2008A&A...487..557P

We aim at the construction of luminosity and mass functions for Galactic open clusters, based on integrated magnitudes and tidal masses. We also aim at studying the evolution of these functions, with the ultimate purpose of deriving the initial luminosity and mass distributions of star clusters, independent of model assumptions regarding the cluster mass-to-light ratio. Finally we aim at a new determination of the percentage of field stars that have originated in open clusters. The integrated magnitudes are computed from individual photometry of cluster members selected from the ASCC-2.5 catalogue. The cluster masses we assumed to be the estimated tidal mass recently published by us elsewhere. Analysis of the cluster brightness distribution as a function of apparent integrated magnitudes shows that the cluster sample drawn from the ASCC-2.5 is complete down to apparent integrated magnitude I_V=8, with 440 clusters and compact associations above this completeness limit. This, on average, corresponds to a completeness area in the solar neighbourhood with an effective radius of about 1 kpc. The observed luminosity function can be constructed in a range of absolute integrated magnitudes I_MV=[-10,-0.5]mag, i.e. about 5mag deeper than in the most nearby galaxies. It increases linearly from the brightest limit to a turnover at about I_MV≃-2.5. The slope of this linear portion is a=0.41±0.01, which agrees perfectly with the slope deduced for star cluster observations in nearby galaxies. The masses of the Galactic clusters span a range from a few M_☉ to logM_c/M_☉≃5.5. The mass function of these clusters can be fit as a linear function with log mass for logM_c/M_☉>2.5, and shows a broad maximum between log M_c/M_☉=1.5 and 2.5. For logM_c/M_☉>2.5, the linear part of the upper cluster mass function has a slope α=2.03±0.05, again in agreement with data on extragalactic clusters. We regard this agreement as indirect evidence that the tidal masses for Galactic clusters and the luminosity-based masses for extragalactic clusters are on the same scale. Considering the evolution of the cluster mass function now reveals a slight but significant steepening of the slope with increasing age from α=1.66±0.14 at logt≤6.9 to α=2.13±0.08 at logt≤8.5. This indicates that open clusters are formed with a flatter (initial) mass distribution than the overall observed cluster mass distribution averaged over all ages. Interestingly, the luminosity function of open clusters does not show the same systematic steepening with age as the mass function does. We find that the initial mass function of open clusters (CIMF) has a two-segment structure with the slopes α=1.66±0.14 in the range log M_c/M_☉=3.374.93 and α=0.82±0.14 in the range logM_c/M_☉=1.73.37. The average mass of open clusters at birth is 4.5x10³M_☉, which should be compared to the average observed mass of about 700M_☉. The average cluster formation rate derived from the comparison of initial and observed mass functions is <υ≥0.4/kpc2/Myr. Multiplying by the age of the Galactic disc (T=13Gyr) the predicted surface density of Galactic disc field stars originating from dissolved open clusters amounts to 22M_☉/pc2 which is about 40% of the total surface density of the Galactic disc in the solar neighbourhood. Thus, we conclude that almost half of all field stars were born in open clusters, a much higher fraction than previously thought.