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Roman V Baluev - One of the best experts on this subject based on the ideXlab platform.
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Keplerian Periodogram for Doppler exoplanet detection: optimized computation and analytic significance thresholds
Monthly Notices of the Royal Astronomical Society, 2014Co-Authors: Roman V BaluevAbstract:We consider the so-called Keplerian Periodogram, in which the putative detectable signal is modelled by a highly non-linear Keplerian radial velocity function, appearing in Doppler exoplanetary surveys. We demonstrate that for planets on high-eccentricity orbits the Keplerian Periodogram is far more efficient than the classic Lomb-Scargle Periodogram and even the multiharmonic Periodograms, in which the periodic signal is approximated by a truncated Fourier series. We provide new numerical algorithm for computation of the Keplerian Periodogram. This algorithm adaptively increases the parameteric resolution where necessary, in order to uniformly cover all local optima of the Keplerian fit. Thanks to this improvement, the algorithm provides more smooth and reliable results with minimized computing demands. We also derive a fast analytic approximation to the false alarm probability levels of the Keplerian Periodogram. This approximation has the form $(P z^{3/2} + Q z) W \exp(-z)$, where $z$ is the observed Periodogram maximum, $W$ is proportional to the settled frequency range, and the coefficients $P$ and $Q$ depend on the maximum eccentricity to scan.
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detecting non sinusoidal periodicities in observational data the von mises Periodogram for variable stars and exoplanetary transits
Monthly Notices of the Royal Astronomical Society, 2013Co-Authors: Roman V BaluevAbstract: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 attention is paid to the problem of estimating the statistical significance of candidate periodicities found using such non-linear Periodograms. This problem is related to the task of quantifying the distributions of maximum values of these Periodograms. Based on recent results in the mathematical theory of extreme values of random field (the generalized Rice method), we give a general approach to find handy analytic approximation for these distributions. This approximation has the general form $e^{-z} P(\sqrt z)$, where $P$ is an algebraic polynomial and $z$ being the Periodogram maximum. The general tools developed in this paper can be used in a wide variety of astronomical applications, for instance in the studies of variable stars and extrasolar planets. For this goal, we develop and consider in details the so-called von Mises Periodogram: a specialized non-linear Periodogram where 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 lightcurves of many astronomical objects that show periodic photometric variability of different nature. We prove that our approach can be perfectly applied to this non-linear Periodogram. We provide a package of auxiliary C++ programs, attached as the online-only material. They should faciliate the use of the von Mises Periodogram in practice.
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Assessing the statistical significance of Periodogram peaks
Monthly Notices of the Royal Astronomical Society, 2008Co-Authors: Roman V BaluevAbstract:The least-squares (or Lomb-Scargle) Periodogram is a powerful tool that is routinely used in many branches of astronomy to search for periodicities in observational data. The problem of assessing the statistical significance of candidate periodicities for a number of Periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. These include an upper limit to the false alarm probability (or a lower limit to the significance). The estimations are tested numerically in order to establish regions of their practical applicability.
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assessing statistical significance of Periodogram peaks
arXiv: Astrophysics, 2007Co-Authors: Roman V BaluevAbstract:The least-squares (or Lomb-Scargle) Periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different Periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. They include an upper limit to the false alarm probability (or a lower limit to the significance). These estimations are tested numerically in order to establish regions of their practical applicability.
A Mortier - One of the best experts on this subject based on the ideXlab platform.
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bgls a bayesian formalism for the generalised lomb scargle Periodogram
Astronomy and Astrophysics, 2015Co-Authors: A Mortier, J P Faria, Carlos Correia, A Santerne, N C SantosAbstract:Context. Frequency analyses are very important in astronomy today, not least in the ever-growing field of exoplanets, where shortperiod signals in stellar radial velocity data are investigated. Periodograms are the main (and powerful) tools for this purpose. However, recovering the correct frequencies and assessing the probability of each frequency is not straightforward. Aims. We provide a formalism that is easy to implement in a code, to describe a Bayesian Periodogram that includes weights and a constant offset in the data. The relative probability between peaks can be easily calculated with this formalism. We discuss the differences and agreements between the various Periodogram formalisms with simulated examples. Methods. We used the Bayesian probability theory to describe the probability that a full sine function (including weights derived from the errors on the data values and a constant offset) with a specific frequency is present in the data. Results. From the expression for our Baysian generalised Lomb-Scargle Periodogram (BGLS), we can easily recover the expression for the non-Bayesian version. In the simulated examples we show that this new formalism recovers the underlying periods better than previous versions. A Python-based code is available for the community.
Erik W. Kruyt - One of the best experts on this subject based on the ideXlab platform.
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Searching for biological rhythms: peak detection in the Periodogram of unequally spaced data.
