The Globular Cluster Luminosity Function

The main aspects of the globular cluster luminosity function needing to be explained by a general theory of cluster formation are reviewed, and the importance of simultaneously understanding globular cluster systematics (the fundamental plane) within such a theory is pointed out.Comment: 7 pages, to appear in Proceedings of the ESO Workshop on Extragalactic Globular Cluster Systems, ed. M. Kissler-Pati

Density Dependence of the Mass Function of Globular Star Clusters in the Sombrero Galaxy and its Dynamical Implications

We have constructed the mass function of globular star clusters in the Sombrero galaxy in bins of different internal half-mass density rho_h and projected galactocentric distance R. This is based on the published measurements of the magnitudes and effective radii of the clusters by Spitler et al. (2006) in BVR images taken with the ACS on HST. We find that the peak of the mass function M_p increases with rho_h by a factor of about 4 but remains nearly constant with R. Our results are almost identical to those presented recently by McLaughlin & Fall (2007) for globular clusters in the Milky Way. The mass functions in both galaxies agree with a simple, approximate model in which the clusters form with a Schechter initial mass function and evolve subsequently by stellar escape driven by internal two-body relaxation. These findings therefore undermine recent claims that the present peak of the mass function of globular clusters must have been built into the initial conditions.Comment: Astrophysical Journal Letters, in press. 4 page

A Model for the Internal Structure of Molecular Cloud Cores

We generalize the classic Bonnor-Ebert stability analysis of pressure-truncated, self-gravitating gas spheres, to include clouds with arbitrary equations of state. A virial-theorem analysis is also used to incorporate mean magnetic fields into such structures. The results are applied to giant molecular clouds (GMCs), and to individual dense cores, with an eye to accounting for recent observations of the internal velocity-dispersion profiles of the cores in particular. We argue that GMCs and massive cores are at or near their critical mass, and that in such a case the size-linewidth and mass-radius relations between them are only weakly dependent on their internal structures; any gas equation of state leads to essentially the same relations. We briefly consider the possibility that molecular clouds can be described by polytropic pressure-density relations (of either positive or negative index), but show that these are inconsistent with the apparent gravitational virial equilibrium, 2U + W = 0 of GMCs and of massive cores. This class of models would include clouds whose nonthermal support comes entirely from Alfven wave pressure. The simplest model consistent with all the salient features of GMCs and cores is a ``pure logotrope,'' in which P/P_c = 1 + A ln(rho/rho_c). Detailed comparisons with data are made to estimate the value of A, and an excellent fit to the observed dependence of velocity dispersion on radius in cores is obtained with A = 0.2.Comment: 33 pages, LaTeX with 3 PS figures; ApJ in press (October 1 1996