Relations Between the Luminosity, Mass, and Age Distributions of Young Star Clusters

We derive and interpret some relations between the luminosity, mass, and age distributions of star clusters, denoted here by phi(L), psi(M), and chi(tau), respectively. Of these, phi(L) is the easiest to determine observationally, whereas psi(M) and chi(tau) are more informative about formation and disruption processes. For populations of young clusters, with a relatively wide range of ages, phi(L) depends on both psi(M) and chi(tau) and thus cannot serve as a proxy for psi(M) in general. We demonstrate this explicitly by four illustrative examples with specific forms for either psi(M) or chi(tau). In the special case in which psi(M) is a power law and is independent of chi(tau), however, phi(L) is also a power law with the same exponent as psi(M). We conclude that this accounts for the observed similarity between phi(L) and psi(M) for the young clusters in the Antennae galaxies. This result reinforces our picture in which clusters form with psi(M) propto M^{-2} and are then disrupted rapidly at a rate roughly independent of their masses. The most likely disruptive process in this first stage is the removal of interstellar matter by the energy and momentum input from young stars (by photoionization, winds, jets, and supernovae). The few clusters that avoid this "infant mortality" are eventually disrupted in a second stage by the evaporation of stars driven by two-body relaxation, a process with a strong dependence on mass. We suspect this picture may apply to many, if not all, populations of star clusters, but this needs to be verified observationally by determinations of psi(M) and chi(tau) in more galaxies.Comment: Ten pages. Astrophysical Journal. Submitted 2005 October 20. Accepted 2006 August 15. V2--Minor improvements for consistency with published articl

Similarities in Populations of Star Clusters

We compare the observed mass functions and age distributions of star clusters in six well-studied galaxies: the Milky Way, Magellanic Clouds, M83, M51, and Antennae. In combination, these distributions span wide ranges of mass and age: 10^2\lea M/M_{\odot}\lea10^6 and 10^6\lea\tau/yr \lea10^9. We confirm that the distributions are well represented by power laws: $dN/dM\propto M^{\beta}$ with $\beta \approx-1.9$ and $dN/d\tau\propto\tau^{\gamma}$ with $\gamma\approx -0.8$. The mass and age distributions are approximately independent of each other, ruling out simple models of mass-dependent disruption. As expected, there are minor differences among the exponents, at a level close to the true uncertainties, $\epsilon_{\beta}\sim\epsilon_{\gamma}\sim$~0.1--0.2. However, the overwhelming impression is the similarity of the mass functions and age distributions of clusters in these different galaxies, including giant and dwarf, quiescent and interacting galaxies. This is an important empirical result, justifying terms such as "universal" or "quasi-universal." We provide a partial theoretical explanation for these observations in terms of physical processes operating during the formation and disruption of the clusters, including star formation and feedback, subsequent stellar mass loss, and tidal interactions with passing molecular clouds. A full explanation will require additional information about the molecular clumps and star clusters in galaxies beyond the Milky Way.Comment: 20 pages, 4 figures, 2 tables; published in the Astrophysical Journal, 752:96 (2012 June 20

The Age Distribution of Massive Star Clusters in the Antennae Galaxies

We determine the age distribution of star clusters in the Antennae galaxies (NGC 4038/9) for two mass-limited samples (M > 3 x 10^4 M_{\odot} and M > 2 x 10^5 M_{\odot}). This is based on integrated broadband UBVI and narrowband H-alpha photometry from deep images taken with the Hubble Space Telescope. We find that the age distribution of the clusters declines steeply, approximately as dN/d\tau \propto \tau^{-1}. The median age of the clusters is ~10^7 yr, which we interpret as evidence for rapid disruption ("infant mortality"). It is very likely that most of the young clusters are not gravitationally bound and were disrupted near the times they formed by the energy and momentum input from young stars to the interstellar matter of the protoclusters. At least 20% and possibly all stars form in clusters and/or associations, including those that are unbound and short-lived.Comment: 11 pages, 2 figures. To appear in the ApJ Letters; Submitted 2004 July 29; accepted 2005 August