Analytic Marginalization of Absorption Line Continua

Abstract

Abstract Absorption line spectroscopy is a powerful way of measuring properties of stars and the interstellar medium. Absorption spectra are often analyzed manually, an approach that limits reproducibility and which cannot practically be applied to modern data sets consisting of thousands or even millions of spectra. Simultaneous probabilistic modeling of absorption features and continuum shape is a promising approach for automating this analysis. Existing implementations of this approach use numerical methods such as Markov Chain Monte Carlo to marginalize over the continuum parameters. When continua are parameterized as linear functions such as polynomials or splines, it is possible to reduce continuum parameter marginalization to an integral over a multivariate normal distribution, which has a known closed form. Analytic marginalization makes it possible to combine optimization for absorption line parameters with marginalization of nuisance continuum parameters. We compare the accuracy to within which absorption line parameters can be recovered using different continuum placement methods and find that marginalization with an informative prior on continuum parameters is a clear improvement over other continuum placement methods over a broad range of signal-to-noise ratios. We implement analytic marginalization over linear continuum parameters in the open-source package amlc.