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6 Resolving YMCs in the galaxies

  The ishape algorithm was applied to all the star clusters identified as described in Sect. 3.3. For the shape model the MOFFAT15 profile was chosen because of its similarity with the models adopted by Elson et al. (1987), and the PSF was generated using DAOPHOT. The cleaning radius was set to 2 pixels and the fitting radius to 4 pixels, and the CTRESH parameter was set to 2.

Figure 12: The effective radii $R_{\rm e}$ in pixel units of clusters measured on V and B band frames plotted against each other. Only clusters with S/N > 50 are included in these plots

\includegraphics [width=8.8cm,clip]{}\end{figure} Figure 13: Histogram of the effective radii of objects in NGC 5236 with V < 19.5 and B-V > 0.6, assumed to be mostly foreground stars. Only objects in the region 300 < x < 1700 pixels and 300 < y < 1700 pixels were included. For easier comparison with Fig. 14 the effective radii have been converted into parsec (1 pc $\approx$0.05$^{\prime\prime}$)

\includegraphics [width=88mm,clip]{}

\includegraphics [width=88mm,clip]{}\end{figure} Figure 14: Histograms of the effective radius $R_{\rm e}$ for clusters in the "red'' and "blue'' groups in NGC 5236 (top) and NGC 1313 (bottom). The effective radii in pixels were converted into parsec using the distances to the galaxies given in Paper I. The horizontal bar indicates the typical uncertainty

The effective radii were derived both on B and V band images for the 6 most cluster-rich galaxies in order to check the results. In Fig. 12 the effective radii (in pixel units) derived by ishape from B and V band frames are plotted against each other for objects with S/N > 50, leaving out about 20% of the objects. If objects with lower S/N were included, the scatter was found to increase somewhat, although the correlations in Fig. 12 would remain evident.

As another test, radii were derived for sources in the NGC 5236 frame with B-V > 0.6 and V < 19.5. Most of these objects are expected to be foreground stars, and they are indeed distributed quite uniformly across the CCD frame. Figure 13 shows the $R_{\rm e}$ distribution for all such objects located within the central $1400 \times 1400$ pixels of the image, roughly corresponding to the area covered by the galaxy. For convenience, the effective radii have been converted to parsec. It can be seen from Fig. 13 that ishape finds $R_{\rm e}<1$ pc (0.05$^{\prime\prime}$) for the vast majority of the objects with B-V>0.6, in agreement with the assumption that they are in fact foreground stars. The fact that foreground stars appear virtually unresolved by ishape adds confidence to the algorithm's ability to recognise extended objects.

The number of clusters in most of the galaxies are really too sparse that it makes sense to discuss the $R_{\rm e}$ distributions for individual galaxies. However, Fig. 14 shows $R_{\rm e}$ histograms for two of the most cluster-rich galaxies, NGC 5236 and NGC 1313. These are also the two most nearby galaxies, at m-M=27.84 and 28.2 respectively (see Paper I). Separate histograms are given for the "red'' (U-B > -0.4) and "blue'' ($U-B\leq -0.4$) cluster samples. Several systematic effects might influence the observed $R_{\rm e}$ distributions, for example the fact that the most extended clusters are detected with a much lower efficiency, and one should be careful not to overinterpret the data in Fig. 14. Nevertheless, the objects in the "blue'' sample generally seem to be less concentrated, which might imply that many of the blue objects are loosely bound associations that do not survive for long, rather than bound clusters. It is emphasised, however, that this statement could only be justified by a more detailed study of the structure of the objects, something that is not feasible from ground-based observations. Figure 14 also seems to indicate that many of the objects in NGC 5236 are more concentrated than those in NGC 1313, although the statistics are poor for the latter galaxy.

From the discussion in Sect. 4.3 and Fig. 12 the uncertainty on the cluster radii is estimated to be about 0.5 pixels. 1 DFOSC pixel ($0.4\hbox{$^{\prime\prime}$}$) corresponds to about 7 pc at the distance of NGC 5236 and NGC 1313, so we expect an uncertainty of about 4 pc on the individual cluster radii in Fig. 14, as indicated by the horizontal error bars. The fact that we do not observe any lower limit in the $R_{\rm e}$ distribution may be an effect of the limited resolution, causing clusters with larger radii to scatter into the low $R_{\rm e}$ region, but the lower $R_{\rm e}$ limit in our sample cannot be higher than a few pc.

How do the sizes of the clusters discussed here compare with other results? Accurate measurements of cluster sizes are available only in the Milky Way and in the LMC. Most globular clusters in the Milky Way have $R_{\rm e} < 10$ pc with a peak in the $R_{\rm e}$ distribution at about 3 pc, although clusters with $R_{\rm e}$ up to $\sim 30$ pc exist (Harris 1996). Elson et al. (1987) found typical half-mass radii for young LMC clusters in the range 5-15 pc, corresponding to $R_{\rm e}$ values between 4 and 12 pc (Spitzer 1987).

Effective radii have been estimated also for young clusters in the Antennae by Whitmore & Schweizer (1995, WS95) using HST/WFPC data, and in the merger remnant NGC 7252 (Whitmore et al. 1993), in both cases by assuming Gaussian cluster profiles. WS95 found an average $R_{\rm e}$ of 12 pc for the Antennae clusters, but new WFPC/2 data lead to a revised mean value of $R_{\rm e} = 4\pm 1$ pc (Whitmore et al. 1999). In the case of NGC 7252, Whitmore et al. (1993) found a mean effective radius of 9.9 pc for clusters located at distances larger than 3.5$^{\prime\prime}$ from the centre of NGC 7252. Östlin et al. (1998) used the model profile of Lugger et al. (1995) to estimate core radii (one half times the FWHM) for YMCs in the blue compact galaxy ESO 338-IG04, and found a distribution that peaked at 2.5 pc with all clusters having core radii less than 10 pc. The Lugger et al. (1995) profile does not have a well-defined effective radius, but Östlin et al. (1998) also found that if the clusters were instead fitted with Gaussian profiles (for which the core radius equals $R_{\rm e}$) the core radii were about 2 times larger than for the Lugger et al. (1995) profiles, so their $R_{\rm e}$ distribution should peak at about 5 pc and have an upper limit at 20 pc.

Our observed $R_{\rm e}$ distributions thus seem to resemble those observed for YMCs in other galaxies quite well. We note, however, that the effective radii have been estimated by a variety of methods in the different studies, and this could account for some of the differences. The effective radii for the YMCs in our sample are also comparable with those of Galactic globular clusters and young LMC clusters.

The velocity dispersion in a star cluster or OB association is typically of the order of 1-10 km s-1, so an unbound object will expand by 1-10 pc/Myr. A U-B colour of -0.4 corresponds to an age of about 50 Myr (Girardi et al. 1995), so most of the objects in the "red'' group would have expanded to sizes much larger than what is observed and would have effectively disappeared if they were not gravitationally bound. Like all star clusters they will eventually be subject to dynamical erosion, but this acts on much longer timescales and the lifetimes are difficult to estimate without a detailed knowledge of the morphology of individual clusters and their orbits within the host galaxies.

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