Bayesian analysis of solar oscillations

A Bayesian probability-based approach is applied to the problem of detecting and parameterizing oscillations in the upper solar atmosphere for the first time. Due to its statistical origin, this method provides a mechanism for determining the number of oscillations present, gives precise estimates of the oscillation parameters with a self-consistent statistical error analysis, and allows the oscillatory model signals to be reconstructed within these errors. A highly desirable feature of the Bayesian approach is the ability to resolve oscillations with extremely small frequency separations. The code is applied to SOHO CDS O v lambda 629 observations and resolves four distinct P-4; P-5; P-6, and P-7 p-modes within the same sunspot transition region. This suggests that a spectrum of photospheric p-modes is able to propagate into the upper atmosphere of the Sun and Sun-like stars, and places precise observational constraints on models of umbral eigenmodes.