Detecting non-sinusoidal periodicities in observational data: the von Mises periodogram for variable stars and exoplanetary transits

作者：Baluev Roman V^*

来源：Monthly Notices of the Royal Astronomical Society, 2013, 431(2): 1167-1179.

DOI：10.1093/mnras/stt238

• methods: analytical
• methods: data analysis
• methods: statistical
• surveys

This paper introduces an extension of the linear least-squares (or Lomb-Scargle) periodogram for the case when the model of the signal to be detected is non-sinusoidal and depends on unknown parameters in a non-linear manner. The problem of estimating the statistical significance of candidate periodicities found using such non-linear periodograms is examined. This problem is related to the task of quantifying the distributions of the maximum values of these periodograms. Based on recent results in the mathematical theory of extreme values of a random field (the generalized Rice method), a general approach is provided to find a useful analytic approximation for these distributions. This approximation has the general form e-P-z(root z), where P is an algebraic polynomial and z is the periodogram maximum. %26lt;br%26gt;The general tools developed in this paper can be used in a wide variety of astronomical applications, for instance in the study of variable stars and extra-solar planets. With this in mind, we develop and consider in detail the so-called von Mises periodogram - a specialized non-linear periodogram in which the signal is modelled by the von Mises periodic function exp (nu cos omega t). This simple function with an additional non-linear parameter nu can model the light curves of many astronomical objects that show various types of periodic photometric variability. We prove that our approach can be perfectly applied to this non-linear periodogram. %26lt;br%26gt;We provide a package of auxiliary C++ programs, attached as online-only material. These programs should facilitate the use of the von Mises periodogram in practice.

• 出版日期2013-5