Bayesian Spectral Analysis of Metal Abandance Deficient Stars

Abstract

Metallicity can be measured by analyzing the spectra in the X-ray region and comparing the flux in spectral lines to the flux in the underlying Bremsstrahlung continuum. In this paper we propose new Bayesian methods which directly model the Poisson nature of the data and thus are expected to exhibit improved sampling properties. Our model also accounts for the Poisson nature of background contamination of the observations, image blurring due to instrument response, and the absorption of photons in space. The resulting highly structured hierarchical model is fit using the Gibbs sampler, data augmentation and Metropolis-Hasting. We demonstrate our methods with the X-ray spectral analysis of several "Metal Abundance Deficient" stars. The model is designed to summarize the relative frequency of the energy of photons (X-ray or gamma-ray) arriving at a detector. Independent Poisson distributions are more appropriate to model the counts than the commonly used normal approximation. We model the high energy tail of the ASCA spectrum of each of the stars as a combination of a Bremsstrahlung continuum and ten narrow emission lines, included at positions of known strong lines. Statistical analysis is based on two source observations and one background observation. We use sequential Bayesian analysis for the two source observations; the posterior distribution from the first analysis is used to construct a prior for the second. Sensitivity of the final results to the choise of prior is investigated by altering the prior.