Computing Limb Darkening Coefficients from Stellar Atmosphere Models
  We explore the sensitivity of limb darkening coefficients computed from stellar atmosphere models to different least-squares fitting methods. We demonstrate that conventional methods are strongly biased to fitting the stellar limb. Our suggested method of fitting by minimizing the radially integrated squared residual yields improved fits with better flux conservation. The differences of the obtained coefficients from commonly used values are observationally significant. We show that the new values are in better agreement with solar limb darkening measurements as well as with coefficients reported from analyses of eclipsing binary light curves. 
David Heyrovsky