L. Rimoldini

Random forest automated supervised classification of Hipparcos periodic variable stars

We present an evaluation of the performance of an automated classification of the Hipparcos periodic variable stars into 26 types. The sub-sample with the most reliable variability types available in the literature is used to train supervised algorithms to characterize the type dependencies on a number of attributes. The most useful attributes evaluated with the random forest methodology include, in decreasing order of importance, the period, the amplitude, the V − I colour index, the absolute magnitude, the residual around the folded light-curve model, the magnitude distribution skewness and the amplitude of the second harmonic of the Fourier series model relative to that of the fundamental frequency. Random forests and a multistage scheme involving Bayesian network and Gaussian mixture methods lead to statistically equivalent results. In standard 10-fold cross-validation (CV) experiments, the rate of correct classification is between 90 and 100 per cent, depending on the variability type. The main mis-classification cases, up to a rate of about 10 per cent, arise due to confusion between SPB and ACV blue variables and between eclipsing binaries, ellipsoidal variables and other variability types. Our training set and the predicted types for the other Hipparcos periodic stars are available online.

Exploring the Variable Sky with LINEAR. III. Classification of Periodic Light Curves

We describe the construction of a highly reliable sample of ~7000 optically faint periodic variable stars with light curves obtained by the asteroid survey LINEAR across 10,000 deg^2 of the northern sky. The majority of these variables have not been cataloged yet. The sample flux limit is several magnitudes fainter than most other wide-angle surveys; the photometric errors range from ~0.03 mag at r = 15 to ~0.20 mag at r = 18. Light curves include on average 250 data points, collected over about a decade. Using Sloan Digital Sky Survey (SDSS) based photometric recalibration of the LINEAR data for about 25 million objects, we selected ~200,000 most probable candidate variables with r < 17 and visually confirmed and classified ~7000 periodic variables using phased light curves. The reliability and uniformity of visual classification across eight human classifiers was calibrated and tested using a catalog of variable stars from the SDSS Stripe 82 region and verified using an unsupervised machine learning approach. The resulting sample of periodic LINEAR variables is dominated by 3900 RR Lyrae stars and 2700 eclipsing binary stars of all subtypes and includes small fractions of relatively rare populations such as asymptotic giant branch stars and SX Phoenicis stars. We discuss the distribution of these mostly uncataloged variables in various diagrams constructed with optical-to-infrared SDSS, Two Micron All Sky Survey, and Wide-field Infrared Survey Explorer photometry, and with LINEAR light-curve features. We find that the combination of light-curve features and colors enables classification schemes much more powerful than when colors or light curves are each used separately. An interesting side result is a robust and precise quantitative description of a strong correlation between the light-curve period and color/spectral type for close and contact eclipsing binary stars (β Lyrae and W UMa): as the color-based spectral type varies from K4 to F5, the median period increases from 5.9 hr to 8.8 hr. These large samples of robustly classified variable stars will enable detailed statistical studies of the Galactic structure and physics of binary and other stars and we make these samples publicly available.

Gaia Data Release 1 - The Cepheid and RR Lyrae star pipeline and its application to the south ecliptic pole region

