Theoretical Implications of the PSR B1620−26 Triple System and Its Planet

We present a new theoretical analysis of the PSR B1620-26 triple system inthe globular cluster M4, based on the latest radio pulsar timing data, whichnow include measurements of five time derivatives of the pulse frequency. Thesedata allow us to determine the mass and orbital parameters of the secondcompanion completely (up to the usual unknown orbital inclination angle $i_2$).The current best-fit parameters correspond to a second companion of planetarymass, $m_2 \sin i_2 \simeq 7\times10^{-3} M_\odot$, in an orbit of eccentricity$e_2\simeq 0.45$ and semimajor axis $a_2\simeq 60 $AU. Using numericalscattering experiments, we study a possible formation scenario for the triplesystem, which involves a dynamical exchange interaction between the binarypulsar and a primordial star-planet system. The current orbital parameters ofthe triple are consistent with such a dynamical origin, and suggest that theseparation of the parent star-planet system was very large, $\go 50 $AU. Wealso examine the possible origin of the anomalously high eccentricity of theinner binary pulsar. While this eccentricity could have been induced during thesame dynamical interaction that created the triple, we find that it couldequally well arise from long-term secular perturbation effects in the triple,combining the general relativistic precession of the inner orbit with theNewtonian gravitational perturbation of the planet. The detection of a planetin this system may be taken as evidence that large numbers of extrasolarplanetary systems, not unlike those discovered recently in the solarneighborhood, also exist in old star clusters.Comment: 34 pages, including 11 figures, to appear in ApJ, Jan 1, 2000. Revised version, including some significant addition