The density and drag of the accretion wake of a massive body moving through a uniform stellar distribution

We calculate the change in density within a uniform distribution of field stars (point masses) caused by a single massive body passing through with a constant velocity. Starting with the simplest case in which the field stars are initially stationary this leads to an infinite density wake behind the body. Introducing a small thermalisation within the field stars removes this infinity whilst leading to similar results off the path of the massive body. Results are in good agreement with those previously derived. An approximation can be made for the density in the thermalised case and this can be used to deduce the force exerted on the massive body due to the drag caused by the accretion wake

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 Effect of Stars on the Dark Matter Spike Around a Black Hole: A Tale of Two Treatments

We revisit the role that gravitational scattering off stars plays in establishing the steady-state distribution of collisionless dark matter (DM) around a massive black hole (BH). This is a physically interesting problem that has potentially observable signatures, such as $\gamma-$rays from DM annihilation in a density spike. The system serves as a laboratory for comparing two different dynamical approaches, both of which have been widely used: a Fokker-Planck treatment and a two-component conduction fluid treatment. In our Fokker-Planck analysis we extend a previous analytic model to account for a nonzero flux of DM particles into the BH, as well as a cut-off in the distribution function near the BH due to relativistic effects or, further out, possible DM annihilation. In our two-fluid analysis, following an approximate analytic treatment, we recast the equations as a "heated Bondi accretion" problem and solve the equations numerically without approximation. While both the Fokker-Planck and two-fluid methods yield basically the same DM density and velocity dispersion profiles away from the boundaries in the spike interior, there are other differences, especially the determination of the DM accretion rate. We discuss limitations of the two treatments, including the assumption of an isotropic velocity dispersion.Comment: 12 pages, 6 figure

Predictions for Triple Stars with and without a Pulsar in Star Clusters

Though about 80 pulsar binaries have been detected in globular clusters so far, no pulsar has been found in a triple system in which all three objects are of comparable mass. Here we present predictions for the abundance of such triple systems, and for the most likely characteristics of these systems. Our predictions are based on an extensive set of more than 500 direct simulations of star clusters with primordial binaries, and a number of additional runs containing primordial triples. Our simulations employ a number N_{tot} of equal mass stars from N_{tot}=512 to N_{tot}=19661 and a primordial binary fraction from 0-50%. In addition, we validate our results against simulations with N=19661 that include a mass spectrum with a turn-off mass at 0.8 M_{sun}, appropriate to describe the old stellar populations of galactic globular clusters. Based on our simulations, we expect that typical triple abundances in the core of a dense cluster are two orders of magnitude lower than the binary abundances, which in itself already suggests that we don't have to wait too long for the first comparable-mass triple with a pulsar to be detected.Comment: 11 pages, minor changes to match MNRAS accepted versio

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

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

Gravothermal Expansion in an NN-Body System

This paper describes the numerical evolution of an $N$-body system with a slight ``temperature inversion''; i.e. the maximum velocity dispersion occurs not at the centre but further out. Fluid models predict that the core of such a system expands on a time-scale of thousands of central relaxation times, and here this behaviour is qualitatively confirmed for an $N$-body system of over 3000 bodies. With certain qualifications, this demonstrates the existence in N-body systems of one of the fundamental mechanisms which, in fluid models, drive the gravothermal oscillations discovered by Bettwieser & Sugimoto.Comment: 25pp and 12 figures (available from [email protected]), te

Tackling reporting issues and variation in behavioural weight management interventions: Design and piloting of the standardized reporting of adult behavioural weight management interventions to aid evaluation (STAR-LITE) template.

In the United Kingdom, the National Institute for Health and Care Excellence make recommendations to guide the local-level selection and implementation of adult behavioural weight management interventions (BWMIs) which lack specificity. The reporting of BWMIs is generally poorly detailed, resulting in difficulties when comparing effectiveness, quality and appropriateness for participants. This non-standardized reporting makes meta-analysis of intervention data impossible, resulting in vague guidance based on weak evidence, reinforcing the urgent need for consistency and detail within BWMI description. STAR-LITE - a 4-section, 119-item standardized adult BWMI reporting template - was developed and tested using a two-phase process. After initial design, the template was piloted using adult behavioural weight management RCTs and currently implemented UK BWMI mapping information to further refine the template and examine current reporting and variance. Overall, reporting quality of weight management RCTs was poor, and large variance across different components of real-world BWMIs was observed. Non-specific guidance and wide variation in adult BWMIs are likely linked to inadequate RCT reporting quality and the inability to perform reliable comparisons of data. Future use of STAR-LITE would facilitate the consistent, detailed reporting of adult BWMIs, supporting their evaluation and comparison, to ultimately inform effective policy and improve weight management practice

On the mass-radius relation of hot stellar systems

Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. Objects that are somewhat in between globular clusters and low-mass galaxies, such as ultra-compact dwarf galaxies, have a mass-radius relation consistent with the extension of the relation for bright ellipticals. Here we show that at an age of 10 Gyr a break in the mass-radius relation at ~10^6 Msun is established because objects below this mass, i.e. globular clusters, have undergone expansion driven by stellar evolution and hard binaries. From numerical simulations we find that the combined energy production of these two effects in the core comes into balance with the flux of energy that is conducted across the half-mass radius by relaxation. An important property of this `balanced' evolution is that the cluster half-mass radius is independent of its initial value and is a function of the number of bound stars and the age only. It is therefore not possible to infer the initial mass-radius relation of globular clusters and we can only conclude that the present day properties are consistent with the hypothesis that all hot stellar systems formed with the same mass-radius relation and that globular clusters have moved away from this relation because of a Hubble time of stellar and dynamical evolution.Comment: 5 pages, 3 figures, MNRAS Letters (accepted