Abstract. We studied in detail the binary cluster candidates SL 538 and NGC 2006. This apparent cluster pair is located in the northwestern part of the large OB association LH 77 in supergiant shell LMC 4. A third star cluster, KMHK 1019, is located within 5' from the double cluster (see Fig. 2). We derived ages by isochrone fits to colour-magnitude diagrams (CMDs) and found that all three star clusters are (nearly) coeval which makes simultaneous formation likely, possibly all in the same giant molecular cloud. We identified Be star candidates and find the same ratio N(Be)/N(B) for the components of the binary cluster while the amount of Be stars detected in KMHK 1019 and in the surrounding field is considerably lower. Since Be stars are usually rapid rotators this may indicate intrinsically higher rotational velocities in the components of the cluster pair. Also the initial mass function (IMF) derived from the CMDs shows the same slope for both SL 538 and NGC 2006 and is consistent with a Salpeter IMF. We suggest that SL 538 and NGC 2006 are a true binary cluster.

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1. Introduction

The existence of gravitationally bound pairs of star clusters is important for the understanding of formation and evolution of star clusters. Since the probability of tidal capture of one cluster by another one is very small (Bhatia et al. 1991), we can assume that the components of a true binary star cluster have a common origin. Thus, they should have the same or similar properties such as age, metallicity, and stellar content.

Bhatia & Hatzidimitriou (1988), Hatzidimitriou & Bhatia (1990), and Bhatia et al. (1991), have surveyed the Magellanic Clouds in order to catalog the binary cluster candidates. They found 69 pairs in the LMC and 9 pairs in the SMC with a maximum projected centre-to-centre separation of 18 pc (limit for gravitationally bound clusters) or less. However, two clusters may also appear to be a binary cluster due to chance line-up. Estimating the number of chance pairs with the formula by Page (1975) and accounting for a non-uniform distribution of star clusters, one may expect 31 pairs in the LMC and 3 pairs in the SMC. Considerably more pairs have been found, which suggests that a number of them may be true binary clusters.

In the Milky Way only few binary clusters are known, which may be explained in different ways: The evolution of a gravitationally bound cluster pair depends on the interaction between the components as well as on the tidal forces of the parent galaxy. Innanen et al. (1972) suggest that due to stronger tidal forces in the Milky Way a binary cluster will execute only a fraction of an orbit around its barycentre before its components are detached, but it will survive for several orbits in the less massive Magellanic Clouds. The study of binary clusters may help to evaluate the tidal field of the parent galaxy. Subramaniam et al. (1995) argue that in the distant Magellanic Clouds binary clusters can easily be detected due to their closeness on the sky. In the Milky Way detection is more difficult since we are looking at the Galaxy from inside, and distances to Galactic open clusters are often poorly known. In the Lyngå catalogue Subramaniam et al. (1995) found 16 binary cluster candidates and conclude that binary clusters in the Milky Way may not be uncommon.

2. Ages of the star clusters

We derived ages of the clusters SL 538, NGC 2006, KMHK 1019 and the surrounding field star populations by comparing our colour-magnitude diagrams (CMDs) with isochrones. The isochrones we used are based on the stellar models of the Geneva group (Schaerer et al. 1993). All CMDs are plotted in Fig. 1.

Each cluster CMD has a wide blue main sequence and contains very few supergiants. The width of the main sequence is caused in part by photometric errors, crowding and the presence of Be stars (marked with crosses in the CMDs). The scarcity of supergiants is well within the expected fluctuations for sparse clusters. We find the following ages: SL 538: 18±2 Myr, NGC 2006: 22.5±2.5 Myr, KMHK 1019: 16 Myr, youngest field: 16 Myr.

[Click here to see Fig. 1!]

3. Comparison to earlier photometry

Our study is the first age determination of SL 538 and NGC 2006 (see Fig. 2 for a colour composite of the field) based on CMDs. Previous studies derived ages based on integrated colours, a less accurate method. In Table 1 we compare our results with ages from integrated photometry of Bica et al. (1996) and Bhatia (1992).

Reference	Aperture size	Age (SL 538)	Age (NGC 2006)
Bica et al. (1996)	50"	0-10 Myr	10-30 Myr
Bhatia (1992)	33"	12.6 Myr	7.9 Myr
this work	34" (CMD)	18 Myr	22.5 Myr

[Click here to see Fig. 2!]

