Is There a Planet in the PSR 1620-26 Triple System?

The unusually large eccentricity ($e_1=0.025$) of the low-mass binary millisecond pulsar PSR B1620-26 can be explained naturally as arising from the secular perturbation of a second, more distant companion. Such a triple configuration has been proposed recently as the most likely cause of the anomalous second period derivative of the pulsar. The current timing data are consistent with a second companion mass $m_2$ as low as $\sim10^{-3}\,M_\odot$, i.e., comparable to that of Jupiter. However, {\em if\/} the eccentricity is indeed produced by secular perturbations, then the second companion must be another star, most likely of mass m_2\lo1M_\odot and in a very eccentric (e_2\go0.5) orbit of period $P_2\sim10^2$--$10^3\,$yr. A second companion of planetary mass cannot induce the observed eccentricity. Independent of the mass of the second companion, small changes in the binary pulsar's orbit should become detectable with just a few additional years of timing data. This detection would provide direct confirmation of the triple nature of the system, and an accurate measurement of the effects would place important new constraints on the orbital parameters.Comment: 11 pages, uuencoded compressed postscript includes figures, IAS-AST-94-209

A Hierarchical Triple Star System in M4

The radio millisecond pulsar PSR B1620-26 is part of an extraordinary triple star system in the globular cluster M4. The inner companion to the neutron star is thought to be a white dwarf of mass m1 ~0.3 Msun in an orbit of period ~0.5 year. The nature and orbital characteristics of the second, more distant companion, have remained a mystery for many years. A theoretical analysis of the latest available radio pulsar timing data is presented here, allowing us to determine approximately the mass and orbital parameters of the second companion. Remarkably, the current best-fit parameters correspond to a second companion of **planetary mass**, with m2 ~0.007 Msun, in an orbit of eccentricity e2 ~0.45 and with a large semimajor axis a2 ~60 AU. The short dynamical lifetime of this very wide triple in M4 suggests that large numbers of such planets must be present in globular clusters. We also address the question of the anomalously high eccentricity of the inner binary pulsar. While this eccentricity could have been induced during the same dynamical interaction that created the triple, we find that it could also naturally arise from long-term secular perturbation effects in the triple, combining the general relativistic precession of the inner orbit with the Newtonian gravitational perturbation by the outer planet.Comment: 13 pages, to appear in Evolution of Binary and Multiple Star Systems, a Meeting in Celebration of Peter Eggleton's 60th Birthday, Bormio, Italy, ASP Conference Series, eds. P. Podsiadlowski et a

Dynamical Interactions of Planetary Systems in Dense Stellar Environments

We study dynamical interactions of star--planet binaries with other single stars. We derive analytical cross sections for all possible outcomes, and confirm them with numerical scattering experiments. We find that a wide mass ratio in the binary introduces a region in parameter space that is inaccessible to comparable-mass systems, in which the nature of the dynamical interaction is fundamentally different from what has traditionally been considered in the literature on binary scattering. We study the properties of the planetary systems that result from the scattering interactions for all regions of parameter space, paying particular attention to the location of the "hard--soft" boundary. The structure of the parameter space turns out to be significantly richer than a simple statement of the location of the "hard--soft" boundary would imply. We consider the implications of our findings, calculating characteristic lifetimes for planetary systems in dense stellar environments, and applying the results to previous analytical studies, as well as past and future observations. Recognizing that the system PSR B1620-26 in the globular cluster M4 lies in the "new" region of parameter space, we perform a detailed analysis quantifying the likelihood of different scenarios in forming the system we see today.Comment: Accepted for publication in ApJ. Minor changes to reflect accepted version. 14 pages, 14 figure

Hydrodynamics of Binary Coalescence.I. Polytropes with Stiff Equations of State

We have performed a series of three-dimensional hydrodynamic calculations of binary coalescence using the smoothed particle hydrodynamics (SPH) method. The initial conditions are exact polytropic equilibrium configurations with \gam > 5/3, on the verge of dynamical instability. We calculate the emission of gravitational radiation in the quadrupole approximation. The fully nonlinear development of the instability is followed until a new equilibrium configuration is reached. We find that the properties of this final configuration depend sensitively on both the compressibility and mass ratio. An {\em axisymmetric} merged configuration is always produced when \gam\lo2.3. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, {\em triaxial\/} merged configurations are obtained when \gam\go2.3, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios $q\ne1$ typically become dynamically unstable before the onset of mass transfer. Stable mass transfer from one neutron star to another in a close binary is therefore probably ruled out. The maximum amplitude $h_{max}$ and peak luminosity $L_{max}$ of the gravitational waves emitted during the final coalescence are nearly independent of \gam, but depend very sensitively on the mass ratio $q$.Comment: 27 pages, uuencoded compressed postscript, 16 figures upon request from [email protected], IAS-AST-94-

LISA Sources in Globular Clusters

Globular clusters house a population of compact binaries that will be interesting gravitational wave sources for LISA. We provide estimates for the numbers of sources of several categories and discuss the sensitivity of LISA to detecting these sources. The estimated total number of detectable sources ranges from about 10 to about 1000 with gravitational wave frequencies above 1 mHz. These sources are typically undetectable by any other means and thus offer an opportunity for doing true gravitational-wave astronomy. The detection of these sources would provide information about both binary star evolution and the dynamics of globular clusters.Comment: Contribution to Proceedings of 3rd LISA Symposium 7 pages, added reference

Binary-Binary Interactions and the Formation of the PSR B1620-26 Triple System in M4

The hierarchical triple system containing the millisecond pulsar PSR B1620-26 in M4 is the first triple star system ever detected in a globular cluster. Such systems should form in globular clusters as a result of dynamical interactions between binaries. We propose that the triple system containing PSR B1620-26 formed through an exchange interaction between a wide primordial binary and a {\it pre-existing\/} binary millisecond pulsar. This scenario would have the advantage of reconciling the $\sim10^9\,$yr timing age of the pulsar with the much shorter lifetime of the triple system in the core of M4.Comment: 13 pages, uuencoded compressed postscript with figures, IASSNS-AST 94/4