Stephen L. W. McMillan

Young massive star clusters

Young massive clusters (YMCs) are dense aggregates of young stars that form the fundamental building blocks of galaxies. Several examples exist in the Milky Way Galaxy and the Local Group, but they are particularly abundant in starburst and interacting galaxies. The few YMCs that are close enough to resolve are of prime interest for studying the stellar mass function and the ecological interplay between stellar evolution and stellar dynamics. The distant unresolved clusters may be effectively used to study the star-cluster mass function, and they provide excellent constraints on the formation mechanisms of young cluster populations. YMCs are expected to be the nurseries for many unusual objects, including a wide range of exotic stars and binaries. So far only a few such objects have been found in YMCs, although their older cousins, the globular clusters, are unusually rich in stellar exotica. In this review, we focus on star clusters younger than ∼100 Myr, more than a few current crossing times old, and m...

Formation and dynamical evolution of multiple stellar generations in globular clusters

We study the formation and dynamical evolution of clusters with multiple stellar generations. Observational studies have found that some globular clusters host a population of second generation (SG) stars which show chemical anomalies and must have formed from gas containing matter processed in the envelopes of first generation (FG) cluster stars. We study the SG formation process by means of 1D hydrodynamical simulations, starting from a FG already in place and assuming that the SG is formed by the gas ejected by the Asymptotic Giant Branch (AGB) stars. This gas collects in a cooling flow into the cluster core, where it forms SG stars. The SG subsystem emerging from this process is initially strongly concentrated in the cluster innermost regions and its structural properties are largely independent of the FG initial properties. We also present the results of a model in which pristine gas contributes to the SG formation. In this model a very helium-rich SG population and one with a moderate helium enrichment form; the resulting SG bimodal helium distribution resembles that observed for SG stars in NGC 2808. By means of N-body simulations, we then study the two-population cluster dynamical evolution and mass loss. In our simulations, a large fraction of FG stars are lost early in the cluster evolution due to the expansion and stripping of the cluster outer layers resulting from early mass loss associated with FG SN ejecta. The SG population, initially concentrated in the innermost cluster regions, is largely unscathed by this early mass loss, and this early evolution leads to values of the number ratio of SG to FG stars consistent with observations. We also demonstrate possible evolutionary routes leading to the loss of most of the FG population, leaving an SG-dominated cluster. As the cluster evolves and the two populations mix, the local ratio of SG to FG stars, initially a decreasing function of radius, tends to a constant value in the inner parts of the cluster. Until mixing is complete, the radial profile of this number ratio is characterized by a flat inner part and a declining portion in the outer cluster regions.

Formation of massive black holes through runaway collisions in dense young star clusters

A luminous X-ray source is associated with MGG 11—a cluster of young stars ∼200 pc from the centre of the starburst galaxy M 82 (refs 1, 2). The properties of this source are best explained by invoking a black hole with a mass of at least 350 solar masses (350 M[circdot]), which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive cluster (MGG 9) shows no evidence of such an intermediate-mass black hole, raising the issue of just what physical characteristics of the clusters can account for this difference. Here we report numerical simulations of the evolution and motion of stars within the clusters, where stars are allowed to merge with each other. We find that for MGG 11 dynamical friction leads to the massive stars sinking rapidly to the centre of the cluster, where they participate in a runaway collision. This produces a star of 800–3,000 M[circdot], which ultimately collapses to a black hole of intermediate mass. No such runaway occurs in the cluster MGG 9, because the larger cluster radius leads to a mass segregation timescale a factor of five longer than for MGG 11.

The Runaway Growth of Intermediate-Mass Black Holes in Dense Star Clusters

We study the growth rate of stars via stellar collisions in dense star clusters, calibrating our analytic calculations with direct N-body simulations of up to 65,536 stars, performed on the GRAPE family of special-purpose computers. We find that star clusters with initial half-mass relaxation times 25 Myr are dominated by stellar collisions, the first collisions occurring at or near the point of core collapse, which is driven by the segregation of the most massive stars to the cluster center, where they end up in hard binaries. The majority of collisions occur with the same star, resulting in the runaway growth of a supermassive object. This object can grow up to ~0.1% of the mass of the entire star cluster and could manifest itself as an intermediate-mass black hole (IMBH). The phase of runaway growth lasts until mass loss by stellar evolution arrests core collapse. Star clusters older than about 5 Myr and with present-day half-mass relaxation times 100 Myr are expected to contain an IMBH.

