4.1. Specific frequencies
In Table 2 we give the number of clusters identified in each of the observed galaxies. The columns labeled and refer to the number of "blue" and "red" clusters respectively, according to the definition that "blue" clusters are clusters with (and hence ) whereas the "red" clusters have (and ). See also Sect. 3. The data for the LMC are from Bica et al. (1996) and those for M 33 are from Christian & Schommer (1988).
Table 2. Number of clusters identified in each of the galaxies. refer to the `blue' clusters (i.e. clusters with and refer to the `red' clusters (clusters with ). The fourth column is the total number of clusters, . The quantities and are defined in Sect. 3.1. 1Only the central parts of the galaxies were covered by our observations.
The "specific frequencies" for the galaxies in our sample are given in the fourth column of Table 2. The number used to derive is the total number of clusters, "red" and "blue", detected in each galaxy.
The errors on were estimated taking into consideration only the uncertainties of the absolute magnitudes of the host galaxies resulting from the distance errors as given in Table 1 and poisson statistics of the cluster counts. However, it is clear that this is not a realistic estimate of the total uncertainties of the values. Another source of uncertainty arises from incompleteness effects, particularly for the more distant galaxies. For all galaxies with more than 20 clusters we estimated the incompleteness by adding artificial clusters with magnitudes of 18.0, 18.5 21.0, and testing how many of the artificially added clusters were detected by DAOFIND in all of the filters U,B and V. Because the completeness depends critically on the size of the objects, we carried out completeness tests for artificial clusters with pc and pc in each galaxy. The numbers of clusters actually detected in each of the magnitude bins [18.25-18.75], [18.75-19.25] [20.75-21.25] were then corrected by the fraction of artificial clusters recovered in the corresponding bin, and finally the "corrected" values were derived. These are given in the last column of Table 2, labeled , for point sources (first line) and objects with pc (second line). See Larsen (1999) for more details on the completeness corrections.
One additional source of errors affecting which remains uncorrected, is the fact that an uncertainty in the distance also affects the magnitude limit for detection of star clusters. If a galaxy is more distant (or nearby) than the value we have adopted, our limit corresponds to a "too bright" (too faint) absolute magnitude, and we have underestimated (overestimated) the number of clusters. Hence, the true errors are somewhat larger than those given in Table 2, but they depend on the cluster luminosity function. If the clusters follow a luminosity function of the form (Whitmore & Schweizer 1995) then a difference in the magnitude limit of would lead to a difference in the cluster counts of about 7%.
A histogram of the uncorrected values (Fig. 3) shows that a wide range of values are present within our sample. Many of the galaxies in the lowest bins contain only a few massive clusters or none at all, but a few galaxies have much higher values than the average. The most extreme values are found in NGC 1156, NGC 1313, NGC 3621, NGC 5204 and NGC 5236. The galaxy NGC 2997 also hosts a very rich cluster system, but the value is probably severely underestimated because of the large distance of NGC 2997 which introduces significant incompleteness problems. A similar remark applies to two other distant galaxies observed at the Danish 1.54 m. telescope, NGC 1493 and NGC 7424, while all the remaining galaxies in Table 1 are either more nearby, or have been observed at the NOT in better seeing conditions, and hence their values are believed to be more realistic.
4.2. Two-colour diagrams
In Fig. 4 we show the diagrams for six cluster-rich galaxies. These plots also include the so-called "S" sequence defined by Girardi et al. (1995, see also Elson & Fall (1985)), represented as a dashed line. The "S" sequence is essentially an age sequence, derived as a fit to the average colours of bright LMC clusters in the diagram. The age increases as one moves along the S-sequence from blue to red colours. The colours of our cluster candidates are very much compatible with those of the S-sequence, especially if one considers that there is a considerable scatter around the S-sequence also for Magellanic Cloud clusters (Girardi et al. 1995). Also included in the diagrams are stellar models by Bertelli et al. (1994) (dots), in order to demonstrate that the position of clusters within such a diagram is distinctly different from that of single stars. Already from Fig. 4 one can see that there is a considerable age spread among the clusters in each galaxy, with the red cut-off being due to our selection criteriae. The reddening vector corresponding to a reddening of is shown in each plot as an arrow, and it is quite clear that the spread along the S-sequence cannot be entirely due to reddening effects.
