5. WHAT ARE THE INITIAL CLUSTER MASS FUNCTIONS FOR SSCs?

How are SSCs related to globular clusters? Are young SSCs in the local universe precursors to globular clusters? One characteristic that could link globular clusters to SSCs is the cluster mass function. Globular clusters in the Galaxy have a characteristic mass of a few × 10⁵ M, reflecting what appears to be a near-universal globular cluster mass function (GCMF) (Harris 1998). Were globular clusters born with this mass function? Or is the present globular cluster mass function the result of evolution due to dynamical forces such as tidal stripping and disk shocking over billions of years (Fall and Rees 1977, Gnedin and Ostriker 1997, de Grijs 2007, Parmentier and Gilmore 2007, McLaughlin and Fall 2008)? SSCs, as potential precursors to globular clusters, could give us valuable information about the nature vs. nurture question for the GCMF. Is the initial cluster mass function (ICMF) for SSCs universal, and if so, what is it? How does it evolve?

The ICMF has been extensively studied in the Antennae galaxies, where large numbers of SSCs facilitate the statistics. The Antennae are a nearby (13.3 Mpc, Saviane et al. 2008) IR-bright pair of gas-rich interacting galaxies. HST images revealed a system of thousands of young SSCs spread across the galaxy pair (Whitmore and Schweizer 1995, Whitmore et al. 1999). ISO imaging determined that the youngest clusters and brightest infrared emission occur in a dusty and embedded region between the two galaxies (Mirabel et al. 1998). Cluster masses and ages for the visible SSCs of the Antennae have been obtained from multicolor (UBVRI and H) HST photometry combined with modeling of the cluster colors and luminosities with STARBURST99 (Leitherer et al. 1999, Vázquez and Leitherer 2005) The cluster mass function (CMF) in the Antennae is power law with ~ -2 over the range of masses 10⁴ - 10⁶ M (Fall et al. 2005). The median cluster mass in the Antennae appears to be about an order of magnitude less than the median globular cluster mass of giant ellipticals such as M87 (Harris 2002). Ages determined from the SSC colors in the Antennae range from 10⁶ - 10⁸ yr (Zhang and Fall 1999), with a median of 10-20 Myr (Fall et al. 2005, Mengel et al. 2005), but with a small population extending to more than 10⁹ yrs. If the SSC system of the Antennae is typical, one could infer that the characteristic mass of globular clusters is due to selective evolution of clusters of different mass (Fall and Zhang 2001). However, the fact that 70% of the clusters in the Antennae are less than ~ 10 - 20 Myr of age could indicate that very few if any of the Antennae clusters will survive to become globular clusters.

Cluster mass functions have been determined for a number of other nearby galaxies, mostly inferred from cluster luminosity functions. A list of nearby starburst systems is given in de Grijs et al. 2003; many cluster systems appear to have power law slopes of ~ -2.

Direct detection of cluster masses via their stellar velocity dispersions and cluster sizes can be done for the closest systems, thereby giving direct determinations of cluster mass functions. Even in smaller SSC systems, dynamical estimates of cluster masses are an important check on mass functions obtained from cluster luminosity functions. Masses at the high ends are consistent with globular cluster masses. In M82, McCrady & Graham (2007) find a power law mass distribution with slope of = -1.91 for fifteen SSCs, nearly identical to the Antennae.

An intriguing indication of ICMF evolution is the cluster system in NGC 5253. There are several hundred clusters in this galaxy (Caldwell and Phillips 1989), many of intermediate age, ~ 1 Gyr. There is also a younger population of visible and embedded SSCs with ages of ~ 2 - 50 Myr (Calzetti et al. 1997, Gorjian et al. 2001, Alonso-Herrero et al. 2002). The cluster mass function for the intermediate age clusters appears to turn over at a mass of 5× 10⁴ M, while the younger SSCs have a power law mass function (Cresci et al. 2005). Parmentier et al. (2008) suggest that the evolution of the ICMF is due to star formation efficiency (see Section 7).

Future work on stellar cluster mass functions in the coming decade will be done from space with HST and JWST and from the ground with IR AO observations. High resolution and sensitivity are important for these studies, since fields where SSCs are found are usually very crowded. Infrared observations are critical for getting the mass functions of the youngest clusters, the best reflection of the ICMF, since they are likely to be embedded in regions of high extinction.