Star cluster ecology – IV. Dissection of an open star cluster: photometry

The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries is taken self-consistently into account. Initial conditions are chosen to represent relatively young Galactic open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations include a realistic mass function, primordial binaries and the external potential of the parent Galaxy. Our model clusters are generally significantly flattened by the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially because of the destruction of soft binaries, but increases later because lower mass single stars escape more easily than the more massive binaries. At late times, the cluster core is quite rich in giants and white dwarfs. There is no evidence for preferential evaporation of old white dwarfs. On the contrary, the white dwarfs formed are likely to remain in the cluster. Stars tend to escape from the cluster through the first and second Lagrange points, in the direction of and away from the Galactic Centre. Mass segregation manifests itself in our models well within an initial relaxation time. As expected, giants and white dwarfs are much more strongly affected by mass segregation than main-sequence stars. Open clusters are dynamically rather inactive. However, the combined effects of stellar mass-loss and evaporation of stars from the cluster potential drive the dissolution of a cluster on a much shorter time-scale than if these effects are neglected. The often-used argument that a star cluster is barely older than its relaxation time and therefore cannot be dynamically evolved is clearly in error for the majority of star clusters. An observation of a blue straggler in an eccentric orbit around an unevolved star or a blue straggler of more than twice the turn-off mass might indicate past dynamical activity. We find two distinct populations of blue stragglers: those formed above the main-sequence turn-off, and those which appear as blue stragglers as the clusters turn-off drops below the mass of the rejuvenated star.

Black Hole Mergers in the Universe

Mergers of black hole binaries are expected to release large amounts of energy in the form of gravitational radiation. However, binary evolution models predict merger rates that are too low to be of observational interest. In this Letter, we explore the possibility that black holes become members of close binaries via dynamical interactions with other stars in dense stellar systems. In star clusters, black holes become the most massive objects within a few tens of millions of years; dynamical relaxation then causes them to sink to the cluster core, where they form binaries. These black hole binaries become more tightly bound by superelastic encounters with other cluster members and are ultimately ejected from the cluster. The majority of escaping black hole binaries have orbital periods short enough and eccentricities high enough that the emission of gravitational radiation causes them to coalesce within a few billion years. We predict a black hole merger rate of about 1.6x10-7 yr-1 Mpc-3, implying gravity-wave detection rates substantially greater than the corresponding rates from neutron star mergers. For the first-generation Laser Interferometer Gravitational-Wave Observatory (LIGO-I), we expect about one detection during the first 2 years of operation. For its successor LIGO-II, the rate rises to roughly one detection per day. The uncertainties in these numbers are large. Event rates may drop by about an order of magnitude if the most massive clusters eject their black hole binaries early in their evolution.

A Neutron Star with a Massive Progenitor in Westerlund 1

We report the discovery of an X-ray pulsar in the young, massive Galactic star cluster Westerlund 1. We detected a coherent signal from the brightest X-ray source in the cluster, CXO J164710.2–455216, during two Chandra observations on 2005 May 22 and June 18. The period of the pulsar is 10.6107(1) s. We place an upper limit to the period derivative of u P 1M⊙. Taken together, the properties of the pulsar indicate that it is a magnetar. The rarity of slow X-ray pulsars and the position of CXO J164710.2–455216 only 1.6 ′ from the core of Westerlund 1 indicates that it is a member of the cluster with >99.97% confidence. Westerlund 1 contains 07V stars with initial masses Mi�35M⊙ and >50 post-main-sequence stars that indicate the cluster is 4±1 Myr old. Therefore, the progenitor to this pulsar had an initial mass Mi>40M⊙. This is the most secure result among a handful of observational limits to the masses of the progenitors to neutron stars. Subject headings: X-rays: stars — neutron stars — open clusters and associations: individual (Westerlund 1)

