Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms

Abstract

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multi-harmonic' periodogram, which is being used for detection of non-sinusoidal signals, and is based on the least-squares fitting of truncated Fourier series. The recent investigation (Baluev 2008) made for the Lomb-Scargle periodogram is extended to the more general multi-harmonic periodogram. As a result, closed and efficient analytic approximations to the false alarm probability, associated with multi-harmonic periodogram peaks, are obtained. The resulting analytic approximations are tested under various conditions using Monte Carlo simulations. The simulations showed a suitable precision and robustness of these approximations.

8 pages, 6 figures, 1 table. Accepted to MNRAS

References in corpus (5)

• Assessing statistical significance of periodogram peaks
• The Lick Planet Search: Detectability and Mass Thresholds
• Detectability of Extrasolar Planets in Radial Velocity Surveys
• Accounting for velocity jitter in planet search surveys
• The ELODIE survey for northern extra-solar planets III. Three planetary candidates detected with ELODIE

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