Ratios of star cluster core and half-mass radii: a cautionary note on intermediate-mass black holes in star clusters

There is currently much interest in the possible presence of intermediate-mass black holes in the cores of globular clusters. Based on theoretical arguments and simulation results it has previously been suggested that a large core radius -- or particularly a large ratio of the core radius to half-mass radius -- is a promising indicator for finding such a black hole in a star cluster. In this study N-body models of 100000 stars with and without primordial binaries are used to investigate the long-term structural evolution of star clusters. Importantly, the simulation data is analysed using the same processes by which structural parameters are extracted from observed star clusters. This gives a ratio of the core and half-mass (or half-light) radii that is directly comparable to the Galactic globular cluster sample. As a result, it is shown that the ratios observed for the bulk of this sample can be explained without the need for an intermediate-mass black hole. Furthermore, it is possible that clusters with large core to half-light radius ratios harbour a black-hole binary (comprised of stellar mass black holes) rather than a single massive black hole. This work does not rule out the existence of intermediate-mass black holes in the cores of at least some star clusters.Comment: 14 pages, 7 figures, accepted for publication in MNRA

The Binary Second Sequence in Cluster Colour--Magnitude Diagrams

We show how the second sequence seen lying above the main sequence in cluster colour magnitude diagrams results from binaries with a large range of mass ratios and not just from those with equal masses. We conclude that the presence of a densely populated second sequence, with only sparse filling in between it and the single star main sequence, does not necessarily imply that binary mass ratios are close to unity.Comment: Accepted to MNRAS. 5 Pages including 3 figure

Populating the Galaxy with low-mass X-ray binaries

We perform binary population synthesis calculations to investigate the incidence of low-mass X-ray binaries and their birth rate in the Galaxy. We use a binary evolution algorithm that models all the relevant processes including tidal circularization and synchronization. Parameters in the evolution algorithm that are uncertain and may affect X-ray binary formation are allowed to vary during the investigation. We agree with previous studies that under standard assumptions of binary evolution the formation rate and number of black-hole low-mass X-ray binaries predicted by the model are more than an order of magnitude less than what is indicated by observations. We find that the common-envelope process cannot be manipulated to produce significant numbers of black-hole low-mass X-ray binaries. However, by simply reducing the mass-loss rate from helium stars adopted in the standard model, to a rate that agrees with the latest data, we produce a good match to the observations. Including low-mass X-ray binaries that evolve from intermediate-mass systems also leads to favourable results. We stress that constraints on the X-ray binary population provided by observations are used here merely as a guide as surveys suffer from incompleteness and much uncertainty is involved in the interpretation of results.Comment: 17 pages and 9 figures; accepted by MNRA

A direct N-body model of core-collapse and core oscillations

We report on the results of a direct N-body simulation of a star cluster that started with N = 200 000, comprising 195 000 single stars and 5 000 primordial binaries. The code used for the simulation includes stellar evolution, binary evolution, an external tidal field and the effects of two-body relaxation. The model cluster is evolved to 12 Gyr, losing more than 80% of its stars in the process. It reaches the end of the main core-collapse phase at 10.5 Gyr and experiences core oscillations from that point onwards -- direct numerical confirmation of this phenomenon. However, we find that after a further 1 Gyr the core oscillations are halted by the ejection of a massive binary comprised of two black holes from the core, producing a core that shows no signature of the prior core-collapse. We also show that the results of previous studies with N ranging from 500 to 100 000 scale well to this new model with larger N. In particular, the timescale to core-collapse (in units of the relaxation timescale), mass segregation, velocity dispersion, and the energies of the binary population all show similar behaviour at different N.Comment: 9 pages, 8 figures, accepted for publication in MNRA

The long and the short of it: modelling double neutron star and collapsar Galactic dynamics

The work presented here examines populations of double compact binary systems and tidally enhanced collapsars. We make use of BINPOP and BINKIN, two components of a recently developed population synthesis package. Results focus on correlations of both binary and spatial evolutionary population characteristics. Pulsar and long duration gamma-ray burst observations are used in concert with our models to draw the conclusions that: double neutron star binaries can merge rapidly on timescales of a few million years (much less than that found for the observed double neutron star population), common envelope evolution within these models is a very important phase in double neutron star formation, and observations of long gamma-ray burst projected distances are more centrally concentrated than our simulated coalescing double neutron star and collapsar Galactic populations. Better agreement is found with dwarf galaxy models although the outcome is strongly linked to the assumed birth radial distribution. The birth rate of the double neutron star population in our models range from 4-160 Myr^-1 and the merger rate ranges from 3-150 Myr^-1. The upper and lower limits of the rates results from including electron capture supernova kicks to neutron stars and decreasing the common envelope efficiency respectively. Our double black hole merger rates suggest that black holes should receive an asymmetric kick at birth.Comment: Accepted by MNRAS, 18 pages, 12 figures, 5 table

McScatter: a Simple Three-Body Scattering Package with Stellar Evolution

We describe a simple computer package which illustrates a method of combining stellar dynamics with stellar evolution. Though the method is intended for elaborate applications (especially the dynamical evolution of rich star clusters) it is illustrated here in the context of three-body scattering, i.e. interactions between a binary star and a field of single stars. We describe the interface between the dynamics and the two independent packages which describe the internal evolution of single stars and binaries. We also give an example application, and introduce a stand alone utility for the visual presentation of simulation results.Comment: 16 pages, Accepted for publication in New Astronomy. Source codes available at: http://manybody.org/manybody/McScatter.html and http://www.manybody.org/manybody/roche.htm

Evolution of binary stars and the effect of tides on binary populations

We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.Comment: 36 pages, 12 figures, to be published in the Monthly Notices of the Royal Astronomical Societ

Dynamical Interactions Make Hot Jupiters in Open Star Clusters

Explaining the origin and evolution of exoplanetary "hot Jupiters" remains a significant challenge. One possible mechanism for their production is planet-planet interactions, which produces hot Jupiters from planets born far from their host stars but near their dynamical stability limits. In the much more likely case of planets born far from their dynamical stability limits, can hot Jupiters can be formed in star clusters? Our N-body simulations of planetary systems inside star clusters answer this question in the affirmative, and show that hot Jupiter formation is not a rare event. We detail three case studies of the dynamics-induced births of hot Jupiters on highly eccentric orbits that can only occur inside star clusters. The hot Jupiters' orbits bear remarkable similarities to those of some of the most extreme exoplanets known: HAT-P-32 b, HAT-P-2 b, HD 80606 b and GJ 876 d. If stellar perturbations formed these hot Jupiters then our simulations predict that these very hot, inner planets are often accompanied by much more distant gas giants in highly eccentric orbits.Comment: 18 pages, 4 figure