The Link between the Formation Rates of Clusters and Stars in Galaxies

Abstract

The goal of this paper is to test whether the formation rate of star clusters is proportional to the star formation rate (SFR) in galaxies. As a first step, we present the mass functions of compact clusters younger than 10 Myr in seven star-forming galaxies of diverse masses, sizes, and morphologies: the Large and Small Magellanic Clouds, NGC 4214, NGC 4449, M83, M51, and the Antennae. These cluster mass functions (CMFs) are well represented by power laws, {dN}/{dM}\propto {M}^β , with similar exponents β =-1.92+/- 0.27, but with amplitudes that differ by factors up to ∼ {10}³, corresponding to vast differences in the sizes of the cluster populations in these galaxies. We then normalize these CMFs by the SFRs in the galaxies, derived from dust-corrected Hα luminosities, and find that the spread in the amplitudes collapses, with a remaining rms deviation of only σ ({log}A)=0.2. This is close to the expected dispersion from random uncertainties in the CMFs and SFRs. Thus, the data presented here are consistent with exact proportionality between the formation rates of stars and clusters. However, the data also permit weak deviations from proportionality, at the factor of two level, within the statistical uncertainties. We find the same spread in amplitudes when we normalize the mass functions of much older clusters, with ages in the range 100-400 Myr, by the current SFR. This is another indication of the general similarity among the cluster populations of different galaxies.