In this contribution we study integrated properties of dynamically segregated star clusters. The observed core radii of segregated clusters can be 50% smaller than the “true” core radius. In addition, the measured radius in the red filters is smaller than those measured in blue filters. However, these difference are small (≲10%), making it observationally challenging to detect mass segregation in extra-galactic clusters based on such a comparison. Our results follow naturally from the fact that in nearly all filters most of the light comes from the most massive stars. Therefore, the observed surface brightness profile is dominated by stars of similar mass, which are centrally concentrated and have a similar spatial distribution.

An exciting recent finding regarding scaling relations among globular clusters is the so-called ‘blue tilt’: clusters of the blue sub-population follow a trend of redder colour with increasing luminosity. In this contribution we estimate by means of collisional N-body simulations to which extent this trend can be explained by field star capture occurring over a Hubble time. We investigate star clusters with 103 to 106 stars. We find that the ratio between captured field stars and total number of clusters stars is very low (≲ 10−4), even for co-rotation of the star cluster in a cold disk. This holds for star clusters in the mass range of both open clusters and globular clusters. Therefore, field star capture is not a probable mechanism for creating the colour-magnitude trend of metal-poor globular clusters.

Three-body stability is fundamental to astrophysical processes on all length and mass scales from planetary systems to clusters of galaxies, so it is vital we have a deep and thorough understanding of this centuries-old problem. Here we summarize an analytical method for determining the stability of arbitrary three-body hierarchies which makes use of the chaos theory concept of resonance overlap. For the first time the dependence on all orbital elements and masses can be given explicitly via simple analytical expressions which contain no empirical parameters. For clarity and brevity, analysis in this paper is restricted to coplanar systems including a description of a practical algorithm for use in N-body and other applications. A Fortran routine for arbitrarily inclined systems is available from the author, and animations of stable and unstable systems are available at www.maths.monash.edu.au/~ro/Capri.

The problem of three stars arises in many connections in stellar dynamics: three-body scattering drives the evolution of star clusters, and bound triple systems form long-lasting intermediate structures in them. Here we address the question of stability of triple stars. For a given system the stability is easy to determine by numerical orbit calculation. However, we often have only statistical knowledge of some of the parameters of the system. Then one needs a more general analytical formula. Here we start with the analytical calculation of the single encounter between a binary and a single star by Heggie (1975). Using some of the later developments we get a useful expression for the energy change per encounter as a function of the pericenter distance, masses, and relative inclination of the orbit. Then we assume that the orbital energy evolves by random walk in energy space until the accumulated energy change leads to instability. In this way we arrive at a stability limit in pericenter distance of the outer orbit for different mass combinations, outer orbit eccentricities and inclinations. The result is compared with numerical orbit calculations.

The various methods for regularisation of the gravitational few-body problem, from the coordinate transformation by the Kustaanheimo-Stiefel method to the more recent methods of algorithmic regularisation, are reviewed. Numerical comparisons of the performance of the methods are presented and future research suggested.

I discuss my stellar evolution code Ev in the context of simulations of large clusters of stars. It has long been able to handle single stars, and also binary stars up to a point. That point is far beyond what other codes are able to do, but well short of what is necessary for believable simulations. A recent version, Ev(Twin), can in principle deal with the contact phase of binary evolution, but it is not yet clear what the physical interaction is that needs to be simulated.

An upgrade, which I hope will be only a few lines, should allow it to follow Kozai cycles with tidal friction, a process that strongly influences the orbital period of close pairs that reside within wide, non-coplanar triples. However, there are many substantial gaps in the physics of even single stars, let alone binaries or triples.

Encounters between binary stars and single stars and between binary stars and other binary stars play a key role in the dynamics of dense stellar systems. In the simple model, in which stars are approximated by point masses, a number of theoretical and numerical results are known. In particular there exist relationships to help to describe the destruction process of binary stars (ionisation) through three-body encounters between binary and single stars. Here we extend these results to the four-body case involving encounters between pairs of binary stars that lead to a disruption of the binaries into single stars.

