New tools for finding and testing of weak periodical variability

Our paper presents new methods for finding and testing of weak periodic variability of stellar objects developed for the purpose of detecting expected regular light variations of magnetic chemically peculiar (mCP) candidates in the Large Magellanic Cloud. We introduce two new periodograms of the mCP star, BS Cir (HD 125630), appropriate for rotating spotted variables and compare the results with those obtained by the well-known Lomb-Scargle periodogram. The usage of periodograms and the testing of the significance of the found period candidates are demonstrated with two examples: the observed and simulated observations of the magnetic field of the mCP star CQ UMa (HD 119213) and the mCP candidate OGLE LMC136.7 16501. Three newly developed tests of the periodic variability - the shuffling, bootstrap and subsidiary ones, are presented. We demonstrate that the found periodic variations known with Signal-to-Noise ratio larger than 6 can be approved as real.