Stars Of Different Masses Research Articles

Dynamics of Spherical Stellar Systems: Properties of Theoretical Models, and Comparison with Clusters and Elliptical Galaxies.

view Abstract Citations (2) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dynamics of Spherical Stellar Systems: Properties of Theoretical Models, and Comparison with Clusters and Elliptical Galaxies. Michie, Richard W. Abstract A wide range of spherical models are now available and result from a distribution function which for the inner regions is obtained from the Boltzmann equation with encounters. It is assumed that encounters and orbital mixing were important in the early stages of the formation and development of the star clusters and elliptical galaxies, and, since this time period, the structure of these systems has not significantly changed. The orbital mixing allows an extension of the distribution function to the regions far from the center, where mathematically it satisfies the collisionless Boltzmann equation. The gravitational potential is obtained from Poisson's equation. The stellar orbits are not restricted to an isotropic velocity distribution everywhere the models range from complete isotropy to highly radial orbits. While the distribution function is obtained for stars of different mass, the comparison with observation has assumed all stars to have the average stellar mass. In a log density versus log distance plot, it is found that for certain degrees of velocity space anisotropy there is an inflection in the curve, and this is a result of the orbits becoming elongated as well as the energy cutoff becoming important. All the models have finite mass, are self-supporting and satisfy the virial theorem. They are all obtained from an analysis of the Boltzmann equation with particular emphasis placed at the high energies. In dimensionless variables the models are characterized by a single model parameter C. The model parameter involves three physical parameters which indicate the total mass, total energy, and degree of velocity space anisotropy. A comparison with rich galactic clusters, globular clusters, dwarf galaxies and spherical galaxies has been made. The theoretical models appear to be in agreement with the observed systems. For example, the log density versus log distance inflection observed in systems such as NGC 3379 is exactly as predicted by the theory. There may be a small inflection for the globular cluster 47 Tuc. Both star clusters and spherical galaxies show a fairly wide range in the model parameter. The star clusters may favor a somewhat larger value of C, but the data are probably not sufficient to firmly establish this trend. Publication: The Astronomical Journal Pub Date: June 1962 DOI: 10.1086/108880 Bibcode: 1962AJ.....67R.582M full text sources ADS |

Self-Gravitating Star Systems. II

The general problem of the motion of a star system in the smoothed gravitational field which the system itself produces has been considered previously for the special case in which the stars are of equal mass. This restriction is now shown to be unnecessary. By a suitable definition of the velocity-distribution function the three equations which are involved in this problem can be written without any reference to the distribution of stars of different mass. The complexity of the problem is not affected by the increased generality. For a star system with complete spherical symmetry the problem is reduced to solving a single non-linear partial differential equation. A number of special solutions have been obtained, including solutions which correspond to isothermal and polytropic gravitating gas-spheres. For three different models the variation of the projected density with radius has been found, and this is compared with observations of the variation of luminosity with radius in globular clusters. The best agreement is obtained in the case of a model which has never previously been considered, but which is essentially a modification of Plummer's model in which terms involving the angular momentum have been introduced.