Numerical solutions for the 3-body problem can be extremely sensitive to small errors. We consider how small errors in calculations can affect the lifetime of these systems. In particular, we show that numerical errors can shorten the average lifetime of a 3-body system. This is illustrated using the Sitnikov Problem as an example. To give a theoretical explanation, we construct an approximate Poincaré map for this problem and delineate the structure of the escape regions. We show that numerical errors can destroy escape regions and can cause orbits to migrate to a region in which escape is faster.

In this brief proceedings article I summarize the review talk I gave at the IAU 246 meeting in Capri, Italy, glossing over the well-known results from the literature, but paying particular attention to new, previously unpublished material. This new material includes a careful comparison of the apparently contradictory results of two independent methods used to simulate the evolution of binary populations in dense stellar systems (the direct N-body method of Hurley, Aarseth, & Shara (2007) and the approximate Monte Carlo method of Ivanova et al. (2005)), that shows that the two methods may not actually yield contradictory results, and suggests future work to more directly compare the two methods.

We explore a Boltzmann scheme for studying the evolution of compact binary populations in globular clusters. We include processes of compact binary formation by tidal capture and exchange encounters, binary destruction by exchange and dissociation mechanisms and binary hardening by encounters, gravitational radiation and magnetic braking, as also the orbital evolution during mass transfer, following Roche lobe contact. From the evolution of compact-binary population, we investigate the dependence of the model number of X-ray binaries NXB on two essential cluster properties, namely, the star-star and star-binary encounter-rate parameters Γ and γ (Verbunt parameters). We find that the values of NXB and their expected scaling with the Verbunt parameters are in good agreement with results from recent X-ray observations of Galactic globular clusters.

We performed N-body simulations of star clusters with primordial binaries using a new code, GORILLA. It is based on Makino and Aarseth (1992)'s integration scheme on GRAPE, and includes a special treatment for relatively isolated binaries. Using the new code, we investigated effects of hardness of primordial binaries on whole evolution of the clusters. We simulated seven N=16384 equal-mass clusters containing 10% (in mass) primordial binaries whose binding energies are 1, 3, 10, 30, 100, 300, and 1000kT, respectively. Additionally, we also simulated a cluster without primordial binaries and that in which all binaries are replaced by stars with double mass, as references of soft and hard limits, respectively. We found that, in both soft (≤ 3kT) and hard (≥ 1000kT) limits, clusters experiences deep core collapse and shows gravothermal oscillations. On the other hands, in the intermediate hardness (10-300kT), the core collapses halt halfway due an energy releases of the primordial binaries.

The evolution of a star cluster is strongly influenced by the presence of primordial binaries and of a central black hole, as dynamical interactions within the core prevents a deep core collapse under these conditions. We present the results from a large set of direct N-body simulations of star clusters that include an intermediate mass black hole, single and binary stars. We highlight the structural and dynamical differences for the various cases showing in particular that on a timescale of a few relaxation times the density profile of the star cluster does no longer depend on the details of the initial conditions but only on the efficiency of the energy generation due to gravitational encounters at the center of the system.

The results in the N-body simulations in Giersz & Heggie (1996) show that although the masses segregate as expected during core collapse, after core collapse there is self-similar evolution with very little further evidence of mass segregation even though the system has not reached equipartition. Binary stars halt core collapse and it is possible that they also halt the tendency toward equipartition. To investigate this problem, we construct two models. One model is a two-component model which assumes that binary stars form in the region dominated by heavy stars. The other model is a single mass model which assumes that binary stars form only in the region of the core. In both models, when the binary heating term is included, we find the post-collapse evolution to be self-similar. The aim of our work is to combine these two models to form a two-component model which assumes that binary formation only occurs in the core.

