On cross-spectrum capabilities for detecting stellar oscillation modes

¹ Institut d'Astrophysique Spatiale, Université Paris XI–CNRS, Bâtiment 121, 91405 Orsay Cedex, France e-mail: [Thierry.Appourchaux;Patrick.Boumier]@ias.u-psud.fr
² National Solar Observatory, Tucson, Arizona, USA e-mail: John.Leibacher@ias.u-psud.fr

Received: 24 March 2006
Accepted: 30 November 2006

Abstract

Aims.Long-lived stellar oscillation modes are usually detected using Fourier transforms of time series of stellar radial velocities or brightness. It is commonly thought that one could use the cross spectrum of the two signals, or alternatively use the interleaved series of a single signal, to considerably improve the detection level by reducing the noise level.

Methods.We use a statistical analysis of the cross spectrum to compute its mean value and rms value, and use the associated signal-to-noise ratio for stochastically excited modes.

Results.Here, we demonstrate that the gain in the signal-to-noise ratio can indeed be improved for modes with a shorter lifetime than the observation time, but not those with a longer lifetime than the observation time.