Integrated parameters of star clusters: a comparison of theory and observations

This paper presents integrated magnitudes and colours for synthetic clusters. The integrated parameters have been obtained for the whole cluster population as well as for the main-sequence (MS) population of star clusters. We have also estimated observed integrated magnitudes and colours of the MS population of galactic open clusters, Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) star clusters. It is found that the colour evolution of the MS population of star clusters is not affected by the stochastic fluctuations, however, these fluctuations significantly affect the colour evolution of the whole cluster population. The fluctuations are maximum in (V - I) colour in the age range 6.7 < log(age) < 7.5. Evolution of integrated colours of the MS population of clusters in the Milky Way, LMC and SMC, obtained in the present study is well explained by the present synthetic cluster model. The observed integrated (B - V) colours of the MS population of LMC star clusters having age >= 500 Myr seem to be distributed around the Z = 0.004 model, whereas (V - I) colours are found to be bluer than those predicted by the Z = 0.004 model. The (V - I) versus (B - V) two-colour diagram for the MS population of the Milky Way star clusters shows a fair agreement between the observations and present model, however, the diagrams for LMC and SMC clusters indicate that observed (V - I) colours are relatively bluer. Possible reasons for this anomaly have been discussed. Comparison of the synthetic (U - B) versus (B - V) relation with the observed integrated parameters of the whole cluster population of the Milky Way, LMC and SMC star clusters indicates that the majority of the bluest clusters [(B - V)(0) < 0.0] follow the MS population relation. The colour evolution of young Milky Way, LMC and SMC clusters [6.5 < log(age) < 8.0] also indicates that a large number of young clusters follow the MS population relation. Therefore, in the absence of a careful modelling of stochastic effects, age determination of young star clusters by comparing their integrated colours with whole cluster synthetic colours may yield erroneous results.