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

Evolution of star clusters on eccentric orbits

We study the evolution of star clusters on circular and eccentric orbits using direct N-body simulations. We model clusters with initially N = 8k and 16k single stars of the same mass, orbiting around a point-mass galaxy. For each orbital eccentricity that we consider, we find the apogalactic radius at which the cluster has the same lifetime as the cluster with the same N on a circular orbit. We show that then, the evolution of bound particle number and half-mass radius is approximately independent of eccentricity. Secondly, when we scale our results to orbits with the same semimajor axis, we find that the lifetimes are, to first order, independent of eccentricity. When the results of Baumgardt and Makino for a singular isothermal halo are scaled in the same way, the lifetime is again independent of eccentricity to first order, suggesting that this result is independent of the galactic mass profile. From both sets of simulations, we empirically derive the higher order dependence of the lifetime on eccentricity. Our results serve as benchmark for theoretical studies of the escape rate from clusters on eccentric orbits. Finally, our results can be useful for generative models for cold streams and cluster evolution models that are confined to spherical symmetry and/or time-independent tides, such as Fokker-Planck models, Monte Carlo models, and (fast) semi-analytic models.FWN – Publicaties zonder aanstelling Universiteit Leide

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the 1-dimensional Newtonian gravitational three-body system (three masses on a line with $-1/r$ pairwise potential). We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change (with negative total energy). For two mass choices we have calculated 18000 full orbits (with initial states on a $100\times 180$ lattice on the Poincar\'e section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincar\'e maps for $10\times 18$ starting points. Our results show that the Poincar\'e section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: 1) There is a region of fast scattering, with a minimum of pairwise collisions and smooth dependence on initial values. 2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincar\'e section. For both 1) and 2) the initial and final states consists of a binary + single particle. 3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is the periodic Schubart orbit, whose stability turns out to correlate strongly with the global behavior.Comment: 24 pages of text (REVTEX 3.0) + 21 pages of figures. Figures are only available in paper form, ask for a preprint from the author

N-body simulations of gravitational dynamics

We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development. We briefly touch upon the history of N-body simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu

The mass-to-light ratio of rich star clusters

We point out a strong time-evolution of the mass-to-light conversion factor eta commonly used to estimate masses of unresolved star clusters from observed cluster spectro-photometric measures. We present a series of gas-dynamical models coupled with the Cambridge stellar evolution tracks to compute line-of-sight velocity dispersions and half-light radii weighted by the luminosity. We explore a range of initial conditions, varying in turn the cluster mass and/or density, and the stellar population's IMF. We find that eta, and hence the estimated cluster mass, may increase by factors as large as 3 over time-scales of 50 million years. We apply these results to an hypothetic cluster mass distribution function (d.f.) and show that the d.f. shape may be strongly affected at the low-mass end by this effect. Fitting truncated isothermal (Michie-King) models to the projected light profile leads to over-estimates of the concentration parameter c of delta c ~ 0.3 compared to the same functional fit applied to the projected mass density.Comment: 6 pages, 2 figures, to appear in the proceedings of the "Young massive star clusters", Granada, Spain, September 200

Periodic Orbits and Escapes in Dynamical Systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central "bumpy" black hole. When the energy reaches its escape value a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical Astronomy

Dense Stellar Populations: Initial Conditions

This chapter is based on four lectures given at the Cambridge N-body school "Cambody". The material covered includes the IMF, the 6D structure of dense clusters, residual gas expulsion and the initial binary population. It is aimed at those needing to initialise stellar populations for a variety of purposes (N-body experiments, stellar population synthesis).Comment: 85 pages. To appear in The Cambridge N-body Lectures, Sverre Aarseth, Christopher Tout, Rosemary Mardling (eds), Lecture Notes in Physics Series, Springer Verla

A MODEST review

We present an account of the state of the art in the fields explored by the research community invested in 'Modeling and Observing DEnse STellar systems'. For this purpose, we take as a basis the activities of the MODEST-17 conference, which was held at Charles University, Prague, in September 2017. Reviewed topics include recent advances in fundamental stellar dynamics, numerical methods for the solution of the gravitational N-body problem, formation and evolution of young and old star clusters and galactic nuclei, their elusive stellar populations, planetary systems, and exotic compact objects, with timely attention to black holes of different classes of mass and their role as sources of gravitational waves. Such a breadth of topics reflects the growing role played by collisional stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next decade, many revolutionary instruments will enable the derivation of positions and velocities of individual stars in the Milky Way and its satellites and will detect signals from a range of astrophysical sources in different portions of the electromagnetic and gravitational spectrum, with an unprecedented sensitivity. On the one hand, this wealth of data will allow us to address a number of long-standing open questions in star cluster studies; on the other hand, many unexpected properties of these systems will come to light, stimulating further progress of our understanding of their formation and evolution.Comment: 42 pages; accepted for publication in 'Computational Astrophysics and Cosmology'. We are much grateful to the organisers of the MODEST-17 conference (Charles University, Prague, September 2017). We acknowledge the input provided by all MODEST-17 participants, and, more generally, by the members of the MODEST communit

Deep water renewals in resurrection Bay Alaska

Resurrection Bay, a fjord estuary on the south-central Alaskan coastline is approximately 30 km in length and 4.5 km in width. An inner basin (290 m) is separated from the outer fjord and the continental shelf of the Gulf of Alaska by a sill at 185 m. Hydrographic data were obtained from five stations along the length of the fjord at approximately monthly intervals during 1973 to 1975. During 1973 current meters were installed in the inner basin at depths of 46, 93, 185, and 286 m during March to May, and again during September to October. Two stations were selected to represent oceanographic conditions in the inner fjord (Res-2.5) and adjacent marine source waters (Res-4). Data discussed relate to these two stations