The Effect of Encounters on the Eccentricity of Binaries in Clusters

We derive analytical expressions for the change in the orbital eccentricity of a binary following a distant encounter with a third star on a hyperbolic or parabolic orbit. To establish the accuracy of these expressions, we present detailed comparisons with the results of direct numerical integrations of the equations of motion for the three bodies. We treat with particular care the difficult case of a binary with zero initial eccentricity. In this case, we show that the eccentricity $\delta e$ induced by the encounter declines in general as a power-law, \delta e\propto (a/\rp)^{5/2}, where $a$ is the binary semi-major axis and \rp is the periastron distance of the encounter. This power-law arises from the octupole-level secular perturbation of the binary. In contrast, non-secular quadrupole-level perturbations induce an eccentricity change that declines exponentially with \rp. These non-secular effects can become dominant at sufficiently small \rp, for a sufficiently high relative velocity, or for a sufficiently massive perturber. We also derive cross sections for eccentricity change and compare our results with those of previous studies based on numerical scattering experiments. Our results have important implications for a number of astrophysical problems including, in particular, the evolution of binary millisecond pulsars in globular clusters.Comment: final version with minor revisions, uses MNRAS TeX macros, 23 pages, to appear in MNRAS, also available from http://ensor.mit.edu/~rasio/papers

First Principles Simulations of Boron Diffusion in Graphite

Boron strongly modifies electronic and diffusion properties of graphite. We report the first ab initio study of boron interaction with the point defects in graphite, which includes structures, thermodynamics, and diffusion. A number of possible diffusion mechanisms of boron in graphite are suggested. We conclude that boron diffuses in graphite by a kick-out mechanism. This mechanism explains the common activation energy, but large magnitude difference, for the rate of boron diffusion parallel and perpendicular to the basal plane. © 2007 The American Physical Society

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

A Parallel Monte Carlo Code for Simulating Collisional N-body Systems

We present a new parallel code for computing the dynamical evolution of collisional N-body systems with up to N~10^7 particles. Our code is based on the the Henon Monte Carlo method for solving the Fokker-Planck equation, and makes assumptions of spherical symmetry and dynamical equilibrium. The principal algorithmic developments involve optimizing data structures, and the introduction of a parallel random number generation scheme, as well as a parallel sorting algorithm, required to find nearest neighbors for interactions and to compute the gravitational potential. The new algorithms we introduce along with our choice of decomposition scheme minimize communication costs and ensure optimal distribution of data and workload among the processing units. The implementation uses the Message Passing Interface (MPI) library for communication, which makes it portable to many different supercomputing architectures. We validate the code by calculating the evolution of clusters with initial Plummer distribution functions up to core collapse with the number of stars, N, spanning three orders of magnitude, from 10^5 to 10^7. We find that our results are in good agreement with self-similar core-collapse solutions, and the core collapse times generally agree with expectations from the literature. Also, we observe good total energy conservation, within less than 0.04% throughout all simulations. We analyze the performance of the code, and demonstrate near-linear scaling of the runtime with the number of processors up to 64 processors for N=10^5, 128 for N=10^6 and 256 for N=10^7. The runtime reaches a saturation with the addition of more processors beyond these limits which is a characteristic of the parallel sorting algorithm. The resulting maximum speedups we achieve are approximately 60x, 100x, and 220x, respectively.Comment: 53 pages, 13 figures, accepted for publication in ApJ Supplement

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

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

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