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 (Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer) O V 629Å observations and resolves four distinct P4, P5, P6 and P7 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 eigen modes. Subject headings: Methods: statistical — Sun: helioseismology — Sun: oscillations — sunspots — Stars: oscillations — Waves