Replacing standard galaxy profiles with mixtures of Gaussians

Exponential, de Vaucouleurs, and S\'ersic profiles are simple and successful models for fitting two-dimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or correlation) of the models with the telescope point-spread function (PSF); these operations are slow, and easy to get slightly wrong at small radii. Here we exploit the realization that these models can be approximated to arbitrary accuracy with a mixture (linear superposition) of two-dimensional Gaussians (MoGs). MoGs are fast to render and fast to affine-transform. Most importantly, if you have a MoG model for the pixel-convolved PSF, the PSF-convolved, affine-transformed galaxy models are themselves MoGs and therefore very fast to compute, integrate, and render precisely. We present worked examples that can be directly used in image fitting; we are using them ourselves. The MoG profiles we provide can be swapped in to replace the standard models in any image-fitting code; they sped up model fitting in our projects by an order of magnitude; they ought to make any code faster at essentially no cost in precision.