Context. The European Space Agency spacecraft Gaia is expected to observe about 10 000 Galactic Cepheids and over 100 000 Milky Way RR Lyrae stars (a large fraction of which will be new discoveries), during the five-year nominal lifetime spent scanning the whole sky to a faint limit of G = 20.7 mag, sampling their light variation on average about 70 times. Aims. We present an overview of the Specific Objects Study (SOS) pipeline developed within the Coordination Unit 7 (CU7) of the Data Processing and Analysis Consortium (DPAC), the coordination unit charged with the processing and analysis of variable sources observed by Gaia , to validate and fully characterise Cepheids and RR Lyrae stars observed by the spacecraft. The algorithms developed to classify and extract information such as the pulsation period, mode of pulsation, mean magnitude, peak-to-peak amplitude of the light variation, subclassification in type, multiplicity, secondary periodicities, and light curve Fourier decomposition parameters, as well as physical parameters such as mass, metallicity, reddening, and age (for classical Cepheids) are briefly described. Methods. The full chain of the CU7 pipeline was run on the time series photometry collected by Gaia during 28 days of ecliptic pole scanning law (EPSL) and over a year of nominal scanning law (NSL), starting from the general Variability Detection, general Characterization, proceeding through the global Classification and ending with the detailed checks and typecasting of the SOS for Cepheids and RR Lyrae stars (SOS Cep&RRL). We describe in more detail how the SOS Cep&RRL pipeline was specifically tailored to analyse Gaia ’s G -band photometric time series with a south ecliptic pole (SEP) footprint, which covers an external region of the Large Magellanic Cloud (LMC), and to produce results for confirmed RR Lyrae stars and Cepheids to be published in Gaia Data Release 1 ( Gaia DR1). Results. G -band time series photometry and characterisation by the SOS Cep&RRL pipeline (mean magnitude and pulsation characteristics) are published in Gaia DR1 for a total sample of 3194 variable stars (599 Cepheids and 2595 RR Lyrae stars), of which 386 (43 Cepheids and 343 RR Lyrae stars) are new discoveries by Gaia . All 3194 stars are distributed over an area extending 38 degrees on either side from a point offset from the centre of the LMC by about 3 degrees to the north and 4 degrees to the east. The vast majority are located within the LMC. The published sample also includes a few bright RR Lyrae stars that trace the outer halo of the Milky Way in front of the LMC.

Automated classification of Hipparcos unsolved variables

We present an automated classification of stars exhibiting periodic, non-periodic and irregular light variations. The Hipparcos catalogue of unsolved variables is employed to complement the training set of periodic variables of Dubath et al. with irregular and non-periodic representatives, leading to 3881 sources in total which describe 24 variability types. The attributes employed to characterize light-curve features are selected according to their relevance for classification. Classifier models are produced with random forests and a multistage methodology based on Bayesian networks, achieving overall misclassification rates under 12 per cent. Both classifiers are applied to predict variability types for 6051 Hipparcos variables associated with uncertain or missing types in the literature.

Search for high-amplitude δ Scuti and RR Lyrae stars in Sloan Digital Sky Survey Stripe 82 using principal component analysis

We propose a robust principal component analysis framework for the exploitation of multiband photometric measurements in large surveys. Period search results are improved using the time-series of the first principal component due to its optimized signal-to-noise ratio. The presence of correlated excess variations in the multivariate time-series enables the detection of weaker variability. Furthermore, the direction of the largest variance differs for certain types of variable stars. This can be used as an efficient attribute for classification. The application of the method to a subsample of Sloan Digital Sky Survey Stripe 82 data yielded 132 high-amplitude δ Scuti variables. We also found 129 new RR Lyrae variables, complementary to the catalogue of Sesar et al., extending the halo area mapped by Stripe 82 RR Lyrae stars towards the Galactic bulge. The sample also comprises 25 multiperiodic or Blazhko RR Lyrae stars.

Improved methodology for the automated classification of periodic variable stars

We present a novel automated methodology to detect and classify periodic variable stars in a large database of photometric time series. The methods are based on multivariate Bayesian statistics and use a multi-stage approach. We applied our method to the ground-based data of the TrES Lyr1 field, which is also observed by the Kepler satellite, covering ~26000 stars. We found many eclipsing binaries as well as classical non-radial pulsators, such as slowly pulsating B stars, Gamma Doradus, Beta Cephei and Delta Scuti stars. Also a few classical radial pulsators were found.

