Reliability of light curves for photometric imaging

An error analysis of the inverse photometric problem is performed. The unce rtainties of the input parameters, which are the brightness measurements an d the linear limb-darkening coefficients at the effective wavelength of the observations, are analytically propagated to compute the uncertainties of the solution parameters [size (r), latitude (beta), inclination of rotation axis (i), and spot temperatures (T-s)] from the light curves of a spherica l star with a cool circular spot. The uncertainties of the solution paramet ers are mostly caused by the uncertainties of the brightness. The error con tribution from the uncertainty of the limb-darkening coefficients is neglig ible. According to the test models, with maculation wave of about 0.15 mag amplitude, for the light curves which are accurate +/- 0.005 mag in brightn ess and +/- 0.005 in linear limb-darkening coefficients, the uncertainty of the spot size is about the original spot size. The uncertainties of i and beta are much bigger. Light curves with such uncertainties are not good at all for determining the inclinations and the latitudes because predicted un certainties are even bigger than the allowed limits, that is, greater than +/- 90 degrees. The spot temperatures, on the other hand, are estimated to be uncertain about +/- 500 K for the models which are assumed with a spot 1 300 K cooler than photospheric temperature with T-eff = 4820 K. In order to determine unique surface maps of spotted stars and the inclination of thei r rotation axis with a reasonable accuracy (approximate to +/- 10 degrees), highly accurate light curves (approximate to +/- 0.0001 mag) are required. The uniqueness problem of the light curve modeling and its consequences ar e discussed.