Nonparametric Estimation of Galaxy Cluster Emissivity and Detection of Point Sources in Astrophysics With Two Lasso Penalties

Astrophysicists are interested in recovering the three-dimensional gas emissivity of a galaxy cluster from a two-dimensional telescope image. Blurring and point sources make this inverse problem harder to solve. The conventional approach requires in a first step to identify and mask the point sources. Instead we model all astrophysical components in a single Poisson generalized linear model. To enforce sparsity on the parameters, maximum likelihood estimation is regularized with two l1 penalties with weights <i>λ</i>₁ for the radial emissivity and <i>λ</i>₂ for the point sources. The method has the advantage of not employing cross-validation to select <i>λ</i>₁ and <i>λ</i>₂. To judge the significance of interesting features, we quantify uncertainty with the bootstrap. We apply our method to two X-ray telescopes (XMM-Newton and Chandra) data to estimate gas emissivity. The results are more stable and seems less biased than the conventional method, in particular in the outskirt of galaxy clusters. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.