2009A&A...494..539L

The initial cluster mass function (ICMF) in spiral discs is constrained and compared with data for old globular clusters and young clusters in starbursts. 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, M_c. 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).A single Schechter ICMF with an M_c of a few times 10⁵M_☉ 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 M_c=(2.1±0.4)x10⁵M_☉. The MFs in cluster-poor and cluster-rich spirals are statistically indistinguishable. An M_c=2.1x10⁵M_☉ 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 M>10⁵M_☉ will form about once every 10⁷years, while an M>10⁶M_☉ cluster will form only once every 50Gyr. Luminosity functions (LFs) of model cluster populations drawn from an M_c=2.1x10⁵M_☉ Schechter ICMF generally agree with LFs observed in spiral galaxies. The ICMF in present-day spiral discs can be modelled as a Schechter function with M_c≃2x10⁵M_☉. However, the presence of significant numbers of M>10⁶M_☉ (and even M>10⁷M_☉) clusters in some starburst galaxies makes it unlikely that the M_c value derived for spirals is universal. In high-pressure environments, such as those created by complex gas kinematics and feedback in mergers, M_c can shift to higher masses than in quiescent discs.