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A unified N-body and statistical treatment of stellar dynamics. III - Early postcollapse evolution of globular clusters

The period immediately following the core collapse phase in the evolution of a globular cluster is studied using a hybrid N-body/Fokker-Planck stellar dynamical code. Several core oscillations of the type predicted in earlier work are seen. The oscillations are driven by the formation, hardening, and ejection of binaries by three-body processes, and appear to decay on a timescale of about 10 to the 7th yr, for the choice of 'typical' cluster parameters made here. There is no evidence that they are gravothermal in nature. The mechanisms responsible for the decay are discussed in some detail. The distribution of hard binaries produced by the oscillations is compared with theoretical expectations and the longer term evolution of the system is considered.

Mcmillan, S. L. W.↗

Rates of collapse and evaporation of globular clusters

Observational estimates of the dynamical relaxation times of Galactic globular clusters are used here to estimate the present rate at which core collapse and evaporation are occurring in them. A core collapse rate of 2 +/- 1 per Gyr is found, which for a Galactic age of about 12 Gyr agrees well with the fact that 27 clusters have surface brightness profiles with the morphology expected for the postcollapse phase. A destruction and evaporation rate of 5 +/- 3 per Gyr is found, suggesting that a significant fraction of the Galaxy's original complement of globular clusters have perished through the combined effects of mechanisms such as relaxation-driven evaporation and shocking due to interaction with the Galactic disk and bulge.

Hut, Piet↗

Dynamics of the intermediate-age elliptical LMC cluster NGC 1978

BV CCD images and echelle spectra of 35 giants are used to examine the internal dynamics of the elliptical LMC cluster NGC 1978. Projected radii for the giants range from 1.4 to 20.0, and the mean estimated stellar velocity uncertainty is 1.6 km/s; the mean cluster velocity is 293.3 +/-1.0 km/s. BV profiles were constructed to projected radii of greater than 100 pc. The single-mass models provided better agreement with the surface photometry. Among multimass models, there is slightly better agreement seen for the models with shallow mass functions. The nonrotating model was found to be in better agreement with the kinematic data, although the rotating models could not be completely ruled out. No morphological evidence for a merger was found.

Fischer, Philippe↗

Dynamics and Thermodynamics of Dense and Dilute Clusters of Drops

Collective drop behavior is encountered in sprays produced for a variety of applications. The existence of clusters of drops indicates that the interaction among the drops is important in determining the dynamics of the drops because the drop proximity changes the flow around the individual drops in a way that affects the drag on each drop. Additionally, if there is a phase change between the liquid drops and the gaseous surroundings (either evaporation or condensation), this will also influence the flow around the individual drops; and phase change is also affected by the drop proximity. What will be discussed are studies of collections of drops where the dynamics and thermodynamics of the drops are coupled. This means the modification of the drag force due to the drop number density, the evaporation rate and the slip velocity are all taken into account. In turn, the enhancement in the evaporation rate due to the slip velocity , and the hindering of evaporation due to the drop proximity are also part of the models.

thermodynamics↗

The curvature of radio jets and tails in the intracluster media of Abell 1446 and 2220

X-ray observations are reported for two rich clusters which contain prominent tailed radio galaxies. These X-ray data are used as probes of the cluster gas to explore mechanisms which may distort radio jets and tails. A nonrelativistic hydrodynamic flow model is invoked to examine the plasma beam parameters needed to bend the radio streams in a manner consistent with the radio and X-ray data. Within the context of this model, the wide-angle tailed radio structure of 1159 + 583 in A1446 is explained by a combination of a buoyancy pressure gradient in the cluster gas and dynamic pressure arising from slow galaxy motion (200 km/sec). The second cluster observed, A2220, contains a clumped X-ray structure with peaks near two dominant galaxies. The strongly bent radio jets of 1638 + 538 (associated with one of the bright galaxies) are consistent with about 1000 km/sec motion, possibly in a binary orbit, through the X-ray emitting cluster gas; a curved feature in the northern tail, however, may be attributable to buoyancy forces. These X-ray data also suggest that the radio jets and tails are thermally confined by the hot intracluster media.

Burns, J. O.↗

Quasars in rich galaxy clusters

The evolution of AGN activity in rich clusters of galaxies is found to be approximately 5 times more rapid than that in poor clusters. This rapid evolution may be driven by evolution in the dynamics of galaxy cluster cores. Results from our spectroscopic studies of galaxies associated with quasars are consistent with this scenario, in that bright AGN are preferentially found in regions of lower velocity dispersion. Alternately, the evolution may be driven by formation of a dense intra-cluster medium (ICM). Galaxies close to quasars in rich cluster cores are much bluer (presumably gas rich) than galaxies in the cores of other rich clusters, in support of this model.

