Colour-colour diagrams and extragalactic globular cluster ages - Systematic uncertainties using the (V-K)-(V-I) diagram

Context. Age and metallicity estimates for extragalactic globular clusters, from integrated colour-colour diagrams, are examined. Aims. We investigate biases in cluster ages and [ Fe/H] estimated from the (V-K)-(V-I) diagram, arising from inconsistent Horizontal Branch morphology, metal mixture, treatment of core convection between observed clusters and the theoretical colour grid employed for age and metallicity determinations. We also study the role played by statistical fluctuations of the observed colours, caused by the low total mass of typical globulars. Methods. Synthetic samples of globular cluster systems are created, by means of Monte-Carlo techniques. Each sample accounts for a different possible source of bias, among the ones addressed in this investigation. Cumulative age and [Fe/H] distributions are then retrieved by comparisons with a reference theoretical colour-colour grid, and analyzed. Results. Horizontal Branch morphology is potentially the largest source of uncertainty. A single-age system harbouring a large fraction of clusters with an HB morphology systematically bluer than the one accounted for in the theoretical colour grid, can simulate a bimodal population with an age difference as large as similar to 8 Gyr. When only the redder clusters are considered, this uncertainty is almost negligible, unless there is an extreme mass loss along the Red Giant Branch phase. The metal mixture affects mainly the redder clusters; the effect of colour fluctuations becomes negligible for the redder clusters, or when the integrated M-V is brighter than similar to-8.5 mag. The treatment of core convection is relevant for ages below similar to 4 Gyr. The retrieved cumulative [Fe/H] distributions are overall only mildly affected. Colour fluctuations and convective core extension have the largest effect. When 1 sigma photometric errors reach 0.10 mag, all biases found in our analysis are erased, and bimodal age populations with age differences of up to similar to 8 Gyr go undetected. The use of both (U-I)-(V-K) and (V-I)-(V-K) diagrams may help disclosing the presence of blue HB stars unaccounted for in the theoretical colour calibration.