6 The mass versus age distribution

We discuss the results from the fitting of the observed energy distributions to those of cluster models with solar metallicity and with and upper mass limit of 30 $M_{\odot }$. We have checked that the fits with twice solar metallicity and with an upper limit of 100 $M_{\odot }$ give about the same results.

Figure 10 shows the mass versus age distribution of sources with M_v<-7.5 (to eliminate possible stellar sources) and with energy distributions that could be fitted to that of a cluster models with an accuracy of $\mbox{$\chi^2_{\nu}$ }\le 3.0$. (The distributions for clusters with $\mbox{$\chi^2_{\nu}$ }\le 1$ or 10, not shown here, show the same distribution, but with 294 and 508 clusters respectively.) We see that the lower limit of the mass increases with increasing age, from about 1000 $M_{\odot }$ at $t\simeq 5$ Myrs to about $5\times 10^4$ $M_{\odot }$ at 1 Gyr. This is due to the expected effect of fading of the clusters as they age (see Sect. 4.1). The full line in the figure is the fading line in the R magnitude for clusters which have a limiting magnitude of $R_{\rm lim}=22.0$ at the distance of M 51 for a reddening of E(B-V) = 0. The line in Fig. 10 thus gives the mass of the clusters, that reaches this magnitude detection limit, as a function of age.

Figure 10: The mass versus age relation of the 392 clusters with MV < -7.5, whose energy distribution could be fitted with an accuracy of $\mbox{$\chi^2_{\nu}$ }< 3.0$. The cross shows the characteristic uncertainties (Sect. 5.5). The full line is the predicted fading line due to the evolution of clusters with E(B-V) = 0 and with a limiting magnitude of $R_{\rm lim}=22.0$ at the distance of M 51. This line roughly agrees with the observed lower limit. The distribution is discussed in the text.

These initial mass versus age distribution of the clusters in Fig. 10 show the following characteristics:
- (i) The lower mass limit increases with age due to the fading of the clusters. The observed lower limit agrees with the predicted ones for the R band. There are even hints of the presence of the predicted dips in the lower limit near $\log(t)=6.8$ and 7.2. This strengthens our confidence in the adopted models.
- (ii) There are clear concentrations in the distribution at $\log(t)=6.70$ and 7.45 and possibly also around $\log(t) \simeq 7.2$. These are due to the properties of the cluster models and the adopted method. In Fig. 7 we have shown that the colours of the models do not change monotonically with time, but that there are phases when the colours change rapidly with time. These phases occur in the range of $6.5 < \log(t) < 7.3$. Large changes in the colours of the models occur just before and after the peaks where the slopes of the curves in Fig. 7 are large. It is more difficult to fit the observed energy distributions with high accuracy to models in the age range when the spectral changes are large, than in the age range when the changes are small. So there is a tendency of the model fits to concentrate in agebins just outside the age-regions of large spectral changes. This explains the concentrations and the voids in the derived age distributions of the clusters between about $6.5 < \log(t) < 7.5$.
- (iii) The density of the points drops at $\log(t) > 7.5$. Since the age scale is logarithmic, we might have expected an increasing density of points towards the higher ages, which is not observed. This is due to the disruption or dispersion of the clusters (see first paragraphs of Sect. 7).

We conclude that the mass versus age distribution agrees with the expected evolutionary fading of the clusters and that the decrease in numbers of clusters with age shows the affect of disruption/dispersion of clusters with time. The concentrations of the clusters at ages around $\log(t)=6.8$, 7.2 and 7.45 are due to statistical effects and do not represent periods of enhanced cluster formation.