is a combination of magnetic field decay and long initial period. Further timing, UV and X-ray observations of B0950+08 are required to constrain its origin and evolution better.