4. Be stars in the clusters and the surrounding field

Be stars are non-supergiant B stars with variable Balmer emission and infrared excess originating in circumstellar disks. Usually Be stars are rapid rotators and thus widen the main sequence (Collins & Smith 1985) which is also visible in our CMDs (see Fig. 1). Using the R-Halpha index to detect stars bright in Halpha and B-V as a temperature index we can identify Be star candidates (e.g., Grebel et al. 1992).

Investigating the location of our Be star candidates we found them concentrated on the cluster pair components whereas at the location of KMHK 1019 only two such stars are present.

The visual impression of the concentration of the Be star candidates on SL 538 and NGC 2006 is confirmed when considering the ratio of Be stars to B stars. Since we do not have spectral classifications we simply considered the ratio of all B to Be stars within a magnitude interval of V=14.2 to 19.1 mag. These magnitudes correspond to the mean visual magnitudes, at LMC distance, of B0III to B9V main sequence stars (Zorec & Briot 1991, Table 3). We find the following values:

SL 538:	N(Be)/N(B) = 0.123	+0.134 -0.074
NGC 2006:	N(Be)/N(B) = 0.120	+0.145 -0.078
KMHK 1019:	N(Be)/N(B) = 0.053	+0.233 -0.052
Field:	N(Be)/N(B) = 0.019	+0.022 -0.013

The errors are corresponding to 3σ Gaussian errors and are calculated using the confidence limits for small number statistics from Gehrels (1986). The components of the double cluster show the same fraction of Be stars, and the sixfold amount found in the surrounding field. The difference between the ratios N(Be)/N(B) of SL 538 and the field is 0.104 which is more than a 3σ-effect. The difference between SL 538 and KMHK 1019 is 0.070 which is less than a 2σ-effect according to the upper confidence limit for KMHK 1019. Thus, the Be star content of KMHK 1019 may be comparable to the cluster pair.

5. Initial Mass Function (IMF)

Since crowding and thus completeness depend on the distance to the cluster centre, we determined the completeness correction and the IMF both for an inner circle (radius 10.2") and an outer annulus (width 23.8") centered around the star clusters. As KMHK 1019 only has a very small amount of main sequence stars we did not derive the IMF for this cluster. Our results for the slope of the IMF are:

SL 538, inner circle:	α=-0.92±0.83
SL 538, outer annulus:	α=-1.22±0.31
NGC 2006, inner circle:	α=-1.39±0.34
NGC 2006, outer annulus:	α=-1.27±0.32

The central circle is poorly resolved and our data here suffer from large uncertainties due to small-number statistics. Considering the large errors, all of our IMF slopes are consistent with the Salpeter value of -1.35 (Salpeter 1955).

6. Influence of Be stars on the IMF

To know which stars are Be stars and which ones are ordinary main sequence stars may be important for the determination of the IMF, since the intrinsically brighter Be stars (Zorec & Briot 1991, 1997) will appear to be more massive. Unrecognized Be stars may lead to a too shallow IMF if their numbers are high enough (Grebel et al. 1996; Grebel et al., this conference).

As we do not have spectral classifications for the candidate Be stars, only a crude statistical correction was possible, assuming mean magnitudes and magnitude differences between B and Be stars as found in Zorec & Briot (1997).

This statistical correction did not lead to different IMF slopes, indicating that the amount of Be stars is not high enough to influence the IMF.

However, for more accurate work spectral classifications are needed.

7. Summary and conclusions

The ages of the three clusters are similar enough to suggest near-simultaneous formation in the same giant molecular cloud. The slightly younger KMHK 1019 may have been triggered by the cluster pair. Be stars are concentrated in SL 538 and NGC 2006, and both clusters show the same ratio of N(Be)/N(B). Since Be stars are usually rapid rotators this may indicate intrinsically higher rotational velocities in the components of the cluster pair. The slopes of the IMF agree with each other within the errors and are compatible with the Salpeter value.

The similarity of properties (ages, IMF slope, Be star content) indicates possible joint formation and suggests small spatial separation. We suggest that SL 538 and NGC 2006 are a true binary cluster.

References

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First version:	20th	June,	1998
Last update:	24th	September,	1998

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Jochen M. Braun   &   Tom Richtler
 (E-Mail: jbraun|richtler@astro.uni-bonn.de)

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