Journal of biological rhythms, 1999Co-Authors: Hans P. A. Van Dongen, Erik Olofsen, Jan H. Vanhartevelt, Erik W. KruytAbstract:The classical power spectrum, computed in the frequency domain, outranks traditionally used Periodograms derived in the time domain (such as the [.chi]2 Periodogram) regarding the search for biological rhythms. Unfortunately, classical power spectral analysis is not possible with unequally spaced data (e.g., time series with missing data). The Lomb-Scargle Periodogram fixes this shortcoming. However, peak detection in the Lomb-Scargle Periodogram of unequally spaced data requires some careful consideration. To guide researchers in the proper evaluation of detected peaks, therefore, a novel procedure and a computer program have recently become available. It is recommended that the Lomb-Scargle Periodogram be the default method of Periodogram analysis in future biomedical applications of rhythm investigation.
Bigot L. - One of the best experts on this subject based on the ideXlab platform.
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3D magneto-hydrodynamical simulations of stellar convective noise for improved exoplanet detection. I. Case of regularly sampled radial velocity observations
'EDP Sciences', 2020Co-Authors: Sulis S., Mary D., Bigot L.Abstract:Convective motions at the stellar surface generate a stochastic colored noise source in the radial velocity (RV) data. This noise impedes the detection of small exoplanets. Moreover, the unknown statistics (amplitude, distribution) related to this noise make it difficult to estimate the false alarm probability (FAP) for exoplanet detection tests. In this paper, we investigate the possibility of using 3D magneto-hydrodynamical simulations (MHD) of stellar convection to design detection methods that can provide both a reliable estimate of the FAP and a high detection power. We tested the realism of 3D simulations in producing solar RV by comparing them with the observed disk integrated velocities taken by the GOLF instrument on board the SOHO spacecraft. We presented a new detection method based on Periodograms standardized by these simulated time series, applying several detection tests to these standarized Periodograms. The power spectral density of the 3D synthetic convective noise is consistent with solar RV observations for short periods. For regularly sampled observations, the analytic expressions of FAP derived for several statistical tests applied to the Periodogram standardized by 3D simulation noise are accurate. The adaptive tests considered in this work (Higher-Criticism, Berk-Jones), which are new in the exoplanet field, may offer better detection performance than classical tests (based on the highest Periodogram value) in the case of multi-planetary systems and planets with eccentric orbits. 3D MHD simulations are now mature enough to produce reliable synthetic time series of the convective noise affecting RV data. These series can be used to access to the statistics of this noise and derive accurate FAP of tests that are a critical element in the detection of exoplanets down to the cm/s level.Comment: Accepted for publication in Astronomy and Astrophysic
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3D magneto-hydrodynamical simulations of stellar convective noise for improved exoplanet detection: I. Case of regularly sampled radial velocity observations
'EDP Sciences', 2020Co-Authors: Sulis S., Mary D., Bigot L.Abstract:International audienceContext. Convective motions at the stellar surface generate a stochastic colored noise source in the radial velocity (RV) data. This noise impedes the detection of small exoplanets. Moreover, the unknown statistics (amplitude, distribution) related to this noise make it difficult to estimate the false alarm probability (FAP) for exoplanet detection tests.Aims. In this paper, we investigate the possibility of using 3D magneto-hydrodynamical (MHD) simulations of stellar convection to design detection methods that can provide both a reliable estimate of the FAP and a high detection power.Methods. We tested the realism of 3D simulations in producing solar RV by comparing them with the observed disk integrated velocities taken by the GOLF instrument on board the SOHO spacecraft. We presented a new detection method based on Periodograms standardized by these simulated time series, applying several detection tests to these standarized Periodograms.Results. The power spectral density of the 3D synthetic convective noise is consistent with solar RV observations for short periods. For regularly sampled observations, the analytic expressions of FAP derived for several statistical tests applied to the Periodogram standardized by 3D simulation noise are accurate. The adaptive tests considered in this work (Higher-Criticism, Berk-Jones), which are new in the exoplanet field, may offer better detection performance than classical tests (based on the highest Periodogram value) in the case of multi-planetary systems and planets with eccentric orbits.Conclusions. 3D MHD simulations are now mature enough to produce reliable synthetic time series of the convective noise affecting RV data. These series can be used to access to the statistics of this noise and derive accurate FAP of tests that are a critical element in the detection of exoplanets down to the cm s−1 level
Martin Kürster - One of the best experts on this subject based on the ideXlab platform.
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The generalised Lomb-Scargle Periodogram. A new formalism for the floating-mean and Keplerian Periodograms
Astronomy & Astrophysics, 2009Co-Authors: Mathias Zechmeister, Martin KürsterAbstract:The Lomb-Scargle Periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights (χ 2 fitting). Compared to the Lomb-Scargle Periodogram, the generalisation is superior as it provides more accurate frequencies, is less susceptible to aliasing, and gives a much better determination of the spectral intensity. Only a few modifications are required for the computation and the computational effort is similar. Our approach brings together several related methods that can be found in the literature, viz. the date-compensated discrete Fourier transform, the floating-mean Periodogram, and the “spectral significance” estimator used in the SigSpec program, for which we point out some equivalences. Furthermore, we present an algorithm that implements this generalisation for the evaluation of the Keplerian Periodogram that searches for the period of the best-fitting Keplerian orbit to radial velocity data. The systematic and non-random algorithm is capable of detecting eccentric orbits, which is demonstrated by two examples and can be a useful tool in searches for the orbital periods of exoplanets.
