On the separation of T Tauri star spectra using non-negative matrix factorization and Bayesian positive source separation

The objective of this study is to compare and evaluate Bayesian and deterministic methods of positive source separation of young star spectra. In the Bayesian approach, the proposed Bayesian Positive Source Separation (BPSS) method uses Gamma priors to enforce non-negativity in the source signals and mixing coefficients and a Markov Chain Monte Carlo (MCMC) algorithm, modified by suggesting simpler proposal distributions and randomly initializing the MCMC to correctly separate spectra. In the deterministic approach, two Non-negative Matrix Factorization (NNMF) algorithms, the multiplicative update rule algorithm and an alternating least squares algorithm, are used to separate the star spectra into sources. The BPSS and NNMF algorithms are applied to the field of Astrophysics by applying the source separation techniques to T Tauri star spectra, resulting in a successful decomposition of the spectra into their sources. These methods are for the first time being applied and evaluated in optical spectroscopy. The results show that, while both methods perform well, BPSS outperforms NNMF. The NNMF and BPSS algorithms improve upon the current methodology used in Astrophysics iu two important ways. First, they permit the identification of additional components of the spectra in addition to the photosphere and boundary layer which can be modeled with current methods. Second, by applying a statistical algorithm, the modeling of T Tauri stars becomes less subjective. These methods may be further extrapolated to model spectra from other types of stars or astrophysical phenomena.