An Algorithm For A Period Search In A Sparsely Covered Time Series At A Fixed Phase

. Researchers are sometimes faced with a set of observations that constitute a sparse coverage of a time series, suspected to be periodic. The period is unknown, but one can identify in the observed data a few points that are presumed to occur at the same phase, in different cycles of the unknown periodicity. We propose an algorithm that finds all periods which are compatible with such observed data, and suggest how to assess their statistical significance. The algorithm also provides stringent limits on the epochs of the fixed phase. We give three examples, from the field of astronomy, for application of our new algorithm. In the first one the algorithm reveals, on the basis of very few photometric observations, a highly significant period in the light curve of the recent classical Nova Herculis 1991. In the second example, in the series of arrival times of neutrinos from the supernova SN1987A, our algorithm yields a definite negative result. It proves that no significant exact periodicity is present in the data. In the third application, the algorithm provides new constraints on the epoch of one of the minima in the light curve of the stellar binary system 44i Bootis. We compare the method with other period search techniques, pointing out a few of its advantages, as well as some of its weaknesses.