On detecting short-lived p modes in a stellar oscillation spectrum

The false alarm probability for detecting peaks embedded in a power spectrum of noise was given by [CITE]. This test has been used in helioseismology to detect long-lived modes such as g modes [CITE]. With the development of asteroseismology, there is now a need to define a similar test but for short-lived p modes. In this article, I define a false alarm test for detecting short-lived p modes, and I give the probability of detecting such modes given their signal-to-noise ratio, their linewidths and the duration of observation.