4 Models

Figure 1: This figure presents Starburst99 (Leitherer et al. 1999) model tracks illustrating the effect of changing the mass of the star cluster. All model tracks are for an instantaneous burst. Asterisks mark the time at 1, 5, 10, 20, 50, 100, and 500 Myr. Note that the only effect of a lower mass is to shift the tracks downward at constant color; stochastic effects are not included.

Figure 2: This figure presents Starburst99 (Leitherer et al. 1999) model tracks illustrating the effect of changing metallicity. All model tracks are for an instantaneous burst of $10^{6}~M_{\odot}$. Asterisks mark the time at 1, 5, 10, 20, 50, 100, and 500 Myr.

We are using the Starburst99 evolutionary models (Leitherer et al. 1999) to compare our colors and magnitudes. We calculate a magnitude for each WFPC2 filter using standard response functions at the selected ages and metallicities. Clusters are represented by an instantaneous burst of $10^{6}~M_{\odot}$ with an upper mass limit of 100 $M_{\odot}$ and a lower mass limit of 1 $M_{\odot}$. Varying the mass of the burst affects the magnitude as shown in Fig. 1, but not the colors. This means that our two-color comparisons are mass-independent, insofar as stochastic effects are not important in the real star clusters (see Lançon & Mouhcine 2000). Varying the metallicity affects both the magnitudes and the colors; this effect is shown for a two-color diagram in Fig. 2. We do not account for stochastic effects, which should introduce a spread in colors at cluster masses below $10^{5}~M_{\odot}$ (see Cerviño et al. 2002).

For clarity, we have chosen to plot only a single metallicity track for comparison with the NGC 7673 star clusters, Z=0.008, or just under half $Z_{\odot}$. The abundance of this galaxy has been found to be 12 + log O/H $\sim 8.6$ for the various clumps, slightly above that of the LMC (Duflot-Augarde & Alloin 1982), which is confirmed by a reanalysis of the spectrophotometry reported by Gallagher et al. (1989).

4.1 Nebular emission

Figure 3: This figure presents Starburst99 (Leitherer et al. 1999) model tracks illustrating the difference between models with only stellar emission and those with stellar and nebular continuum emission for an instantaneous burst of $10^{6}~M_{\odot}$. Time steps are as for Fig. 2.

The models we have chosen to use include only stellar emission. Starburst99 also offers the opportunity to include nebular continuum emission, calculated by assuming that every photon below 912 Å is converted into free-free and free-bound photons at longer wavelengths (nebular case B). Although the model assumptions may not apply, for comparison we show in Fig. 3 the variation in the two-color diagram for star cluster models including stellar emission only vs. stellar + nebular continuum. Here we can see that the difference is significant only for ages <7 Myr.

In young systems we also need to consider the influence of strong nebular line emission, as well as the weaker nebular continuum. Johnson et al. (1999) investigated the effects of nebular emission lines on WFPC2 star cluster colors. The main effect is due to strong emission lines of [OIII] and H$\beta$ in the F555W filter. While the nebular continuum emission makes the models redder in [555-814], they found the line emission makes them bluer, and the difference can be large for ages <10 Myr, depending on the strengths of the emission lines relative to a cluster's stellar continuum (e.g., Olofsson 1989; Zackrisson et al. 2001).

Unfortunately, the issue is not as simple as deciding whether to include nebular emission or not. For example, the nebular emission, both continuum and line, may be subtracted as part of the background if it extends smoothly beyond the cluster. So unless the nebular emission characteristics are known, e.g., from high angular resolution spectra, it is difficult to extract accurate ages from optical broad band colors of very young star clusters. Nevertheless, we proceed with fortitude, comparing our data with purely stellar continuum model tracks, aware that nebular effects may be important.

A rough estimate of the kind of effect that could occur can be estimated from the 10 arcsec circular aperture spectrum of Clump A presented in Gallagher et al. (1989). The combined emission equivalent widths from the H$\beta$ line (corrected for underlying absorption; as in Gallagher et al. 1989) and the [OIII] $\lambda$5007$+ \lambda$4959 doublet is about 90 Å. This then would produce an excess brightness of $\approx$0.07 mag in the F555W filter, and smaller offsets in the other two filters. Of course this emission correction would be an underestimate if the emission lines preferentially are associated with the individual star clusters. We can derive a different correction for this case by assuming all of the line emission is included in the photometry of the star clusters in Table 6. In this case we find a substantial correction of 0.3 mag due to the emission lines in the F555W filter.

In summary, the figures subsequently found throughout this paper show only and always the model track for purely stellar emission from a $10^{6}~M_{\odot}$cluster at a metallicity of Z = 0.008.