Weighted skewness and kurtosis unbiased by sample size and Gaussian uncertainties

Abstract Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data, automated classification techniques and other applications. Estimators of higher order moments that are robust against outliers are more stable but might miss characteristic features of the data, as in the case of astronomical time series exhibiting brief events like stellar bursts or eclipses of binary systems, while weighting can help identify reliable measurements from uncertain or spurious outliers. Furthermore, noise is an unavoidable part of most measurements and their uncertainties need to be taken properly into account during the data analysis or biases are likely to emerge in the results, including basic descriptive statistics. This work provides unbiased estimates of the weighted skewness and kurtosis moments and cumulants, corrected for biases due to sample size and Gaussian noise, under the assumption of independent data. A comparison of biased and unbiased weighted estimators is illustrated with simulations as a function of sample size and signal-to-noise ratio, employing different data distributions and weighting schemes related to measurement uncertainties and the sampling of the signal. Detailed derivations and figures of simulation results are presented in the Appendices available online.

Gaia Data Release 2: Summary of the variability processing and analysis results

Context. The Gaia Data Release 2 (DR2) contains more than half a million sources that are identified as variable stars. Aims: We summarise the processing and results of the identification of variable source candidates of RR Lyrae stars, Cepheids, long-period variables (LPVs), rotation modulation (BY Dra-type) stars, δ Scuti and SX Phoenicis stars, and short-timescale variables. In this release we aim to provide useful but not necessarily complete samples of candidates. Methods: The processed Gaia data consist of the G, GBP, and GRP photometry during the first 22 months of operations as well as positions and parallaxes. Various methods from classical statistics, data mining, and time-series analysis were applied and tailored to the specific properties of Gaia data, as were various visualisation tools to interpret the data. Results: The DR2 variability release contains 228 904 RR Lyrae stars, 11 438 Cepheids, 151 761 LPVs, 147 535 stars with rotation modulation, 8882 δ Scuti and SX Phoenicis stars, and 3018 short-timescale variables. These results are distributed over a classification and various Specific Object Studies tables in the Gaia archive, along with the three-band time series and associated statistics for the underlying 550 737 unique sources. We estimate that about half of them are newly identified variables. The variability type completeness varies strongly as a function of sky position as a result of the non-uniform sky coverage and intermediate calibration level of these data. The probabilistic and automated nature of this work implies certain completeness and contamination rates that are quantified so that users can anticipate their effects. Thismeans that even well-known variable sources can be missed or misidentified in the published data. Conclusions: The DR2 variability release only represents a small subset of the processed data. Future releases will include more variable sources and data products; however, DR2 shows the (already) very high quality of the data and great promise for variability studies.

A comparative study of four significance measures for periodicity detection in astronomical surveys

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 sky biases that are dicult to assess. Second, the computational loads should be kept feasible even for millions of time series. Using the Gaia case, we compare the F M method (Paltani 2004; Schwarzenberg-Czerny 2012), the Baluev method (Baluev 2008) and ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

Gaia eclipsing binary and multiple systems: Two-Gaussian models applied to OGLE-III eclipsing binary light curves in the Large Magellanic Cloud ⋆

The advent of large scale multi-epoch surveys raises the need for automated light curve (LC) processing. This is particularly true for eclipsing binaries (EBs), which form one of the most populated types of variable objects. The Gaia mission, launched at the end of 2013, is expected to detect of the order of few million EBs over a 5-year mission. We present an automated procedure to characterize EBs based on the geometric morphology of their LCs with two aims: first to study an ensemble of EBs on a statistical ground without the need to model the binary system, and second to enable the automated identification of EBs that display atypical LCs. We model the folded LC geometry of EBs using up to two Gaussian functions for the eclipses and a cosine function for any ellipsoidal-like variability that may be present between the eclipses. The procedure is applied to the OGLE-III data set of EBs in the Large Magellanic Cloud (LMC) as a proof of concept. The bayesian information criterion is used to select the best model among models containing various combinations of those components, as well as to estimate the significance of the components. Based on the two-Gaussian models, EBs with atypical LC geometries are successfully identified in two diagrams, using the Abbe values of the original and residual folded LCs, and the reduced