On posterior probability and significance level: application to the power spectrum of HD 49 933 observed by CoRoT^*

¹ Institut d'Astrophysique Spatiale, UMR8617, Université Paris XI, Bâtiment 121, 91405 Orsay Cedex, France e-mail: Thierry.Appourchaux@ias.u-psud.fr
² Observatoire de Paris, LESIA, UMR8109, 92195 Meudon Cedex, France
³ Institut d'Astrophysique et de Géophysique de l'Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium

Received: 19 September 2008
Accepted: 21 May 2009

Abstract

Context. The CoRoT mission provides asteroseismic data of very high quality allowing one to adopt new statistical approaches for mode detection in power spectra, especially with respect to testing the null hypothesis (H₀, which assumes that what is observed is pure noise).

Aims. We emphasize that the significance level when rejecting the null hypothesis can lead to the incorrect conclusion that the H₀ hypothesis is unlikely to occur at that significance level. We demonstrate that the significance level is unrelated to the posterior probability of H₀, given the observed data set, and that this posterior probability is very much higher than implied by the significance level.

Methods. We use Bayes theorem to derive the posterior probability of that H₀ is true assuming an alternative hypothesis H₁ that a mode is present, taking some prior for the mode height, mode amplitude and linewidth.

Results. We compute the posterior probability of H₀ for the p modes detected on HD 49 933 by CoRoT.

Conclusions. We conclude that the posterior probability of H₀ provide a much more conservative quantification of the mode detection than the significance level. This framework can be applied to any similar stellar power spectra obtained to complete asteroseismology.