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The kinematics and orbital dynamics of the PSR B1259$-$63/LS 2883 system from 23 years of pulsar timing

We present an analysis of $23~$yr of pulse arrival times for PSR B1259$-$63. The pulsar is in a binary orbit about its approximately $20~M_{\odot}$ companion LS$~$2883. Our best-fitting timing solution has none of the pulse-number ambiguities that have plagued previous attempts to model the binary orbit. We measure significant first and second time derivatives of the projected semimajor axis and longitude of the periastron of the orbit. These variations are found to be consistent with the precession of the orbital plane due to classical spin-orbit coupling. The derived moment of inertia and spin of the companion are consistent with the companion rotating at near-breakup velocity. The system configuration is also consistent with the geometry derived from both the polarisation of the radio emission and the eclipse of the pulsar by the equatorial disc of the companion. We find strong evidence for orbital period decay that can be attributed to mass loss from the companion star. We also measure a significant proper motion that locates the birth of the system in the Centaurus OB1 association. By combining proper motion of the pulsar with radial velocity measurements of the companion, we measure the three-dimensional velocity of the system. This velocity is used to constrain the masses of the stars prior to the supernova explosion and the kick the pulsar received at or immediately after the explosion.