Bresolin et al. (1996) used HST data to carry out photometry for star clusters in the giant Sc-type spiral M 101. A comparison between their data and photometry for clusters in one of our galaxies (NGC 1313) is shown in Fig. 5. It is evident that the colours of clusters in the two galaxies are very similar. NGC 1313 was chosen as an illustrative example because it contains a relatively rich cluster system, although not so rich that the diagram becomes too crowded.
In Fig. 5 we have also included a curve showing the colours of star clusters according to the population synthesis models of Bruzual & Charlot (1993, hereafter BC93). The agreement between the synthetic and observed colours is very good for U-B , but for U-B the B-V colours of the BC93 models are systematically too blue compared to our data and the S sequence. The "red loop" that extends out to B-V0.3 and U-B-0.5 is due to the appearance of red supergiants at an age of about years (Girardi & Bica 1993) and is strongly metallicity dependent. Girardi et al. (1995) constructed population synthesis models based on a set of isochrones by Bertelli et al. (1994) and found very good agreement between the S-sequence and their synthetic colours. The models (solar metallicity) are included in Fig. 5 as a solid line. In these models the "red loop" is not as pronounced as in the BC93 models, and the youngest models are in general not as blue as those of BC93, resulting in a much better fit to the observed cluster colours.
4.3. Ages and masses
A direct determination of the mass of an unresolved star cluster requires a knowledge of the M/L ratio, which in turn depends on many other quantities, in particular the age and the IMF of the cluster. However, if one assumes that the IMF does not vary too much from one star cluster to another, then the luminosities alone should facilitate a comparison of star clusters with similar ages .
Applying the S-sequence age calibration to the clusters in our sample, the luminosities of each cluster can then be directly compared to Milky Way clusters of similar age, as shown in Fig. 6. Ages and absolute visual magnitudes for Milky Way open clusters are from the Lyngå (1982) catalogue, and are represented in each plot as small crosses. In the diagrams in Fig. 6 we have also indicated the effect of a reddening of E(B-V) = 0.30. In these plots the "reddening vector" depends in principle on the original position of the cluster within the (U-B,B-V) diagram from which the age was derived, but we have included two typical reddening vectors, corresponding to two different ages.
In all of the galaxies in Fig. 6 but NGC 2403, the absolute visual magnitudes of the brightest clusters are 2-3 magnitudes brighter than the upper limit of Milky Way open clusters of similar ages. Accordingly they should be nearly 10 times more massive. In the case of NGC 2403, the most massive clusters are not significantly more massive than open clusters found in the Milky Way. Fig. 6 also confirms the suspicion that the cluster data in NGC 2997 are incomplete, particularly for .
We have included population synthesis models for the luminosity evolution of single-burst stellar populations of solar metallicity by BC93 in Fig. 6, scaled to a total mass of . Models for three different IMFs are plotted: Salpeter (1955), Miller-Scalo (1979) and Scalo (1986), all covering a mass range from 0.1-65 . The different assumptions about the shape of the IMF obviously affect the evolution of the magnitude per unit mass quite strongly, and unfortunately the effect is most severe just in the age interval we are interested in. The difference between the Miller-Scalo and the Scalo IMF amounts to almost 2 magnitudes, but in any case the most massive clusters appear to have masses around .
In Fig. 6 we have also indicated the location of a "typical" old globular cluster system with an error bar centered on the coordinates 15 Gyr, and with mags. Although the comparison of masses at high and low age based on population synthesis models is extremely sensitive to the exact shape of the IMF, it seems that the masses of the young massive star clusters are at least within the range of "true" globular clusters.
Reddening effects alone are unlikely to affect the derived ages to a high degree, as a scatter along the "reddening vectors" in Fig. 6 would then be expected. Basically this would mean that one would expect a much steeper rate of decrease in vs. the derived age, while the observed relation between age and the upper luminosity limit is in fact remarkably compatible with that predicted by the models. The comparison with model calculations implies that the upper mass limit for clusters must have remained relatively unchanged over the entire period during which clusters have been formed in each galaxy.
© European Southern Observatory (ESO) 1999
Online publication: April 12, 1999