Physical parameters of rich LMC clusters from modeling of deep HST colour–magnitude diagrams

We present the analysis of deep colour–magnitude diagrams (CMDs) of five rich LMC clusters. The data were obtained with HST/WFPC2 in the F555W(~V) and F814W(~I) filters, reaching $V_{555} \sim 25$. The sample of clusters is composed of NGC 1805 and NGC 1818, the youngest ones ($\tau < 100$Myr), NGC 1831 and NGC 1868, of intermediate-age ($ 400 < \tau < 1000 $Myr), and Hodge 14, the oldest ($\tau > 1200$Myr). We discuss and apply a statistical method for correcting the CMD for sampling incompleteness and field star contamination. Efficient use of the CMD data was made by means of direct comparisons of the observed to model CMDs. The CMD modeling process generates a synthetic Main Sequence (MS), where we introduce as model inputs the information about age, chemical composition, present day mass function (PDMF), fraction of unresolved binaries, distance modulus and light extinction. The photometric uncertainties were empirically determined from the data and incorporated into the model as well. Statistical techniques of CMD comparisons using 1 and 2 dimensions are presented and applied as an objective method to assess the compatibility between model and data CMDs. By modeling the CMDs from the central region we infer the metallicity (Z), the intrinsic distance modulus ($(m-M)_0$) and the reddening value ($E(B-V)$) for each cluster. We also determined the age for the clusters with $\tau > 400$Myr. By means of two-dimensional CMD comparisons we infer the following values: for NGC 1805, $Z=0.007 \pm 0.003$, $(m-M)_{0}=18.50 \pm 0.11$, $E(B-V)=0.03 \pm 0.01$; for NGC 1818, $Z=0.005 \pm 0.002$, $(m-M)_{0}=18.49 \pm 0.14$, $E(B-V) \sim 0.00$; for NGC 1831, $Z=0.012 \pm 0.002$, log($\tau/$yr$)=8.70 \pm 0.03$, $(m-M)_{0}=18.70 \pm 0.03$, $E(B-V) \sim 0.00$; for NGC 1868, $Z=0.008 \pm 0.002$, log($\tau/$yr$)=8.95 \pm 0.03$, $(m-M)_{0}=18.70 \pm 0.03$, $E(B-V) \sim 0.00$; for Hodge 14, $Z=0.008 \pm 0.004$, log($\tau/$yr$)=9.23 \pm 0.10$, $(m-M)_{0}=18.51 \pm 0.13$, $E(B-V)=0.02 \pm 0.02$. Taking into account the uncertainties, these values are in accordance with the ones obtained applying the one-dimensional CMD analysis, adding reliability to these determinations.