Galaxy Modeling with Compound Elliptical Shapelets

Gauss-Hermite and Gauss-Laguerre ("shapelet") decompositions of images have become important tools in galaxy modeling, particularly for the purpose of extracting ellipticity and morphological information from astronomical data. However, the standard shapelet basis functions cannot compactly represent galaxies with high ellipticity or large Sersic index, and the resulting underfitting bias has been shown to present a serious challenge for weak-lensing methods based on shapelets. We present here a new convolution relation and a compound "multi-scale" shapelet basis to address these problems, and provide a proof-of-concept demonstration using a small sample of nearby galaxies.