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

Excitation and Propagation of Eccentricity Disturbances in Planetary Systems

The high eccentricities of the known extrasolar planets remain largely unexplained. We explore the possibility that eccentricities are excited in the outer parts of an extended planetary disk by encounters with stars passing at a few hundreds of AU. After the encounter, eccentricity disturbances propagate inward due to secular interactions in the disks, eventually exciting the innermost planets. We study how the inward propagation of eccentricity in planetary disks depends on the number and masses of the planets and spacing between them and on the overall surface-density distribution in the disk. The main governing factors are the large-scale surface-density distribution and the total size of the system. If the smeared-out surface density is approximated by a power-law \Sigma(r)\propto r^{-q}, then eccentricity disturbances propagate inward efficiently for flat density distributions with q < 1. If this condition is satisfied and the size of the planetary system is 50 AU or larger, the typical eccentricities excited by this mechanism by field star encounters in the solar neighborhood over 5 Gyr are in the range 0.01-0.1. Higher eccentricities (> 0.1) may be excited in planetary systems around stars that are formed in relatively dense, long-lived open clusters. Therefore, this mechanism may provide a natural way to excite the eccentricities of extrasolar planets.Comment: 23 pages including 4 b/w figures and 1 color figure, accepted to A

The M/L ratio of massive young clusters

We point out a strong time-evolution of the mass-to-light conversion factor \eta commonly used to estimate masses of dense star clusters from observed cluster radii and stellar velocity dispersions. We use a gas-dynamical model coupled with the Cambridge stellar evolution tracks to compute line-of-sight velocity dispersions and half-light radii weighted by the luminosity. Stars at birth are assumed to follow the Salpeter mass function in the range [0.15--17 M_\sun]. We find that $\eta$, and hence the estimated cluster mass, increases by factors as large as 3 over time-scales of 20 million years. Increasing the upper mass limit to 50 M_\sun leads to a sharp rise of similar amplitude but in as little as 10 million years. Fitting truncated isothermal (Michie-King) models to the projected light profile leads to over-estimates of the concentration par ameter c of $\delta c\approx 0.3$ compared to the same functional fit applied to the proj ected mass density.Comment: Draft version of an ApJ lette

Distant Companions and Planets around Millisecond Pulsars

We present a general method for determining the masses and orbital parameters of binary millisecond pulsars with long orbital periods (P_orb >> 1 yr), using timing data in the form of pulse frequency derivatives. We apply our method to analyze the properties of the second companion in the PSR B1620-26 triple system. We use the latest timing data for this system to constrain the mass and orbital parameters of the second companion. We find that all possible solutions have a mass m_2 in the range 2.4 10^-4 M_sun <= m_2 sin i_2 <= 1.2 10^-2 M_sun, i.e., almost certainly excluding a second companion of stellar mass and suggesting instead that the system contains a planet or a brown dwarf. Using Monte-Carlo realizations of the triple configuration in three dimensions we find the most probable value of m_2 to be 0.010(5) M_sun, corresponding to a distance of 38(6) AU from the center of mass of the inner binary (the errors indicate 80% confidence intervals). We also apply our method to analyze the planetary system around PSR B1257+12, where a distant, giant planet may be present in addition to the three well-established Earth-mass planets. We find that the simplest interpretation of the frequency derivatives implies the presence of a fourth planet with a mass of ~100 M_earth in a circular orbit of radius ~40 AU.Comment: 30 pages, Latex, 10 Postscript figures, uses aaspp4.sty. ApJ submitted. Also available at http://ensor.mit.edu/~rasi

Planets in triple star systems--the case of HD188753

We consider the formation of the recently discovered ``hot Jupiter'' planet orbiting the primary component of the triple star system HD188753. Although the current outer orbit of the triple is too tight for a Jupiter-like planet to have formed and migrated to its current location, the binary may have been much wider in the past. We assume here that the planetary system formed in an open star cluster, the dynamical evolution of which subsequently led to changes in the system's orbital parameters and binary configuration. We calculate cross sections for various scenarios that could have led to the multiple system currently observed, and conclude that component A of HD188753 with its planet were most likely formed in isolation to be swapped in a triple star system by a dynamical encounter in an open star cluster. We estimate that within 500pc of the Sun there are about 1200 planetary systems which, like Hd188753, have orbital parameters unfavorable for forming planets but still having a planet, making it quite possible that the HD188753 system was indeed formed by a dynamical encounter in an open star cluster.Comment: ApJ Letters in pres

Eccentric double white dwarfs as LISA sources in globular clusters

We consider the formation of double white dwarfs (DWDs) through dynamical interactions in globular clusters. Such interactions can give rise to eccentric DWDs, in contrast to the exclusively circular population expected to form in the Galactic disk. We show that for a 5-year Laser Interferometer Space Antenna (LISA) mission and distances as far as the Large Magellanic Cloud, multiple harmonics from eccentric DWDs can be detected at a signal-to-noise ratio higher than 8 for at least a handful of eccentric DWDs, given their formation rate and typical lifetimes estimated from current cluster simulations. Consequently the association of eccentricity with stellar-mass LISA sources does not uniquely involve neutron stars, as is usually assumed. Due to the difficulty of detecting (eccentric) DWDs with present and planned electromagnetic observatories, LISA could provide unique dynamical identifications of these systems in globular clusters.Comment: Published in ApJ 665, L5

High Orbital Eccentricities of Extrasolar Planets Induced by the Kozai Mechanism

One of the most remarkable properties of extrasolar planets is their high orbital eccentricities. Observations have shown that at least 20% of these planets, including some with particularly high eccentricities, are orbiting a component of a wide binary star system. The presence of a distant binary companion can cause significant secular perturbations to the orbit of a planet. In particular, at high relative inclinations, a planet can undergo a large-amplitude eccentricity oscillation. This so-called "Kozai mechanism" is effective at a very long range, and its amplitude is purely dependent on the relative orbital inclination. In this paper, we address the following simple question: assuming that every host star with a detected giant planet also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, how well could secular perturbations reproduce the observed eccentricity distribution of planets? Our calculations show that the Kozai mechanism consistently produces an excess of planets with very high (e >0.6) and very low (e < 0.1) eccentricities. The paucity of near-circular orbits in the observed sample cannot be explained solely by the Kozai mechanism, because, even with high enough inclinations, the Kozai mechanism often fails to produce significant eccentricity perturbations when there are other competing sources of orbital perturbations on secular timescales, such as general relativity. On the other hand, the Kozai mechanism can produce many highly eccentric orbits. Indeed the overproduction of high eccentricities observed in our models could be combined with plausible circularizing mechanisms (e.g., friction from residual gas) to create more intermediate eccentricities (e=0.1-0.6).Comment: 24 pages, 6 figures, ApJ, in press, minor changes to reflect the accepted versio

Thermodynamics of the self-gravitating ring model

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply a new iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state