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Register a new userThe generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms
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Added by
Mathias Zechmeister
Publication date
2009
fields
Physics
and research's language is
English
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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 ($chi^{2}$ 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.
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Context. Distinguishing between a signal induced by either stellar activity or a planet is currently the main challenge in radial velocity searches for low-mass exoplanets. Even when the presence of a transiting planet and hence its period are known, stellar activity can be the main barrier to measuring the correct amplitude of the radial velocity signal. Several tools are being used to help understand which signals come from stellar activity in the data. Aims. We aim to present a new tool that can be used for the purpose of identifying periodicities caused by stellar activity, and show how it can be used to track the signal-to-noise ratio (SNR) of the detection over time. The tool is based on the principle that stellar activity signals are variable and incoherent. Methods. We calculate the Bayesian general Lomb-Scargle periodogram for subsets of data and by adding one extra data point we track what happens to the presence and significance of periodicities in the data. Publicly available datasets from HARPS and HARPS-N were used for this purpose. Additionally, we analysed a synthetic dataset that we created with SOAP2.0 to simulate pure stellar activity and a mixture of stellar activity and a planet. Results. We find that this tool can easily be used to identify unstable and incoherent signals, such as those introduced by stellar activity. The SNR of the detection grows approximately as the square root of the number of data points, in the case of a stable signal. This can then be used to make decisions on whether it is useful to keep observing a specific object. The tool is relatively fast and easy to use, and thus lends itself perfectly to a quick analysis of the data.
As part of the NASA-CNES agreement, the NASA Star and Exoplanet Database (NStED) serves as the official US portal for the public CoRoT data products. NStED is a general purpose archive with the aim of providing support for NASAs planet finding and characterization goals. Consequently, the NASA Exoplanet Science Institute (NExScI) developed, and NStED adapted, a periodogram service for CoRoT data to determine periods of variability phenomena and create phased photometric light curves. Through the NStED periodogram interface, the user may choose three different period detection algorithms to use on any photometric time series product, or even upload and analyze their own data. Additionally, the NStED periodogram is remotely accessed by the CoRoT archive as part of its interface. NStED is available at {bf http://nsted.ipac.caltech.edu}.
We present a proof of concept for a new algorithm which can be used to detect exoplanets in high contrast images. The algorithm properly combines mutliple observations acquired during different nights, taking into account the orbital motion of the planet. Methods. We simulate SPHERE/IRDIS time series of observations in which we blindly inject planets on random orbits, at random level of S/N, below the detection limit (down to S/N 1.5). We then use an optimization algorithm to guess the orbital parameters, and take into account the orbital motion to properly recombine the different images, and eventually detect the planets. We show that an optimization algorithm can indeed be used to find undetected planets in temporal sequences of images, even if they are spread over orbital time scales. As expected, the typical gain in S/N ratio is sqrt(n), n being the number of observations combined. We find that the K-Stacker algorithm is able de-orbit and combine the images to reach a level of performance similar to what could be expected if the planet was not moving. We find recovery rates of 50% at S/N=5. We also find that the algorithm is able to determine the position of the planet in individual frames at one pixel precision, even despite the fact that the planet itself is below the detection limit in each frame. Our simulations show that K-Stacker can be used to increase the contrast limit of current exoplanet imaging instruments and to discover fainter bodies. We also suggest that the ability of K-Stacker to determine the position of the planet in every image of the time serie could be used as part of a new observing strategy in which long exposures would be broken into shorter ones spread over months. This could make possible to determine the orbital parameters of a planet without requiring multiple high S/N > 5 detections.
When the interactions of agents on a network are assumed to follow the Deffuant opinion dynamics model, the outcomes are known to depend on the structure of the underlying network. This behavior cannot be captured by existing mean-field approximations for the Deffuant model. In this paper, a generalised mean-field approximation is derived that accounts for the effects of network topology on Deffuant dynamics through the degree distribution or community structure of the network. The accuracy of the approximation is examined by comparison with large-scale Monte Carlo simulations on both synthetic and real-world networks.
In this paper, we use the time super-operator formalism in the 2-level Friedrichs model cite{fried} to obtain a phenomenological model of mesons decay. Our approach provides a fairly good estimation of the CP symmetry violation parameter in the case of K, B and D mesons. We also propose a crucial test aimed at discriminating between the standard approach and the time super-operator approach developed throughout the paper.
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