Probing gas motions in the intra-cluster medium: a mixture model approach

Upcoming high spectral resolution telescopes, particularly Astro-H, are expected to finally deliver firm quantitative constraints on turbulence in the intra-cluster medium (ICM). We develop a new spectral analysis technique which exploits not just the line width but the entire line shape, and show how the excellent spectral resolution of Astro-H can overcome its relatively poor spatial resolution in making detailed inferences about the velocity field. The spectrum is decomposed into distinct components, which can be quantitatively analysed using Gaussian mixture models. For instance, bulk flows and sloshing produce components with offset means, while partial volume-filling turbulence from the active galactic nucleus (AGN) or galaxy stirring leads to components with different widths. The offset between components allows us to measure gas bulk motions and separate them from small-scale turbulence, while component fractions and widths constrain the emission weighted volume and turbulent energy density in each component. We apply mixture modelling to a series of analytic toy models as well as numerical simulations of clusters with cold fronts and AGN feedback, respectively. From Markov chain Monte Carlo and Fisher's matrix estimates which include line blending and continuum contamination, we show that the mixture parameters can be accurately constrained with Astro-H spectra: at an similar to 10 per cent level when components differ significantly in width, and an similar to 1 per cent level when they differ significantly in the mean value. We also study error scalings and use information criteria to determine when a mixture model is preferred. Mixture modelling of spectra is a powerful technique which is potentially applicable to other astrophysical scenarios.