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

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

The Promiscuous Nature of Stars in Clusters

The recent availability of special purpose computers designed for calculating gravitational interactions of N-bodies at extremely high speed has provided the means to model globular clusters on a star-by-star basis for the first time. By endeavouring to make the N-body codes that operate on these machines as realistic as possible, the addition of stellar evolution being one example, much is being learnt about the interaction between the star cluster itself and the stars it contains. A fascinating aspect of this research is the ability to follow the orbits of individual stars in detail and to document the formation of observed exotic systems. This has revealed that many stars within a star cluster lead wildly promiscuous lives, interacting, often intimately and in rapid succession, with a variety of neighbours.Comment: 15 pages, 1 figure, to appear in the Astrophysical Journa

Exotic Hill Problem: Hall motions and symmetries

Our previous study of a system of bodies assumed to move along almost circular orbits around a central mass, approximately described by Hill's equations, is extended to "exotic" [alias non-commutative] particles. For a certain critical value of the angular velocity, the only allowed motions follow the Hall law. Translations and generalized boosts span two independent Heisenberg algebras with different central parameters. In the critical case, the symmetry reduces to a single Heisenberg algebra.Comment: RevTeX, 4 pages, 4 figure

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

Interpreting the M22 Spike Events

Recently Sahu et al., using the Hubble Space Telescope to monitor stars in the direction of the old globular cluster M22, detected six events in which otherwise constant stars brightened by ~50% during a time of <1 day. They tentatively interpret these unresolved events as due to microlensing of background bulge stars by free-floating planets in M22. I show that if these spike events are due to microlensing, the lensing objects are unlikely to be associated with M22, and unlikely to be part of a smoothly distributed Galactic population. Thus either there happens to be a massive, dark cluster of planets along our line-of-sight to M22, or the spike events are not due to microlensing. The lensing planets cannot be bound to stars in the core of M22: if they were closer than 8 AU, the lensing influence of the parent star would have been detectable. Moreover, in the core of M22, all planets with separations > 1 AU would have been ionized by random stellar encounters. Most unbound planets would have escaped the core via evaporation which preferentially affects such low-mass objects. Bound or free-floating planets can exist in the outer halo of M22; however, for reasonable assumptions, the maximum optical depth to such a population falls short of the observed optical depth, tau ~ 3x10^{-6}, by a factor of 5-10. Therefore, if real, these events represent the detection of a significant free-floating Galactic planet population. The optical depth to these planets is comparable to and mutually exclusive from the optical depth to resolved events measured by microlensing survey collaborations toward the bulge, and thus implies a similar additional mass of lensing objects. Such a population is difficult to reconcile with both theory and observations.Comment: Minor changes. 12 pages, 4 figures, 2 tables. Accepted to ApJ. To appear in Feb 10, 2002 issue (v566

Metastable Frenkel pair defect in graphite: source of Wigner energy?

The atomic processes associated with energy storage and release in irradiated graphite have long been subject to untested speculation. We examine structures and recombination routes for interstitial-vacancy (I-V) pairs in graphite. Interaction results in the formation of a new metastable defect (an intimate I-V pair) or a Stone-Wales defect. The intimate I-V pair, although 2.9 eV more stable than its isolated constituents, still has a formation energy of 10.8 eV. The barrier to recombination to perfect graphite is calculated to be 1.3 eV, consistent with the experimental first Wigner energy release peak at 1.38 eV. We expect similar defects to form in carbon nanostructures such as nanotubes, nested fullerenes, and onions under irradiation

Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

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