The shape of the initial mass function (IMF) is an important parameter to understand the fragmentation of molecular clouds and therefore the formation and development of stellar systems. Besides studies of the Solar neighbourhood (Salpeter 1955, Tsujimoto et al. 1997), work on star clusters plays a major role (Scalo 1986) in this field, as age, metallicity, and distance of all stars of a star cluster can generally be assumed to be equal.
Restricted to certain mass intervals, the IMF can be described by a power law in the form
In this notation the "classical" value found by Salpeter (1955) for the Solar neighbourhood is . Average values for from more recent studies, mostly of star clusters, can be found, e.g., in Scalo (1998):
where the "" values refer to a rough range of the slopes derived for the corresponding mass intervals, caused by empirical uncertainties or probable real IMF variations.
Knowledge of membership is essential to derive the IMF especially of open star clusters, where the contamination of the data with field stars presents a major challenge. Two methods for field star subtraction are in use nowadays: separating field and cluster stars by means of membership probabilities from stellar proper motions on one hand, statistical field star subtraction on the other hand. Our work combines these two methods: The proper motions are investigated for the bright stars of the clusters, down to the completeness limit of the photographic plates used, whereas the fainter cluster members are selected with statistical considerations.
From the cleaned data we derive the luminosity and mass functions of the clusters. Including the proper motions, we expect to receive a more reliable IMF, since the small number of bright stars in open clusters would lead to higher uncertainties, if only statistical field star subtraction were applied.
This is the second part of a series of studies of open star clusters, following Sanner et al. (1999). Here we present data on two clusters of the northern hemisphere, NGC 1960 (M 36) and NGC 2194.
NGC 1960 (M 36) is located at , and has a diameter of according to the Lyngå (1987) catalogue. Morphologically, NGC 1960 is dominated by a number of bright () stars, whereas the total stellar density is only marginally enhanced compared to the surrounding field. The cluster has not yet been studied by means of CCD photometry. Photographic photometry was published by Barkhatova et al. (1985), photoelectric photometry of 50 stars in the region of the cluster by Johnson & Morgan (1953). The most recent proper motion studies are from Meurers (1958) and Chian & Zhu (1966). As their epoch differences between first and second epoch plates (36 and 51 years, respectively) are smaller than ours and today's measuring techniques can be assumed to be more precise we are confident to gain more reliable results.
Tarrab (1982) published an IMF study of 75 open star clusters, among them NGC 1960, and found an exteme value for the slope of (in our notation) for this object. Her work includes only 25 stars in the mass range , so that a more detailed study covering more members and reaching towards smaller masses is necessary.
For NGC 2194 (located at , , diameter ), our work is the first proper motion study according to van Leeuwen (1985). The RGU photographic photometry of del Rio (1980) is the most recent publication on NGC 2194 including photometric work.
The cluster is easily detectable as it contains numerous intermediate magnitude () stars, although bright stars with are lacking.
In Sect. 2, we present the data used for our studies and the basic steps of data reduction and analysis. Sects. 3 and 4 include the proper motion studies, an analysis of the colour magnitude diagrams (CMDs), and determination of the IMF of the clusters. We conclude with a summary and discussion in Sect. 5.
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000