Abundance patterns of multiple populations in globular clusters: a chemical evolution model based on yields from AGB ejecta

A large number of spectroscopic studies have provided evidence of the presence of multiple populations in globular clusters by revealing patterns in the stellar chemical abundances. This paper is aimed at studying the origin of these abundance patterns. We explore a model in which second generation (SG) stars form out of a mix of pristine gas and ejecta of the first generation of asymptotic giant branch stars. We first study the constraints imposed by the spectroscopic data of SG stars in globular clusters on the chemical properties of the asymptotic and super asymptotic giant branch ejecta. With a simple one-zone chemical model, we then explore the formation of the SG population abundance patterns focussing our attention on the Na-O, Al-Mg anticorrelations and on the helium distribution function. We carry out a survey of models and explore the dependence of the final SG chemical properties on the key parameters affecting the gas dynamics and the SG formation process. Finally, we use our chemical evolution framework to build specific models for NGC 2808 and M4, two Galactic globular clusters which show different patterns in the Na–O and Mg–Al anticorrelation and have different helium distributions. We find that the amount of pristine gas involved in the formation of SG stars is a key parameter to fit the observed O–Na and Mg–Al patterns. The helium distribution function for these models is in general good agreement with the observed one. Our models, by shedding light on the role of different parameters and their interplay in determining the final SG chemical properties, illustrate the basic ingredients, constraints and problems encountered in this self-enrichment scenario which must be addressed by more sophisticated chemical and hydrodynamic simulations.

Multi-physics simulations using a hierarchical interchangeable software interface

Abstract We introduce a general-purpose framework for interconnecting scientific simulation programs using a homogeneous, unified interface. Our framework is intrinsically parallel, and conveniently separates all component numerical modules in memory. This strict separation allows automatic unit conversion, distributed execution of modules on different cores within a cluster or grid, and orderly recovery from errors. The framework can be efficiently implemented and incurs an acceptable overhead. In practice, we measure the time spent in the framework to be less than 1% of the wall-clock time. Due to the unified structure of the interface, incorporating multiple modules addressing the same physics in different ways is relatively straightforward. Different modules may be advanced serially or in parallel. Despite initial concerns, we have encountered relatively few problems with this strict separation between modules, and the results of our simulations are consistent with earlier results using more traditional monolithic approaches. This framework provides a platform to combine existing simulation codes or develop new physical solver codes within a rich “ecosystem” of interchangeable modules.

THE ECOLOGY OF STAR CLUSTERS AND INTERMEDIATE-MASS BLACK HOLES IN THE GALACTIC BULGE

We simulate the inner 100 pc of the Milky Way to study the formation and evolution of the population of star clusters and intermediate-mass black holes (IMBHs). For this study we perform extensive direct N-body simulations of the star clusters that reside in the bulge, and of the inner few tenth of parsecs of the supermassive black hole in the Galactic center. In our N-body simulations the dynamical friction of the star cluster in the tidal field of the bulge are taken into account via semianalytic solutions. The N-body calculations are used to calibrate a semianalytic model of the formation and evolution of the bulge. We find that similar to 10% of the clusters born within similar to 100 pc of the Galactic center undergo core collapse during their inward migration and form IMBHs via runaway stellar merging. After the clusters dissolve, these IMBHs continue their inward drift, carrying a few of the most massive stars with them. We predict that a region within similar to 10 pc of the supermassive black hole (SMBH) is populated by similar to 50 IMBHs of similar to 1000 M-circle dot. Several of these are still expected to be accompanied by some of the most massive stars from the star cluster. We also find that within a few milliparsecs of the SMBH there is a steady population of several IMBHs. This population drives the merger rate between IMBHs and the SMBH at a rate of about one per 10 Myr, sufficient to build the accumulated majority of mass of the SMBH. Mergers of IMBHs with SMBHs throughout the universe are detectable by LISA at a rate of about two per week.