What is the Temperature Dependence of the Casimir Effect?

There has been recent criticism of our approach to the Casimir force between real metallic surfaces at finite temperature, saying it is in conflict with the third law of thermodynamics and in contradiction with experiment. We show that these claims are unwarranted, and that our approach has strong theoretical support, while the experimental situation is still unclear.Comment: 6 pages, REVTeX, final revision includes two new references and related discussio

On the origin of the distribution of binary-star periods

Pre-main sequence and main-sequence binary systems are observed to have periods, P, ranging from one day to 10^(10) days and eccentricities, e, ranging from 0 to 1. We pose the problem if stellar-dynamical interactions in very young and compact star clusters may broaden an initially narrow period distribution to the observed width. N-body computations of extremely compact clusters containing 100 and 1000 stars initially in equilibrium and in cold collapse are preformed. In all cases the assumed initial period distribution is uniform in the narrow range 4.5 < log10(P) < 5.5 (P in days) which straddles the maximum in the observed period distribution of late-type Galactic-field dwarf systems. None of the models lead to the necessary broadening of the period distribution, despite our adopted extreme conditions that favour binary--binary interactions. Stellar-dynamical interactions in embedded clusters thus cannot, under any circumstances, widen the period distribution sufficiently. The wide range of orbital periods of very young and old binary systems is therefore a result of cloud fragmentation and immediate subsequent magneto-hydrodynamical processes operating within the multiple proto-stellar system.Comment: 11 pages, 4 figures, ApJ, in pres

Star Clusters

This review concentrates almost entirely on globular star clusters. It emphasises the increasing realisation that few of the traditional problems of star cluster astronomy can be studied in isolation: the influence of the Galaxy affects dynamical evolution deep in the core, and the spectrum of stellar masses; in turn the evolution of the core determines the highest stellar densities, and the rate of encounters. In this way external tidal effects indirectly influence the formation and evolution of blue stragglers, binary pulsars, X-ray sources, etc. More controversially, the stellar density appears to influence the relative distribution of normal stars. In the opposite sense, the evolution of individual stars governs much of the early dynamics of a globular cluster, and the existence of large numbers of primordial binary stars has changed important details of our picture of the dynamical evolution. New computational tools which will become available in the next few years will help dynamical theorists to address these questions.Comment: 10 pages, 3 figures, Te

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.

Analytical and Numerical Verification of the Nernst Theorem for Metals

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersion model gives consistent results for the Casimir free energy at low temperatures. Specifically, for the free energy near T=0 we find the leading term to be proportional to T^2 and the next-to-leading term proportional to T^{5/2}. These terms give rise to zero Casimir entropy as T approaches zero, and is thus in accordance with Nernst's theorem.Comment: 19 pages latex, 3 figures. v4: Figures updated. This is the final version, accepted for publication in Physical Review

Casimir energy and entropy between dissipative mirrors

We discuss the Casimir effect between two identical, parallel slabs, emphasizing the role of dissipation and temperature. Starting from quite general assumptions, we analyze the behavior of the Casimir entropy in the limit T->0 and link it to the behavior of the slab's reflection coefficients at low frequencies. We also derive a formula in terms of a sum over modes, valid for dissipative slabs that can be interpreted in terms of a damped quantum oscillator.Comment: 8 pages, 1 figur

A pilgrimage to gravity on GPUs

In this short review we present the developments over the last 5 decades that have led to the use of Graphics Processing Units (GPUs) for astrophysical simulations. Since the introduction of NVIDIA's Compute Unified Device Architecture (CUDA) in 2007 the GPU has become a valuable tool for N-body simulations and is so popular these days that almost all papers about high precision N-body simulations use methods that are accelerated by GPUs. With the GPU hardware becoming more advanced and being used for more advanced algorithms like gravitational tree-codes we see a bright future for GPU like hardware in computational astrophysics.Comment: To appear in: European Physical Journal "Special Topics" : "Computer Simulations on Graphics Processing Units" . 18 pages, 8 figure

Phase transitions in simplified models with long-range interactions

We study the origin of phase transitions in some simplified models with long range interactions. For the ring model, we show that a possible new phase transition predicted in a recent paper by Nardini and Casetti from an energy landscape analysis does not occur. Instead of such phase transitions we observe a sharp, although without any non-analiticity, change from a core-halo to an only core configuration in the spatial distribution functions for low energies. By introducing a new class of solvable simplified models without any critical points in the potential energy, we show that a similar behaviour to the ring model is obtained, with a first order phase transition from an almost homogeneous high energy phase to a clustered phase, and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features of the simplified models, and show that the first order phase transition comes from the maximization of the entropy of the system as a function of energy an an order parameter, as previously discussed by Kastner, which seems to be the main mechanism causing phase transitions in long-range interacting systems

N-body models of globular clusters: metallicity, half-light radii and mass-to-light ratios

Size differences of approx. 20% between red (metal-rich) and blue (metal-poor) sub-populations of globular clusters have been observed, generating an ongoing debate as to weather these originate from projection effects or the difference in metallicity. We present direct N-body simulations of metal-rich and metal-poor stellar populations evolved to study the effects of metallicity on cluster evolution. The models start with N = 100000 stars and include primordial binaries. We also take metallicity dependent stellar evolution and an external tidal field into account. We find no significant difference for the half-mass radii of those models, indicating that the clusters are structurally similar. However, utilizing observational tools to fit half-light (or effective) radii confirms that metallicity effects related to stellar evolution combined with dynamical effects such as mass segregation produce an apparent size difference of 17% on average. The metallicity effect on the overall cluster luminosity also leads to higher mass-to-light ratios for metal-rich clusters.Comment: 14 pages, 10 figures, accepted for publication in MNRA

Shape parameters of Galactic open clusters

(abridged) In this paper we derive observed and modelled shape parameters (apparent ellipticity and orientation of the ellipse) of 650 Galactic open clusters identified in the ASCC-2.5 catalogue. We provide the observed shape parameters of Galactic open clusters, computed with the help of a multi-component analysis. For the vast majority of clusters these parameters are determined for the first time. High resolution ("star by star") N-body simulations are carried out with the specially developed $\phi$GRAPE code providing models of clusters of different initial masses, Galactocentric distances and rotation velocities. The comparison of models and observations of about 150 clusters reveals ellipticities of observed clusters which are too low (0.2 vs. 0.3), and offers the basis to find the main reason for this discrepancy. The models predict that after $\approx 50$ Myr clusters reach an oblate shape with an axes ratio of $1.65:1.35:1$, and with the major axis tilted by an angle of $q_{XY} \approx 30^\circ$ with respect to the Galactocentric radius due to differential rotation of the Galaxy. Unbiased estimates of cluster shape parameters require reliable membership determination in large cluster areas up to 2-3 tidal radii where the density of cluster stars is considerably lower than the background. Although dynamically bound stars outside the tidal radius contribute insignificantly to the cluster mass, their distribution is essential for a correct determination of cluster shape parameters. In contrast, a restricted mass range of cluster stars does not play such a dramatic role, though deep surveys allow to identify more cluster members and, therefore, to increase the accuracy of the observed shape parameters.Comment: 13 pages, 12 figures, accepted for publication in Astronomy and Astrophysic