Relation between photometric and parameter errors of star clusters

Many observations supply only photometry data with large uncertainties. The study of star clusters based on such data is important for astrophysical studies, although photometric uncertainty affects the accuracy of results. In order to estimate the parameter uncertainties that are caused by photometric errors, this work quantifies the influence of photometric error on the uncertainties of some basic parameters when colour-magnitude diagram (CMD) fitting is used to determine these parameters. The observed data are derived from Hubble Space Telescope (HST) observations with the WFPC2 in four bands because of the large coverage of photometric error. The photometric errors that are estimated by Artificial Star Test (AST) are taken, and a binary star stellar population synthesis model and the Powerful CMD code are adopted to determine the parameters of star clusters. Two popular types of stellar population models, i.e. binary star simple stellar population (bsSSP) and single star simple stellar population (ssSSP), are used. The effects of photometric errors on the uncertainties of distance modulus (m - M), colour excess (E), metallicity (Z), and age (t), i.e. & UDelta;m - M, & UDelta;E, & UDelta;Z, and & UDelta;t, are studied via 19 globular clusters. The results show that & UDelta;m - M, & UDelta;E, & UDelta;Z, and & UDelta;t have positive correlations with photometric error. Some linear fitting formulae are given to make the results easy to use. The results can be used to estimate the errors of parameters that are caused by photometric error when determining the parameters by CMD fitting, for star clusters with relatively large photometric uncertainties (>& SIM;0.01 mag).