Astronomical time-series analysis - II. A search for periodicity using theShannon entropy

We have recently introduced a new method of searching a time series for per iodic variability. The method uses the Shannon entropy to measure the amoun t of information provided by a set of observations that may contain an unde rlying periodic signal, as a function of the assumed period of this hypothe tical periodic signal. Here we present the analytical arguments that suppor t this algorithm within the broader frame of information theory. We also sh ow that, in the absence of a periodic signal, the entropies follow a Gaussi an distribution, which then provides an easy way of assessing the significa nce of a positive detection. We test this method using simulated data with non-sinusoidal variability, and we show that it is more sensitive than the classical periodograms or those variations adapted to deal with cases where harmonics are involved. Finally, we show that this method is capable of re solving two, almost identical, frequencies present in a given time series, even in cases where the classical periodograms fail to do so.