This paper introduces the multiband periodogram, a general extension of the well-known Lomb-Scargle approach for detecting periodic signals in time-domain data. In addition to advantages of the Lomb-Scargle method such as treatment of non-uniform sampling and heteroscedastic errors, the multiband periodogram significantly improves period finding for randomly sampled multiband light curves (e.g., Pan-STARRS, DES and LSST). The light curves in each band are modeled as arbitrary truncated Fourier series, with the period and phase shared across all bands. The key aspect is the use of Tikhonov regularization which drives most of the variability into the so-called base model common to all bands, while fits for individual bands describe residuals relative to the base model and typically require lower-order Fourier series. This decrease in the effective model complexity is the main reason for improved performance. We use simulated light curves and randomly subsampled SDSS Stripe 82 data to demonstrate the superiority of this method compared to other methods from the literature, and find that this method will be able to efficiently determine the correct period in the majority of LSST's bright RR Lyrae stars with as little as six months of LSST data. A Python implementation of this method, along with code to fully reproduce the results reported here, is available on GitHub.
Detection of a signal hidden by noise within a time series is an important problem in many astronomical searches, i.e. for light curves containing the contributions of periodic/semi-periodic components due to rotating objects and all other astrophysical time-dependent phenomena. One of the most popular tools for use in such studies is the "periodogram", whose use in an astronomical context is often not trivial. The "optimal" statistical properties of the periodogram are lost in the case of irregular sampling of signals, which is a common situation in astronomical experiments. Parts of these pr…
Studies in Astronomical Time Series Analysis: The Double Lomb-Scargle Periodogram and Super Resolution
NASA Ames Research Center（NASA 艾姆斯研究中心）；Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Stanford University（斯坦福大学）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所 (IFAE)）；The Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学技术研究院 (BIST)）
This paper describes the VARTOOLS program, which is an open-source command-line utility, written in C, for analyzing astronomical time-series data, especially light curves. The program provides a general-purpose set of tools for processing light curves including signal identification, filtering, light curve manipulation, time conversions, and modeling and simulating light curves. Some of the routines implemented include the Generalized Lomb-Scargle periodogram, the Box-Least Squares transit search routine, the Analysis of Variance periodogram, the Discrete Fourier Transform including the CLEAN…
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),…
Period estimation is an important task in the classification of many variable astrophysical objects. Here we present GRAPE: Genetic Routine for Astronomical Period Estimation, a genetic algorithm optimised for the processing of survey data with spurious and aliased artefacts. It uses a Bayesian Generalised Lomb-Scargle (BGLS) fitness function designed for use with the Skycam survey conducted at the Liverpool Telescope. We construct a set of simulated light curves using both regular and Skycam survey cadence with four types of signal: sinusoidal, sawtooth, symmetric eclipsing binary and eccentr…
Robust 1-norm periodograms for analysis of noisy non-Gaussian time series with irregular cadences: Application to VLBI astrometry of quasars
United States Naval Observatory（美国海军天文台）；SYRTE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, LNE（巴黎天文台时间频率研究所，巴黎大学，PSL大学，法国国家科学研究中心，索邦大学，法国计量院）
Periodograms are common tools used to search for periodic signals in unevenly spaced time series. The significance of periodogram peaks is often assessed using false alarm probability (FAP), which in most studies assumes uncorrelated noise and is computed using numerical methods such as bootstrapping or Monte Carlo. These methods have a high computational cost, especially for low FAP levels, which are of most interest. We present an analytical estimate of the FAP of the periodogram in the presence of correlated noise, which is fundamental to analyze astronomical time series correctly. The anal…
We introduce an extension of the periodogram concept to time-resolved spectroscopy. USuRPER -- Unit Sphere Representation PERiodogram -- is a novel technique which opens new horizons in the analysis of astronomical spectra. It can be used to detect a wide range of periodic variability of the spectrum shape. Essentially, the technique is based on representing spectra as unit vectors in a multidimensional hyperspace, hence its name. It is an extension of the phase-distance correlation (PDC) periodogram we had introduced in previous papers, to very high-dimensional data like spectra. USuRPER take…
We present a new method of extending the single band Analysis of Variance period estimation algorithm to multiple bands. We use SDSS Stripe 82 RR Lyrae to show that in the case of low number of observations per band and non-simultaneous observations, improvements in period recovery rates of up to $\approx$60\% are observed. We also investigate the effect of inter-band observing cadence on period recovery rates. We find that using non-simultaneous observation times between bands is ideal for the multiband method, and using simultaneous multiband data is only marginally better than using single …
In this letter, we propose a method for period estimation in light curves from periodic variable stars using correntropy. Light curves are astronomical time series of stellar brightness over time, and are characterized as being noisy and unevenly sampled. We propose to use slotted time lags in order to estimate correntropy directly from irregularly sampled time series. A new information theoretic metric is proposed for discriminating among the peaks of the correntropy spectral density. The slotted correntropy method outperformed slotted correlation, string length, VarTools (Lomb-Scargle period…
The first demonstration of narrowband spectral filtering of multimode light on a 3D integrated photonic chip using photonic lanterns and waveguide Bragg gratings is reported. The photonic lanterns with multi-notch waveguide Bragg gratings were fabricated using the femtosecond direct-write technique in boro-aluminosilicate glass (Corning, Eagle 2000). Transmission dips of up to 5 dB were measured in both photonic lanterns and reference single-mode waveguides with 10.4-mm-long gratings. The result demonstrates efficient and symmetrical performance of each of the gratings in the photonic lantern.…
