Bayesian Inference from Observations of Solar-Like Oscillations

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Abstract
Stellar oscillations can provide a wealth of information about a star, which can be extracted from observed time series of the star's brightness or radial velocity. In this paper we address the question of how to extract as much information as possible from such a dataset. We have developed a Markov Chain Monte Carlo (MCMC) code that is able to infer the number of oscillation frequencies present in the signal and their values (with corresponding uncertainties), without having to fit the amplitudes and phases. Gaps in the data do not have any serious consequences for this method; in cases where severe aliasing exists, any ambiguity in the frequency determinations will be reflected in the results. It also allows us to infer parameters of the frequency pattern, such as the large separation Delta nu. We have previously applied this method to the star nu Indi (Bedding et al 2006), and here we describe the method fully and apply it to simulated datasets, showing that the code is able to give correct results even when some of the model assumptions are violated. In particular, the non-sinusoidal nature of the individual oscillation modes due to stochastic excitation and damping has no major impact on the usefulness of our approach.

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