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 12000 single stars and 12000 binaries 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 by 90% as 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 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 is lost, both from the current luminosity function and from the current mass fraction in white dwarfs. The model contains 20 blue stragglers 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 blue stragglers in M67.Comment: 32 pages, 17 figures, submitted to MNRA

A Hybrid N-Body Code Incorporating Algorithmic Regularization and Post-Newtonian Forces

We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's 'algorithmic' chain regularization scheme including post-Newtonian terms up to PN2.5 order. Stars moving beyond the chain are advanced using a fourth-order integrator with forces computed on a GRAPE board. Performance tests confirm that the hybrid code achieves better energy conservation, in less elapsed time, than the standard scheme and that it reproduces the orbits of stars tightly bound to the black hole with high precision. The hybrid code is applied to two sample problems: the effect of finite-N gravitational fluctuations on the orbits of the S-stars; and inspiral of an intermediate-mass black hole into the galactic center.Comment: 12 pages, 15 figures, accepted for publication in MNRA

Direct N-body Modelling of Stellar Populations: Blue Stragglers in M67

We present a state-of-the-art N-body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N-body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N-body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N = 10000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.Comment: 26 pages, 18 figures, accepted for publication in MNRA

Escaping stars from young low-N clusters

With the use of N-body calculations the amount and properties of escaping stars from low-N (N = 100 and 1000) young embedded star clusters prior to gas expulsion are studied over the first 5 Myr of their existence. Besides the number of stars also different initial radii and binary populations are examined as well as virialised and collapsing clusters. It is found that these clusters can loose substantial amounts (up to 20%) of stars within 5 Myr with considerable velocities up to more than 100 km/s. Even with their mean velocities between 2 and 8 km/s these stars will still be travelling between 2 and 30 pc during the 5 Myr. Therefore can large amounts of distributed stars in star-forming regions not necessarily be counted as evidence for the isolated formation of stars.Comment: 10 pages, 10 figures, accepted for publication by MNRA

The Formation and Evolution of Multiple Star Systems

Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are often stable over long times and yet may experience evolution of the internal orbital parameters. We describe an attempt to model the eccentricity change induced by the outer component using an averaging method, together with the effects due to tidal dissipation and apsidal motion acting on the inner binary. This treatment is adopted for systems with high induced eccentricity which gives rise to some interesting outcomes of significant period shrinkage

On the Temperature Dependence of the Casimir Effect

The temperature dependence of the Casimir force between a real metallic plate and a metallic sphere is analyzed on the basis of optical data concerning the dispersion relation of metals such as gold and copper. Realistic permittivities imply, together with basic thermodynamic considerations, that the transverse electric zero mode does not contribute. This results in observable differences with the conventional prediction, which does not take this physical requirement into account. The results are shown to be consistent with the third law of thermodynamics, as well as being consistent with current experiments. However, the predicted temperature dependence should be detectable in future experiments. The inadequacies of approaches based on {\it ad hoc} assumptions, such as the plasma dispersion relation and the use of surface impedance without transverse momentum dependence, are discussed.Comment: 14 pages, 3 eps figures, revtex4. New version includes clarifications and new reference. Accepted for publication in Phys. Rev.