The initial luminosity and mass functions of the Galactic open clusters

¹ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany e-mail: [apiskunov;nkharchenko;rdscholz;hzinnecker]@aip.de
² Institute of Astronomy of the Russian Acad. Sci., 48 Pyatnitskaya Str., 109017 Moscow, Russia e-mail: piskunov@inasan.rssi.ru
³ Astronomisches Rechen-Institut, Mönchhofstraße 12-14, 69120 Heidelberg, Germany e-mail: apiskunov;nkhar;elena;roeser] @ari.uni-heidelberg.de
⁴ Main Astronomical Observatory, 27 Academica Zabolotnogo Str., 03680 Kiev, Ukraine e-mail: nkhar@mao.kiev.ua

Received: 4 February 2008
Accepted: 25 April 2008

Abstract

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-2.5catalogue. 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-2.5is 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  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 . The slope of this linear portion is , 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  to . The mass function of these clusters can be fit as a linear function with log mass for , and shows a broad maximum between and 2.5. For , the linear part of the upper cluster mass function has a slope , 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 at to at . 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 in the range and in the range . The average mass of open clusters at birth is , which should be compared to the average observed mass of about . The average cluster formation rate derived from the comparison of initial and observed mass functions is . Multiplying by the age of the Galactic disc ( Gyr) the predicted surface density of Galactic disc field stars originating from dissolved open clusters amounts to 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.