Sverre J. Aarseth

The formation of a bound star cluster: from the Orion nebula cluster to the Pleiades

Summary Direct N-body calculations are presented of the formation of Galactic clusters using GasEx, which is a variant of the code Nbody6. The calculations focus on the possible evolution of the Orion Nebula Cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10 4 stars, and resembles the Pleiades Cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic-field sub-population. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations. The results have wide implications, also for the formation of globular clusters and the Galactic field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.

A complete N-body model of the old open cluster M67

The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here, we present the first truly direct N-body model for M67, evolved from zero age to 4 Gyr taking full account of cluster dynamics as well as stellar and binary evolution. Our preferred model starts with 36 000 stars (12 000 single stars and 12 000 binaries) and a total mass of nearly 19 000 M � , placed in a Galactic tidal field at 8.0 kpc from the Galactic Centre. Our choices for the initial conditions and for the primordial binary population are explained in detail. At 4 Gyr, the age of M67, the total mass has reduced to 2000 Mas a result of mass loss and stellar escapes. The mass and half-mass radius of luminous stars in the cluster are a good match to observations, although the model is more centrally concentrated than observations indicate. The stellar mass and luminosity functions (LFs) are significantly flattened by preferential escape of low-mass stars. We find that M67 is dynamically old enough that information about the initial mass function (IMF) is lost, both from the current LF and from the current mass fraction in white dwarfs (WDs). The model contains 20 blue stragglers (BSs) at 4 Gyr, which is slightly less than the 28 observed in M67. Nine are in binaries. The blue stragglers were formed by a variety of means and we find formation paths for the whole variety observed in M67. Both the primordial binary population and the dynamical cluster environment play an essential role in shaping the population. A substantial population of short-period primordial binaries (with periods less than a few days) is needed to explain the observed number of BSs in M67. The evolution and properties of two-thirds of the BSs, including all found in binaries, have been altered by cluster dynamics and nearly half would not have formed at all outside the cluster environment. On the other hand, the cluster environment is also instrumental in destroying potential BSs from the primordial binary population, so that the total number is in fact slightly smaller than what would be expected from evolving the same binary stars in isolation. Ke yw ords: stellar dynamics - methods: N-body simulations - binaries: close - blue stragglers - stars: evolution - open clusters and associations: general.

Accelerating nbody6 with graphics processing units

We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct

An implementation ofN-body chain regularization

N

Direct N-body modelling of stellar populations: blue stragglers in M67

-body simulations. Over the years, the

The Core Binary Fractions of Star Clusters from Realistic Simulations

N^2

Origin and ubiquity of short-period earth-like planets: Evidence for the sequential accretion theory of planet formation

nature of the direct force calculation has proved a barrier for extending the particle number. Following an early introduction of force polynomials and individual time-steps, the calculation cost was first reduced by the introduction of a neighbour scheme. After a decade of GRAPE computers which speeded up the force calculation further, we are now in the era of GPUs where relatively small hardware systems are highly cost-effective. A significant gain in efficiency is achieved by employing the GPU to obtain the so-called regular force which typically involves some 99 percent of the particles, while the remaining local forces are evaluated on the host. However, the latter operation is performed up to 20 times more frequently and may still account for a significant cost. This effort is reduced by parallel SSE/AVX procedures where each interaction term is calculated using mainly single precision. We also discuss further strategies connected with coordinate and velocity prediction required by the integration scheme. This leaves hard binaries and multiple close encounters which are treated by several regularization methods. The present nbody6-GPU code is well balanced for simulations in the particle range

Direct methods for N-Body simulations

10^4-2 \times 10^5

The dragon simulations: globular cluster evolution with a million stars

for a dual GPU system attached to a standard PC.

The Cambridge N-body lectures

The chain regularization method (Mikkola and Aarseth 1990) for high accuracy computation of particle motions in smallN-body systems has been reformulated. We discuss the transformation formulae, equations of motion and selection of a chain of interparticle vectors such that the critical interactions requiring regularization are included in the chain. The Kustaanheimo-Stiefel (KS) coordinate transformation and a time transformation is used to regularize the dominant terms of the equations of motion. The method has been implemented for an arbitrary number of bodies, with the option of external perturbations. This formulation has been succesfully tested in a generalN-body program for strongly interacting subsystems. An easy to use computer program, written inFortran, is available on request.