SkyFACT: High-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods

We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), a new approach for studying, modeling and decomposing diffuse gamma-ray emission. Like most previous analyses, the approach relies on predictions from cosmic-ray propagation codes like GALPROP and DRAGON. However, in contrast to previous approaches, we account for the fact that models are not perfect and allow for a very large number ( 10⁵) of nuisance parameters to parameterize these imperfections. We combine methods of image reconstruction and adaptive spatio-spectral template regression in one coherent hybrid approach. To this end, we use penalized Poisson likelihood regression, with regularization functions that are motivated by the maximum entropy method. We introduce methods to efficiently handle the high dimensionality of the convex optimization problem as well as the associated semi-sparse covariance matrix, using the L-BFGS-B algorithm and Cholesky factorization. We test the method both on synthetic data as well as on gamma-ray emission from the inner Galaxy, |ℓ|<90^o and |b|<20^o, as observed by the Fermi Large Area Telescope. We finally define a simple reference model that removes most of the residual emission from the inner Galaxy, based on conventional diffuse emission components as well as components for the Fermi bubbles, the Fermi Galactic center excess, and extended sources along the Galactic disk. Variants of this reference model can serve as basis for future studies of diffuse emission in and outside the Galactic disk.