The “four sigma” limit for significant periodicities

Abstract

Most of the pulsations which have been observed in sdB stars have very low amplitudes. Detection of modes from photometric observations is usually performed by noting the most prominent peaks in a periodogram or, equivalently, an amplitude spectrum. A common strategy is to assume that peaks which exceed four times the mean noise level correspond to significant periodicities. The efficiency of the assumption is investigated by simulation. It is found that the actual significance levels corresponding to the four sigma limit may vary by orders of magnitude, depending on the exact data configuration.