Dynamical evolution of rotating stellar systems - II. Post-collapse, equal mass system

We present the first post core collapse models of initially rotating star clusters, using the numerical solution of an orbit-averaged 2D Fokker-Planck equation. Based on the code developed by Einsel & Spurzem (1999), we have improved the speed and the stability and included the steady three-body binary heating source. We have confirmed that rotating clusters, whether they are in a tidal field or not, evolve significantly faster than non-rotating ones. Consequences for observed shapes, density distribution, and kinematic properties of young and old star clusters are discussed. The results are compared with gaseous and 1D Fokker-Planck models in the non-rotating case.Comment: 12 pages (MNLaTeX), 17 Postscript figures, Submitted to MNRA

New Evolutionary Synthesis code. An application to the irregular galaxy NGC 1560

We have developed a new evolutionary synthesis code, which incorporates the output from chemical evolution models. We compare results of this new code with other published codes, and we apply it to the irregular galaxy NGC 1560 using sophisticated chemical evolution models. The code makes important contributions in two areas: a) the building of synthetic populations with time-dependent star formation rates and stellar populations of different metallicities; b) the extension of the set of stellar tracks from the Geneva group by adding the AGB phases for $m_i/M_\odot \geq 0.8$ as well as the very low mass stars. Our code predicts spectra, broad band colors, and Lick indices by using a spectra library, which cover a more complete grid of stellar parameters. The application of the code with the chemical models to the galaxy NGC 1560 constrain the star formation age for its stellar population around 10.0 Gy.Comment: 10 pages, 15 figures, submited to A&

Solving procedure for a twenty-five diagonal coefficient matrix: direct numerical solutions of the three dimensional linear Fokker-Planck equation

We describe an implicit procedure for solving linear equation systems resulting from the discretization of the three dimensional (seven variables) linear Fokker-Planck equation. The discretization of the Fokker-Planck equation is performed using a twenty-five point molecule that leads to a coefficient matrix with equal number of diagonals. The method is an extension of Stone's implicit procedure, includes a vast class of collision terms and can be applied to stationary or non stationary problems with different discretizations in time. Test calculations and comparisons with other methods are presented in two stationary examples, including an astrophysical application for the Miyamoto-Nagai disk potential for a typical galaxy.Comment: 20 pages, RevTex, no proofreading, accepted in Journal of Computational Physic

Coupling emitted light and chemical yields from stars: a basic constraint to population synthesis models of galaxies

In this paper we emphasize the close connection between the chemical and spectrophotometric evolution of stellar systems: Chemical yields from stars correspond to a precise fraction of their emitted light. We translate this concept quantitatively. Starting from simple stellar populations, we derive useful analytical relations to calculate the stellar fuel consumption (emitted light) as a function of basic quantities predicted by stellar models, i.e. the mass of the core and the chemical composition of the envelope. The final formulas explicate the relation between integrated light contribution (total or limited to particular evolutionary phases), chemical yields and stellar remnants. We test their accuracy in the case of low- and intermediate-mass stars, and indicate the way to extend the analysis to massive stars. This formalism provides an easy tool to check the internal consistency between the different stellar inputs adopted in galaxy models: The fuel computed by means of the analytical formulas (corresponding to a given set of chemical yields) should be compared to the exact values given by the luminosity integration along the stellar evolutionary tracks or isochrones (corresponding to a given set of spectrophotometric models). Only if both estimates of the fuel are similar, the stellar inputs can be considered self-consistent in terms of their energetics. This sets an important requirement to galaxy models, also in consideration of the fact that different sources of input stellar data are frequently used to model their spectro-photometric and chemical evolution.Comment: 17 pages, 7 figures, 3 tables, accepted for publication in A&

Higher order moment models of dense stellar systems: Applications to the modeling of the stellar velocity distribution function

Dense stellar systems such as globular clusters, galactic nuclei and nuclear star clusters are ideal loci to study stellar dynamics due to the very high densities reached, usually a million times higher than in the solar neighborhood; they are unique laboratories to study processes related to relaxation. There are a number of different techniques to model the global evolution of such a system. In statistical models we assume that relaxation is the result of a large number of two-body gravitational encounters with a net local effect. We present two moment models that are based on the collisional Boltzmann equation. By taking moments of the Boltzmann equation one obtains an infinite set of differential moment equations where the equation for the moment of order $n$ contains moments of order $n+1$. In our models we assume spherical symmetry but we do not require dynamical equilibrium. We truncate the infinite set of moment equations at order $n=4$ for the first model and at order $n=5$ for the second model. The collisional terms on the right-hand side of the moment equations account for two-body relaxation and are computed by means of the Rosenbluth potentials. We complete the set of moment equations with closure relations which constrain the degree of anisotropy of our model by expressing moments of order $n+1$ by moments of order $n$. The accuracy of this approach relies on the number of moments included from the infinite series. Since both models include fourth order moments we can study mechanisms in more detail that increase or decrease the number of high velocity stars. The resulting model allows us to derive a velocity distribution function, with unprecedented accuracy, compared to previous moment models.Comment: Accepted for publication by MNRAS after minor correction

