Reconstructing AGN X-ray spectral parameter distributions with Bayesian methods

Abstract

X-ray spectra of active galactic nuclei (AGN) consist of several different emission and absorption components. To determine the spectral parameters, these components are often fitted manually with models chosen on a case-by-case basis. However, this approach has two problems. First, it becomes very hard for a survey with a large number of sources. Second, when the signal-to-noise ratio (S/N) is low, there is a tendency to adopt an overly simplistic model, biasing the parameters and making their uncertainties unrealistic. We developed a Bayesian method for automatically fitting AGN X-ray spectra obtained by XMM-Newton with a consistent and physically motivated model. Our model includes all spectral components, even when the data quality is low. We used a physical model for the X-ray background and an empirical model for the non-X-ray background. Noninformative priors were applied on the parameters of interest, the photon index (Γ) and the hydrogen column density (NH), while informative priors obtained from deep surveys were used to marginalize over the parameter space of the nuisance parameters. To improve speed, we developed a specific spectral extraction and fitting procedure. We tested this method using a realistic sample of 5000 spectra, which was simulated based on our source model, reproducing typical population properties. Spectral parameters were randomly drawn from the priors, taking the luminosity function into account. Well-constrained or meaningful posterior probability density distributions (PDFs) were obtained for the most relevant spectral parameters, for instance, NH, Γ, and LX, even at low S/N, but in this case, we were unable to constrain the parameters of secondary components such as the reflection and soft excess. As a comparison, a maximum-likelihood approach with model selection among six models of different complexities was also applied to this sample. We find clear failures in the measurement of Γ in most cases, and of NH when the source is unabsorbed (NH <  1022 cm−2). The results can hardly be used to reconstruct the parent distributions of the spectral parameters, while our Bayesian method provides meaningful multidimensional posteriors that will be used in a subsequent paper to infer the population.