Abstract

The unusually large $\ddot P$ of the binary millisecond pulsar PSR~B1620-26 in the galactic globular cluster M4 (Backer 1992, Backer \etal 1993, Thorsett \etal 1993), suggests the pulsar is a member of a hierarchical triple. The tertiary may have a mass from $\sim 10^{-3}\,\msun$ to $1\,\msun$, and orbits the inner binary at a distance of between $10$ and $50\, AU$. The observed $\dot P$ constrains the mass, $m_2$, semi--major axis, $a_2$, eccentricity, $e_2$ and angle between the line--of--sight and the semi--major axis, $\omega _2 $, of the tertiary. Measurements of higher time derivatives of the spin period and time derivatives of the orbital elements will soon provide very strong constraints to the orbital parameters of the system. We consider the expected values of some of the observable variables for different $m_2, a_2, e_2$ and show that allowing even moderate values of $e_2$ provides a surprisingly large allowed range of values for $m_2, a_2$. In particular, the apparent mean motion provides a poor measure of $a_2$ when $e_2 \sim 0.3$. We briefly consider the possible effects on the inner binary orbital parameters, in particular the inner binary orbital period, $P_1$. We also discuss scenarios for formation and subsequent evolution of planetary and stellar triples in M4, and the implications for PSR~B1620-26. Whether the tertiary is of planet or stellar mass, there are strong dynamical constraints on the past evolution of the system. If the tertiary is sub--stellar the system must have spent a large fraction of its lifetime outside the core of M4, and probably survived at least one close encounter with a field star. If the tertiary is of stellar mass, the system is most likely younger than inferred from its characteristic age and has undergone multiple encounters with field stars. The eccentricity of the inner binary, $e_1 = 0.025$, is a strong constraint on the dynamical history of the system. Whether the tertiary is of stellar or sub--stellar mass, the confirmation of PSR~B1620-26 as a hierarchical triple pulsar would provide fascinating insight into pulsar formation and stellar dynamics in globular clusters.