The Luminosity Function of Star Clusters in Spiral Galaxies^*

Star clusters in six nearby spiral galaxies are examined using archive images from the Wide Field Planetary Camera 2 (WFPC2) on board the Hubble Space Telescope (HST). The galaxies have previously been studied from the ground and some of them are known to possess rich populations of "young massive clusters." Comparison with the HST images indicates a success rate of ∼75% for the ground-based cluster detections, with typical contaminants being blends or loose groupings of several stars in crowded regions. The luminosity functions (LFs) of cluster candidates identified on the HST images are analyzed and compared with existing data for the Milky Way and the LMC. The LFs are well approximated by power laws of the form dN(L)/dL ∝ L^α, with slopes in the range -2.4 ≲ α≲-2.0. The steeper slopes tend to be found among fits covering brighter magnitude intervals, although direct hints of a variation in the LF slope with magnitude are seen only at low significance in two galaxies. The surface density of star clusters at a reference magnitude of M_V = -8, Σ, scales with the mean star formation rate (SFR) per unit area, Σ_SFR. Assuming that the LF can be generally expressed as dN(L)/dL = cAΣL^α, where A is the galaxy area, γ ∼ 1.0–1.4, α = -2.4, and the normalization constant c is determined from the WFPC2 data analyzed here, the maximum cluster luminosity expected in a galaxy from random sampling of the LF is estimated as a function of Σ_SFR and A. The predictions agree well with existing observations of galaxies spanning a wide range of Σ_SFR values, suggesting that sampling statistics play an important role in determining the maximum observed luminosities of star clusters in galaxies.