1999ApJ...512..386E

An error analysis of the inverse photometric problem is performed. The uncertainties of the input parameters, which are the brightness measurements and 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 (β), inclination of rotation axis (i), and spot temperatures (T_s)] from the light curves of a spherical star with a cool circular spot. The uncertainties of the solution parameters are mostly caused by the uncertainties of the brightness. The error contribution from the uncertainty of the limb-darkening coefficients is negligible. 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 brightness 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 β are much bigger. Light curves with such uncertainties are not good at all for determining the inclinations and the latitudes because predicted uncertainties are even bigger than the allowed limits, that is, greater than ±90°. The spot temperatures, on the other hand, are estimated to be uncertain about ±500 K for the models which are assumed with a spot 1300 K cooler than photospheric temperature with T_eff=4820 K. In order to determine unique surface maps of spotted stars and the inclination of their rotation axis with a reasonable accuracy (~±10°), highly accurate light curves (~±0.0001 mag) are required. The uniqueness problem of the light curve modeling and its consequences are discussed.