Ellingson, Erica↗

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Melott, Adrian L.↗

Dynamic Harris current sheet thickness from Cluster current density and plasma measurements

We use the first accurate measurements of current densities in the plasma sheet to calculate the half-thickness and position of the current sheet as a function of time. Our technique assumes a Harris current sheet model, which is parameterized by lobe magnetic field B(o), current sheet half-thickness h, and current sheet position z(sub o). Cluster measurements of magnetic field, current density, and plasma pressure are used to infer the three parameters as a function of time. We find that most long timescale (6-12 hours) current sheet crossings observed by Cluster cannot be described by a static Harris current sheet with a single set of parameters B(sub o), h, and z(sub o). Noting the presence of high-frequency fluctuations that appear to be superimposed on lower frequency variations, we average over running 6-min intervals and use the smoothed data to infer the parameters h(t) and z(sub o)(t), constrained by the pressure balance lobe magnetic field B(sub o)(t). Whereas this approach has been used in previous studies, the spatial gnuhen& now provided by the Cluster magnetometers were unavailable or not well constrained in earlier studies. We place the calculated hdf&cknessa in a magnetospheric context by examining the change in thickness with substorm phase for three case study events and 21 events in a superposed epoch analysis. We find that the inferred half-thickness in many cases reflects the nominal changes experienced by the plasma sheet during substorms (i.e., thinning during growth phase, thickening following substorm onset). We conclude with an analysis of the relative contribution of (Delta)B(sub z)/(Delta)X to the cross-tail current density during substorms. We find that (Delta)B(sub z)/(Delta)X can contribute a significant portion of the cross-tail c m n t around substorm onset.

Thompson, S. M.↗

A unified N-body and statistical treatment of stellar dynamics. I - The hybrid code. II - Applications to globular cluster cores

A unified N-body and statistical treatment of stellar dynamics is developed and applied to the late stages of core collapse and early stages of post collapse evolution in globular clusters. A 'hybrid' computer code is joined to a direct N-body code which is used to calculate exactly the behavior of particles in the inner spatial region, and the combination is used to follow particles statistically in the outer spatial region. A transition zone allows the exchange of particles and energy between the two regions. The main application results include: formation of a hard central binary system, reversal of core collapse and expansion due to the heat input from this binary, ejection of the binary from the core, and recollapse of the core; density profiles that form a one-parameter sequence during the core oscillations; and indications that these oscillations will eventually cease.

Mcmillan, S. L. W.↗

The morphology of star clusters in the SMC

The projected ellipticities of 34 populous SMC star clusters have been derived by means of PDS 1010A scans and a computer interactive method of reduction implemented on an Apollo 570 workstation. A pair of J and R plates taken with the 1.2 m UK Schmidt telescope in Australia were used. Radial ellipticity variations within individual globular clusters seem to be a common phenomenon for the SMC clusters, similar to that observed in the LMC clusters where the innerparts are more elliptical than the outer ones in 95 percent of the cases. The derived ellipticities which correspond to the innermost part of the cluster at radial distances near to half-mass radii have been found to be statistically more elliptical than those of the LMC, known to be more elliptical than those of the Galaxy. The dynamical masses of the clusters seem to correlate with ellipticities supporting the hypothesis that, either the gravitational field of the parent galaxy being a dominant factor affect slower the shape of the high mass clusters and/or the most massive clusters, being dynamically younger, retain their original shape.

Kontizas, E.↗

Using x ray images to detect substructure in a sample of 40 Abell clusters

Using a method for constraining the dynamical state of a galaxy cluster by examining the moments of its x-ray surface brightness distribution, we determine the statistics of cluster substructure for a sample of 40 Abell clusters. Using x-ray observations from the Einstein Observatory Imaging Proportional Counter (IPC), we measure the first moment M1(r), the ellipsoidal orientation angle theta2(r), and the axial ratio eta(r) at several different radii in the cluster. We determine the effects of systematics such as x-ray point source emission, telescope vignetting, Poisson noise, and characteristics of the IPC by measuring the same parameters on an ensemble of simulated cluster images. Due to the small band-pass of the IPC, the ICM emissivity is nearly independent of temperature so the intensity at each point in the IPC images is simply proportional to the emission measure calculated along the line of sight through the cluster (e.g. Fabricant et al. 1980). Therefore, barring a change superposition of two x-ray emitting clusters, a significant variation in the image centroid M1(r) as a function of radius indicates that the center of mass of the intra-cluster medium (ICM) varies with radius. We argue that such a configuration (essentially an m = 1 component in the ICM density distribution) is a non-equilibrium component; it results from an off-center subclump or a recent merger in the ICM.