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

Hyades dynamics from N-body simulations: Accuracy of astrometric radial velocities from Hipparcos

The internal velocity structure in the Hyades cluster as seen by Hipparcos is compared with realistic N-body simulations using the NBODY6 code, which includes binary interaction, stellar evolution and the Galactic tidal field. The model allows to estimate reliably the accuracy of astrometric radial velocities in the Hyades as derived by Lindegren et al. (2000) and Madsen et al. (2002) from Hipparcos data, by applying the same estimation procedure on the simulated data. The simulations indicate that the current cluster velocity dispersion decreases from 0.35 km/s at the cluster centre to a minimum of 0.20 km/s at 8 pc radius (2-3 core radii), from where it slightly increases outwards. A clear negative correlation between dispersion and stellar mass is seen in the central part of the cluster but is almost absent beyond a radius of 3 pc. It follows that the (internal) standard error of the astrometric radial velocities relative to the cluster centroid may be as small as 0.2 km/s for a suitable selection of stars, while a total (external) standard error of 0.6 km/s is found when the uncertainty of the bulk motion of the cluster is included. Attempts to see structure in the velocity dispersion using observational data from Hipparcos and Tycho-2 are inconclusive.Comment: 12 pages, accepted by A&

N-body Models of Rotating Globular Clusters

We have studied the dynamical evolution of rotating globular clusters with direct $N$-body models. Our initial models are rotating King models; we obtained results for both equal-mass systems and systems composed out of two mass components. Previous investigations using a Fokker-Planck solver have revealed that rotation has a noticeable influence on stellar systems like globular clusters, which evolve by two-body relaxation. In particular, it accelerates their dynamical evolution through the gravogyro instability. We have validated the occurence of the gravogyro instability with direct $N$-body models. In the case of systems composed out of two mass components, mass segregation takes place, which competes with the rotation in the acceleration of the core collapse. The "accelerating" effect of rotation has not been detected in our isolated two-mass $N$-body models. Last, but not least, we have looked at rotating $N$-body models in a tidal field within the tidal approximation. It turns out that rotation increases the escape rate significantly. A difference between retrograde and prograde rotating star clusters occurs with respect to the orbit of the star cluster around the Galaxy, which is due to the presence of a ``third integral'' and chaotic scattering, respectively.Comment: 16 pages, 17 figures, accepted by MNRA

A WFPC2 Study of the Resolved Stellar Population of the Pegasus Dwarf Irregular Galaxy (DDO 216)

The stellar population of the Pegasus dwarf irregular galaxy is investigated in images taken in the F439W (B), F555W (V), and F814W (I) bands with WFPC2. These and ground-based data are combined to produce color-magnitude diagrams which show the complex nature of the stellar population in this small galaxy. A young (< 0.5 Gyr) main sequence stellar component is present and clustered in two centrally-located clumps, while older stars form a more extended disk or halo. The colors of the main sequence require a relatively large extinction of A_V = 0.47 mag. The mean color of the well-populated red giant branch is relatively blue, consistent with a moderate metallicity young, or older, metal-poor stellar population. The red giant branch also has significant width in color, implying a range of stellar ages and/or metallicities. A small number of extended asymptotic giant branch stars are found beyond the red giant branch tip. Near the faint limits of our data is a populous red clump superimposed on the red giant branch. Efforts to fit self-consistent stellar population models based on the Geneva stellar evolution tracks yield a revised distance of 760 kpc. Quantitative fits to the stellar population are explored as a means to constrain the star formation history. The numbers of main sequence and core helium-burning blue loop stars require that the star formation rate was higher in the recent past, by a factor of 3-4 about 1 Gyr ago. Unique results cannot be obtained for the star formation history over longer time baselines without better information on stellar metallicities and deeper photometry. The youngest model consistent with the data contains stars with constant metallicity of Z = 0.001 which mainly formed 2-4 Gyr ago. Even at its peak of star forming activity, the Pegasus dwarf most likely remained relatively dim with M_V ~ -14.Comment: 46 pages, 16 figures, 1 tabl