The initial luminosity and mass functions of the Galactic open clusters

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 5 mag deeper than in the most nearby galaxies. It increases linearly from the brightest limit to a turnover at about I-MV approximate to -2.5. The slope of this linear portion is alpha = 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-circle dot to log M-c/M-circle dot approximate to 5.5. The mass function of these clusters can be fit as a linear function with log mass for log M-c/M-circle dot > 2.5, and shows a broad maximum between log M-c/M-circle dot = 1.5 and 2.5. For log M-c/M-circle dot > 2.5, the linear part of the upper cluster mass function has a slope a = 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 alpha = 1.66 +/- 0.14 at log t <= 6.9 to alpha = 2.13 +/- 0.08 at log t <= 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 alpha = 1.66 +/- 0.14 in the range log M-c/M-circle dot = 3.37... 4.93 and alpha = 0.82 +/- 0.14 in the range log M-c/M-circle dot = 1.7... 3.37. The average mass of open clusters at birth is 4.5 x 10(3) M-circle dot, which should be compared to the average observed mass of about 700 M-circle dot. The average cluster formation rate derived from the comparison of initial and observed mass functions is (nu) over bar = 0.4 kpc(-2) Myr(-1). Multiplying by the age of the Galactic disc (T = 13 Gyr) the predicted surface density of Galactic disc field stars originating from dissolved open clusters amounts to 22 M-circle dot pc(-2) 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.