Mohr, J. J.↗

An initial perspective of S-asteroid subtypes within asteroid families

Many main belt asteroids cluster around certain values of semi-major axis (a), inclination (i), and eccentricity (e). Hirayama was the first to notice these concentrations which he interpreted as evidence of disruptions of larger parent bodies. He called these clusters 'asteroid families'. The term 'families' is increasingly reserved for genetic associations to distinguish them from clusters of unknown or purely dynamical origin (e.g. the Phocaea cluster). Members of a genetic asteroid family represent fragments derived from various depths within the original parent planetesimal. Thus, family members offer the potential for direct examination of the interiors of parent bodies which have undergone metamorphism and differentiation similar to that occurring in the inaccessible interiors of terrestrial planets. The differentiation similar to that occurring in the inaccessible interiors of terrestrial planets. The condition that genetic family members represent the fragments of a parent object provides a critical test of whether an association (cluster in proper element space) is a genetic family. Compositions (types and relative abundances of materials) of family members must permit the reconstruction of a compositionally plausible parent body. The compositions of proposed family members can be utilized to test the genetic reality of the family and to determine the type and degree of internal differentiation within the parent planetesimal. The interpretation of the S-class mineralogy provides a preliminary evaluation of family memberships. Detailed mineralogical and petrological analysis was done based on the reflectance spectra of 39 S-type asteroids. The result is a division of the S-asteroid class into seven subtypes based on compositional differences. These subtypes, designated S(I) to S(VII), correspond to surface silicate assemblages ranging from monomineralic olivine (dunites) through olivine-pyroxene mixtures to pure pyroxene or pyroxene-feldspar mixtures (basalts). The most general conclusion is that the S-asteroids cannot be treated as a single group of objects without greatly oversimplifying their properties. Each S-subtype needs to be treated as an independent group with a distinct evolutionary history.

Kelley, M. S.↗

Very low mass stars and white dwarfs in NGC 6397

Deep Wide Field/Planetary Camera 2 (WFPC2) images in wide bands centered at 606 and 802 nm were taken with the Hubble Space Telescope (HST) 4.6 min from the center of the galactic globular cluster NGC 6397. The images were used to accurately position approximately 2120 stars detected in the field on a color magnitude diagram down to a limiting magnitude m(sub 814) approximately = m(sub I) approximately = 26 determined reliably and solely by counting statistics. A white dwarf sequence and a rich, narrow cluster main sequence are detected for the first time, the latter stretching from m(sub 814) = 18.5 to m(sub 814) = 24.0 where it becomes indistinguishable from the field population. Two changes of slope of the main sequence at m(sub 814) approximately = 20 and m(sub 814) approximately = 22.5 are evident. The corresponding luminosity function increases slowly from M(sub 814) approximately = 6.5 to 8.5 are expected from ground-based observations but then drops sharply from there dwon to the measurement limit. The corresponding mass function obtained bu using the only presently available mass-luminosity function for the cluster's metallicity rises to a plateau between approximately 0.25 and approximately 0.15 solar mass, but drops toward the expected mass limit of the normal hydrogen burning main sequence at approximately 0.1 solar mass. This result is in clear contrast to that obtained from the ground and implies either a substantial modification of the cluster's initial mass function due to dynamical evolution in its lifetime, or that very low mass stars are not produced in any dynamically significant amount by clusters of this type. The white dwarf sequence is in reasonable agreement with a cooling sequence of models of mass 0.5 solar mass at the canonical distance of NGC 6397 with a scatter that is most likely due to photometric errors, but may also reflect real differences in mass or chemical composition. Contamination from unresolved galaxies, which cannot be reliably identified with our filters, makes it difficult to meaningfully compare the observed white dwarf luminosity function with its theoretical counterpart.

Paresce, Francesco↗

Compact objects in globular clusters

The recent flood of progress, both observational and theoretical, relating to compact objects in globular clusters is reviewed. These new results pose a number of problems relating to the stellar populations and dynamics of the clusters.

Bailyn, Charles D.↗

Studies of X-ray clusters of galaxies/intergalactic plasmas

Intergalactic plasmas were investigated from both an observational and theoretical point of view. A multiobject spectrometer, the MX spectrograph was used to obtain detailed dynamical information on clusters of galaxies; this information was then compared with X ray emission from hot gas in these clusters. Several spectra of galaxies are presented, and data reduction of the spectra was discussed. The existence of quasar winds in Seyfert galaxies and the interaction between such a wind and the interstellar medium also were considered.

Scott, J. S.↗

Disentangling Structures in the Cluster of Galaxies Abell 133

A dynamical analysis of the structure of the cluster of galaxies Abell 133 will be presented using multi-wavelength data combined from multiple space and earth based observations. New and familiar statistical clustering techniques are used in combination in an attempt to gain a fully consistent picture of this interesting nearby cluster of galaxies. The type of analysis presented should be typical of cluster studies in the future, especially those to come from the surveys like the Sloan Digital Sky Survey and the 2DF.

Way, Michael J.↗