The mass function of young star clusters in spiral galaxies

Abstract

<i>Aims. <i/> The initial cluster mass function (ICMF) in spiral discs is constrained and compared with data for old globular clusters and young clusters in starbursts. <i>Methods. <i/> For a given absolute magnitude, the cluster age distribution depends on the ICMF. Here, the behaviour of the median age-magnitude relation is analysed in detail for Schechter ICMFs with various cut-off masses, <i>M<i/><sub>c<sub/>. The calculated relations are compared with observations of the brightest clusters in spiral galaxies. Schechter functions are also fitted directly to observed mass functions (MFs).<i>Results. <i/>A single Schechter ICMF with an <i>M<i/><sub>c<sub/> of a few times 10<sup>5<sup/> can reproduce the observed ages and luminosities of the brightest (and 5th brightest) clusters in the spirals if disruption of optically visible clusters is dominated by relatively slow secular evolution. A Schechter function fit to the combined cluster MF for all spirals in the sample yields <i>M<i/><sub>c<sub/> = (2.1<i>±<i/>0.4)10<sup>5<sup/> . The MFs in cluster-poor and cluster-rich spirals are statistically indistinguishable. An <i>M<i/><sub>c<sub/> = 2.110<sup>5<sup/> Schechter function also fits the MF of young clusters in the Large Magellanic Cloud. If the same ICMF applies in the Milky Way, a bound cluster with <i>M<i/> > 10<sup>5<sup/> will form about once every 10<sup>7<sup/> years, while an <i>M<i/> > 10<sup>6<sup/> cluster will form only once every 50 Gyr. Luminosity functions (LFs) of model cluster populations drawn from an <i>M<i/><sub>c<sub/> = 2.110<sup>5<sup/> Schechter ICMF generally agree with LFs observed in spiral galaxies. <i>Conclusions. <i/> The ICMF in present-day spiral discs can be modelled as a Schechter function with <i>M<i/><sub>c<sub/> <i>≈<i/> 210<sup>5<sup/> . However, the presence of significant numbers of <i>M<i/> > 10<sup>6<sup/> (and even <i>M<i/> > 10<sup>7<sup/> ) clusters in some starburst galaxies makes it unlikely that the <i>M<i/><sub>c<sub/> value derived for spirals is universal. In high-pressure environments, such as those created by complex gas kinematics and feedback in mergers, <i>M<i/><sub>c<sub/> can shift to higher masses than in quiescent discs.