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

Результат исследований: Научные публикации в периодических изданияхстатья

7 Цитирования (Scopus)

Выдержка

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^{-z} P(√{z}), where P is an algebraic polynomial and z is the periodogram maximum. 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 cons
Язык оригиналаанглийский
Страницы (с-по)1167-1179
ЖурналMonthly Notices of the Royal Astronomical Society
Том431
Номер выпуска2
DOI
СостояниеОпубликовано - 2013

Отпечаток

variable stars
transit
periodicity
periodic variations
mathematical theory
rice
extrasolar planets
approximation
polynomials
estimating
planet
distribution
method
parameter

Цитировать

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Detecting non-sinusoidal periodicities in observational data: the von Mises periodogram for variable stars and exoplanetary transits. / Baluev, R.V.

В: Monthly Notices of the Royal Astronomical Society, Том 431, № 2, 2013, стр. 1167-1179.

Результат исследований: Научные публикации в периодических изданияхстатья

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AB - 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^{-z} P(√{z}), where P is an algebraic polynomial and z is the periodogram maximum. 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 cons

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