The binary fraction, η, of a globular cluster (GC) is a key parameter in determining its dynamical evolution, as well as its content of rare stars, such as cataclysmic variables and blue stragglers. The precise value of η for a GC was historically difficult to constrain due to an inability to obtain reliable photometry for faint objects in dense stellar fields. However, today, the HST allows us to image the main sequence of the nearest GCs to their terminations. Using HST observations we constrain η for NGC 6397. While the necessary computing power is now available to realistically simulate entire GCs, large discrepancies in the assumed primordial binary fraction, ηp, of GCs still exist. Estimates range from 5% (Hurley et al. 2007) to 100% (Ivanova et al. 2005). The N-body models of Hurley et al. (2007) suggest that η beyond the half-mass radius remains close to ηp, while cluster evolution can increase the value in the core. We find η for NGC 6397 is 15.2±0.8% in a field centered on the core, and 1.1±0.3% in a field beyond the half mass radius. These findings suggests ηp ~ 1%.

Stellar mass compact object binaries are promising sources of gravitational radiation for the current generation of ground-based detectors, VIRGO and LIGO. Accurate templates for gravitational waveforms are needed in order to extract an event from the VIRGO/LIGO data stream. In the case of relativistic, compact object binaries accurate orbital parameters are necessary in order to produce such templates. Binary systems are affected by their stellar environment and thus the parameters of the binary population of a dense star cluster will be different from those of the field population. We propose to investigate the parameters of relativistic binary populations in dense star clusters using direct N-body simulations with a Post-Newtonian treatment of general relativity for the close binaries.

We explore the possibility that all close binaries, i.e. those with periods < 3 days, including contact binaries, are produced from initially wider binaries by the action of a triple companion through the medium of Kozai Cycles with Tidal Friction (KCTF).

The total mass of a distant star cluster is often derived from the virial theorem, using line-of-sight velocity dispersion measurements and half-light radii, under the implicit assumption that all stars are single (although it is known that most stars form part of binary systems). The components of binary stars exhibit orbital motion, which increases the measured velocity dispersion, resulting in a dynamical mass overestimation. In these proceedings we quantify the effect of neglecting the binary population on the derivation of the dynamical mass of a star cluster. We find that the presence of binaries plays an important role for clusters with total mass Mcl ≤ 105 M⊙; the dynamical mass can be significantly overestimated (by a factor of two or more). For the more massive clusters, with Mcl ≥ 105 M⊙, binaries do not affect the dynamical mass estimation significantly, provided that the cluster is significantly compact (half-mass radius ≤qslant 5 pc).

We present preliminary work on the formation scenario of blue straggler stars by mass transfer in binary systems. More precisely, using Smoothed Particle Hydrodynamics (SPH), we want to model only the outer parts of the stars in order to get a much greater spatial resolution of the mass transfer flow itself. The inner boundary conditions are achieved using the so-called ghost particles and by replacing the inner mass by a central point mass. Stability of this central point mass is crucial, and it is shown that we get reasonable results. These simulations should give us indications on which layers of the donor star are actually transferred to the other star as well as how mass is transferred and how it settles on the accretor. This work is aimed at getting distinct observational signatures which would help identifying the dominant formation mechanism of blue straggler stars.

Most stars are formed in a cluster or association, where the number density of stars can be high. This means that a large fraction of initially-single stars will undergo close encounters with other stars and/or exchange into binaries. We describe how such close encounters and exchange encounters can affect the properties of a planetary system around a single star. We define a singleton as a single star which has never suffered close encounters with other stars or spent time within a binary system. It may be that planetary systems similar to our own solar system can only survive around singletons. Close encounters or the presence of a stellar companion will perturb the planetary system, often leaving planets on tighter and more eccentric orbits. Thus planetary systems which initially resembled our own solar system may later more closely resemble some of the observed exoplanet systems.

Recent observations of the Galactic center revealed a nuclear disk of young OB stars, in addition to many similar outlying stars with higher eccentricities and/or high inclinations relative to the disk (some of them possibly belonging to a second disk). Binaries in such nuclear disks, if they exist in non-negligible fractions, could have a major role in the evolution of the disks through binary heating of this stellar system. We suggest that interactions with/in binaries may explain some (or all) of the observed outlying young stars in the Galactic center. Such stars could have been formed in a disk, and later on kicked out from it through binary related interactions, similar to ejection of high velocity runaway OB stars in young clusters throughout the galaxy.