The next generation of telescopes and instruments are facilitating our understanding of the Universe by producing data at a pace that beats all projections, and astronomers today are left in the face of an avalanche of data like never before. In order to cope with this problem and come up with a reliable and innovative solution, Data Centers were created in various locations and the concept of Virtual Observatories elaborated. Based at the National Taiwan Normal University, the Taiwan Extragalactic Astronomical Data Center plan to join in global efforts by proposing 1Pb of data storage dedicat…
We propose a new information theoretic metric for finding periodicities in stellar light curves. Light curves are astronomical time series of brightness over time, and are characterized as being noisy and unevenly sampled. The proposed metric combines correntropy (generalized correlation) with a periodic kernel to measure similarity among samples separated by a given period. The new metric provides a periodogram, called Correntropy Kernelized Periodogram (CKP), whose peaks are associated with the fundamental frequencies present in the data. The CKP does not require any resampling, slotting or …
Period estimation is one of the central topics in astronomical time series analysis, where data is often unevenly sampled. Especially challenging are studies of stellar magnetic cycles, as there the periods looked for are of the order of the same length than the datasets themselves. The datasets often contain trends, the origin of which is either a real long-term cycle or an instrumental effect, but these effects cannot be reliably separated, while they can lead to erroneous period determinations if not properly handled. In this study we aim at developing a method that can handle the trends pr…
We study the problem of periodicity detection in massive data sets of photometric or radial velocity time series, as presented by ESA's Gaia mission. Periodicity detection hinges on the estimation of the false alarm probability (FAP) of the extremum of the periodogram of the time series. We consider the problem of its estimation with two main issues in mind. First, for a given number of observations and signal-to-noise ratio, the rate of correct periodicity detections should be constant for all realized cadences of observations regardless of the observational time patterns, in order to avoid s…
Joint multiband deconvolution for Euclid and Vera C. Rubin images
Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny（天体物理实验室，瑞士洛桑联邦理工学院（EPFL），萨瓦尼观测站）；GEPI, Observatoire de Paris, Université PSL, CNRS（GEPI，巴黎天文台，巴黎-萨克勒大学，国家科学研究中心）；ICC-UB Institut de Ciències del Cosmos, Universitat de Barcelona（ICC-UB宇宙科学研究所，巴塞罗那大学）；ICREA, Pg. Lluís Companys 23, Barcelona（ICREA，巴塞罗那路易斯·康帕尼斯街23号）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎-萨克勒大学，巴黎城市大学，法国原子能委员会，国家科学研究中心，应用数学研究所）；Institutes of Computer Science and Astrophysics, Foundation for Research and Technology Hellas (FORTH), Greece（计算机科学与天体物理学研究所，希腊希腊研究与技术基金会（FORTH））
We present the results of the \textit{Fermi}-LAT 10-years-long light curves (LCs) modeling of selected blazars: six flat spectrum radio quasars (FSRQs) and five BL Lacertae (BL Lacs), examined in 7-, 10-, and 14-day binning. The LCs and power spectral densities (PSDs) were investigated with various methods: Fourier transform, Lomb-Scargle periodogram (LSP), wavelet scalogram, autoregressive moving average (ARMA) process, continuous-time ARMA (CARMA), Hurst exponent ($H$), and the $\mathcal{A}-\mathcal{T}$ plane. First, with extensive simulations we showed that parametric modeling returns unrel…
Computing the periods of variable objects is well-known to be computationally expensive. Modern astronomical catalogs contain a significant number of observed objects. Therefore, even if the period ranges for particular classes of objects are well-constrained due to expected physical properties, periods must be derived for a tremendous number of objects. In this paper, we propose a GPU-accelerated Lomb-Scargle period finding algorithm that computes periods for single objects or for batches of objects as is necessary in many data processing pipelines. We demonstrate the performance of several o…
We present a novel method to produce empirical generative models of all kinds of astronomical transients from datasets of unlabeled light curves. Our hybrid model, that we call ParSNIP, uses a neural network to model the unknown intrinsic diversity of different transients and an explicit physics-based model of how light from the transient propagates through the universe and is observed. The ParSNIP model predicts the time-varying spectra of transients despite only being trained on photometric observations. With a three-dimensional intrinsic model, we are able to fit out-of-sample multiband lig…
The Large Synoptic Survey Telescope (LSST) will produce an unprecedented amount of light curves using six optical bands. Robust and efficient methods that can aggregate data from multidimensional sparsely-sampled time series are needed. In this paper we present a new method for light curve period estimation based on the quadratic mutual information (QMI). The proposed method does not assume a particular model for the light curve nor its underlying probability density and it is robust to non-Gaussian noise and outliers. By combining the QMI from several bands the true period can be estimated ev…
Identifying Light-curve Signals with a Deep Learning Based Object Detection Algorithm. II. A General Light Curve Classification Framework
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；University of Warwick（华威大学）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
The unprecedented volume and rate of transient events that will be discovered by the Large Synoptic Survey Telescope (LSST) demands that the astronomical community update its followup paradigm. Alert-brokers -- automated software system to sift through, characterize, annotate and prioritize events for followup -- will be critical tools for managing alert streams in the LSST era. The Arizona-NOAO Temporal Analysis and Response to Events System (ANTARES) is one such broker. In this work, we develop a machine learning pipeline to characterize and classify variable and transient sources only using…
