Efficient multi-Gaussian expansion of galaxies

We describe a simple, efficient, robust and fully automatic algorithm for the determination of a multi-Gaussian expansion (MGE) fit to galaxy images, to be used as a parametrization for the galaxy stellar surface brightness. In most cases the least-squares solution found by this method essentially corresponds to the minimax, constant relative error, MGE approximation of the galaxy surface brightness, with the chosen number of Gaussians. The algorithm is well suited to be used with multiple-resolution images (e.g. Hubble Space Telescope (HST) and ground-based images). It works orders of magnitude faster and is more accurate than currently available methods. An alternative, more computing-intensive, fully linear algorithm that is guaranteed to converge to the smallest χ² solution is also discussed. Examples of MGE fits are presented for objects with HST or ground-based photometry, including galaxies with significant isophote twist.