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 proportional to L-alpha, with slopes in the range -2.4 less than or similar to alpha less than or similar to -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, Sigma(cl)(-8), scales with the mean star formation rate (SFR) per unit area, Sigma(SFR). Assuming that the LF can be generally expressed as dN(L)/dL = cASigma(SFR)(gamma)L(alpha), where A is the galaxy area, gamma similar to 1.0-1.4, alpha = 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 Sigma(SFR) and A. The predictions agree well with existing observations of galaxies spanning a wide range of Sigma(SFR) values, suggesting that sampling statistics play an important role in determining the maximum observed luminosities of star clusters in galaxies.