Douglas C. Heggie

On the effects of dynamical evolution on the initial mass function of globular clusters

In this paper we show the results of a large set of N-body simulations modelling the evolution of globular clusters driven by relaxation, stellar evolution and disc shocking, and including the effects of the tidal field of the Galaxy. We investigate the evolution of multi-mass models with a power-law initial mass function (IMF) starting with different initial masses, concentrations, slopes of the IMF and located at different galactocentric distances. We show to what extent the effects of the various evolutionary processes alter the shape of the IMF and to what extent these changes depend on the position of the cluster in the Galaxy. The changes in both the global and the local mass functions (measured at different distances from the cluster centre) are investigated, showing whether and where the local mass function keeps memory of the IMF and where it provides a good indication of the current global mass function. The evolution of the population of white dwarfs is also followed in detail, and we supply an estimate of the fraction of the current value of the total mass expected to be in white dwarfs depending on the main initial conditions for the cluster (mass and position in the Galaxy). Simple analytical expressions have been derived by which it is possible to calculate the main quantities of interest (total mass, fraction of white dwarfs, slope of the mass function) at any time t for a larger number of different initial conditions than those investigated numerically.

The time-scale of escape from star clusters

In this paper a cluster is modelled as a smooth potential (due to the cluster stars) plus the steady tidal field of the Galaxy. In this model there is a minimum energy below which stars cannot escape. Above this energy, however, the time-scale on which a star escapes varies with the orbital parameters of the star (mainly its energy) in a way which we attempt to quantify, with both theoretical arguments and computer simulations. Within the limitations of the model we show that the time-scale is long enough to complicate the interpretation of full N-body simulations of clusters, and that stars above the escape energy may remain bound to the cluster for about a Hubble time.

The effects of fly-bys on planetary systems

Most of the observed extrasolar planets are found on tight and often eccentric orbits. The high eccentricities are not easily explained by planet-formation models, which predict that planets should be on rather circular orbits. Here we explore whether fly-bys involving planetary systems with properties similar to those of the gas giants in the Solar system can produce planets with properties similar to the observed planets. Using numerical simulations, we show that fly-bys can cause the immediate ejection of planets, and sometimes also lead to the capture of one or more planets by the intruder. More common, however, is that fly-bys only perturb the orbits of planets, sometimes leaving the system in an unstable state. Over time-scales of a few million to several hundred million years after the fly-by, this perturbation can trigger planet-planet scatterings, leading to the ejection of one or more planets. For example, in the case of the four gas giants of the Solar system, the fraction of systems from which at least one planet is ejected more than doubles in 108 yr after the fly-by. The remaining planets are often left on more eccentric orbits, similar to the eccentricities of the observed extrasolar planets. We combine our results of how fly-bys affect Solar-system-like planetary systems, with the rate at which encounters in young stellar clusters occur. For example, we measure the effects of fly-bys on the four gas giants in the Solar system. We find, that for such systems, between 5 and 15 per cent suffer ejections of planets in 108 yr after fly-bys in typical open clusters. Thus, encounters in young stellar clusters can significantly alter the properties of any planets orbiting stars in clusters. As a large fraction of stars which populate the solar neighbourhood form in stellar clusters, encounters can significantly affect the properties of the observed extrasolar planets. (Less)

Tidal tails of star clusters

Based on recent findings of a formation mechanism of substructure in tidal tails by Kupper et al., we investigate a more comprehensive set of N-body models of star clusters on orbits about a Milky Way like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up.

Peculiarities in velocity dispersion and surface density profiles of star clusters

Based on our recent work on tidal tails of star clusters we investigate star clusters of a few 104 M(circle dot) by means of velocity dispersion profiles and surface density profiles. We use a comprehensive set of N-body computations of star clusters on various orbits within a realistic tidal field to study the evolution of these profiles with time, and ongoing cluster dissolution. From the velocity dispersion profiles we find that the population of potential escapers, i.e. energetically unbound stars inside the Jacobi radius, dominates clusters at radii above about 50 per cent of the Jacobi radius. Beyond 70 per cent of the Jacobi radius nearly all stars are energetically unbound. The velocity dispersion therefore significantly deviates from the predictions of simple equilibrium models in this regime. We furthermore argue that for this reason this part of a cluster cannot be used to detect a dark matter halo or deviations from the Newtonian gravity. By fitting templates to about 104 computed surface density profiles we estimate the accuracy which can be achieved in reconstructing the Jacobi radius of a cluster in this way. We find that the template of King works well for extended clusters on nearly circular orbits, but shows significant flaws in the case of eccentric cluster orbits. This we fix by extending this template with three more free parameters. Our template can reconstruct the tidal radius over all fitted ranges with an accuracy of about 10 per cent, and is especially useful in the case of cluster data with a wide radial coverage and for clusters showing significant extra-tidal stellar populations. No other template that we have tried can yield comparable results over this range of cluster conditions. All templates fail to reconstruct tidal parameters of concentrated clusters, however. Moreover, we find that the bulk of a cluster adjusts to the mean tidal field which it experiences and not to the tidal field at perigalacticon as has often been assumed in other investigations, i.e. a fitted tidal radius is a clusters time average mean tidal radius and not its perigalactic one. Furthermore, we study the tidal debris in the vicinity of the clusters and find it to be well represented by a power law with a slope of -4 to -5. This steep slope we ascribe to the epicyclic motion of escaped stars in the tidal tails. Star clusters close to apogalacticon show a significantly shallower slope of up to -1, however. We suggest that clusters at apogalacticon can be identified by measuring this slope.

Statistics of N-body simulations — III. Unequal masses

We describe results from large numbers of

On the structure of tidal tails

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On the Exponential Instability of N-Body Systems

-body simulations containing from

Long-term evolution of isolated N-body systems

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More on the structure of tidal tails

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