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

Abstract

We derive and interpret some relations between the luminosity, mass, and age distributions of star clusters, denoted here by (L), ψ(M), and χ(τ), respectively. Of these, (L) is the easiest to determine observationally, whereas ψ(M) and χ(τ) are more informative about formation and disruption processes. For a population of young clusters, with a relatively wide range of ages, (L) depends on both ψ(M) and χ(τ) and thus cannot serve as a proxy for ψ(M) in general. We demonstrate this explicitly by four illustrative examples with specific forms for either ψ(M) or χ(τ). In the special case in which ψ(M) is a power law and is independent of χ(τ), however, (L) is also a power law with the same exponent as ψ(M). We conclude that this accounts for the observed similarity between (L) and ψ(M) for the young clusters in the Antennae galaxies. This result reinforces our picture in which clusters form with ψ(M) ∝ 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 ψ(M) and χ(τ) in more galaxies.