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 $\chi^2$. Cleaning the data set from the atypical cases and further filtering out LCs that contain non-significant eclipse candidates, the ensemble of EBs can be studied on a statistical ground using the two-Gaussian model parameters. For illustration purposes, we present the distribution of projected eccentricities as a function of orbital period for the OGLE-III set of EBs in the LMC, as well as the distribution of their primary versus secondary eclipse widths.Comment: 20 pages, 29 figures. Submitted to A&

Student understanding of rotational and rolling motion concepts

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics students with physics juniors who had learned rotational and rolling motion concepts in an intermediate level mechanics course. Interviews were conducted with six physics juniors and ten introductory students using demonstration-based tasks. We also administered free-response and multiple-choice questions to a large number of students enrolled in introductory physics courses, and interviewed six additional introductory students on the test questions (during the test design phase). All students showed similar difficulties regardless of their background, and higher mathematical sophistication did not seem to help acquire a deeper understanding. We found that some difficulties were due to related difficulties with linear motion, while others were tied specifically to the more intricate nature of rotational and rolling motion.Comment: 23 pages, 3 figures, 2 tables; it includes a multiple-choice test (in Appendix B

Large-amplitude variables in Gaia Data Release 2. Multi-band variability characterization

The second data release (DR2) of Gaia provides mean photometry in three bands for $\sim$1.4 billion sources, but light curves and variability properties are available for only $\sim$0.5 million of them. Here, we provide a census of large-amplitude variables with amplitudes larger than $\sim$0.2 mag in the $G$ band for objects with mean brightnesses between 5.5 and 19 mag. To achieve this, we rely on variability amplitude proxies in $G$, $G_{BP}$ and $G_{RP}$ computed from the uncertainties on the magnitudes published in DR2. We then apply successive filters to identify two subsets containing respectively sources with reliable mean $G_{BP}$ and $G_{RP}$ (for studies using colours) and sources having compatible amplitude proxies in $G$, $G_{BP}$ and $G_{RP}$ (for multi-band variability studies). The full catalogue gathers $23\,315\,874$ large-amplitude variable candidates, and the two subsets with increased levels of purity contain respectively $1\,148\,861$ and $618\,966$ sources. A multi-band variability analysis of the catalogue shows that different types of variable stars can be globally categorized in four groups according to their colour and blue-to-red amplitude ratios as determined from the $G$, $G_{BP}$ and $G_{RP}$ amplitude proxies. The catalogue constitutes the first census of Gaia large-amplitude variable candidates, extracted from the public DR2 archive. The overview presented here illustrates the added-value of the mission for multi-band variability studies even at this stage when epoch photometry is not yet available for all sources. (Abridged abstract)Comment: Final version, A&A, in press. Main text: 20 pages, 26 figures. Four appendixe

Gaia Focused Product Release: Radial velocity time series of long-period variables

Context. The third Gaia Data Release (DR3) provided photometric time series of more than 2 million long-period variable (LPV) candidates. Anticipating the publication of full radial-velocity data planned with Data Release 4, this Focused Product Release (FPR) provides radial-velocity time series for a selection of LPV candidates with high-quality observations. Aims. We describe the production and content of the Gaia catalog of LPV radial-velocity time series, and the methods used to compute the variability parameters published as part of the Gaia FPR. Methods. Starting from the DR3 catalog of LPV candidates, we applied several filters to construct a sample of sources with high-quality radial-velocity measurements. We modeled their radial-velocity and photometric time series to derive their periods and amplitudes, and further refined the sample by requiring compatibility between the radial-velocity period and at least one of the G, GBP, or GRP photometric periods. Results. The catalog includes radial-velocity time series and variability parameters for 9614 sources in the magnitude range 6 ≲ G/mag ≲ 14, including a flagged top-quality subsample of 6093 stars whose radial-velocity periods are fully compatible with the values derived from the G, GBP, and GRP photometric time series. The radial-velocity time series contain a mean of 24 measurements per source taken unevenly over a duration of about three years. We identify the great majority of the sources (88%) as genuine LPV candidates, with about half of them showing a pulsation period and the other half displaying a long secondary period. The remaining 12% of the catalog consists of candidate ellipsoidal binaries. Quality checks against radial velocities available in the literature show excellent agreement. We provide some illustrative examples and cautionary remarks. Conclusions. The publication of radial-velocity time series for almost ten thousand LPV candidates constitutes, by far, the largest such database available to date in the literature. The availability of simultaneous photometric measurements gives a unique added value to the Gaia catalog

Gaia Data Release 3. The first Gaia catalogue of eclipsing binary candidates

We present the first Gaia catalogue of eclipsing binary candidates released in Gaia DR3, describe its content, provide tips for its usage, estimate its quality, and show illustrative samples. The catalogue contains 2,184,477 sources with G magnitudes up to 20 mag. Candidate selection is based on the results of variable object classification performed within the Gaia Data Processing and Analysis Consortium, further filtered using eclipsing binary-tailored criteria based on the G light curves. To find the orbital period, a large ensemble of trial periods is first acquired using three distinct period search methods applied to the cleaned G light curve. The G light curve is then modelled with up-to two Gaussians and a cosine for each trial period. The best combination of orbital period and geometric model is finally selected using Bayesian model comparison based on the BIC. A global ranking metric is provided to rank the quality of the chosen model between sources. The catalogue is restricted to orbital periods larger than 0.2 days. About 530,000 of the candidates are classified as eclipsing binaries in the literature as well, out of ~600,000 available crossmatches, and 93% of them have published periods compatible with the Gaia periods. Catalogue completeness is estimated to be between 25% and 50%, depending on the sky region, relative to the OGLE4 catalogues of eclipsing binaries towards the Galactic Bulge and the Magellanic Clouds. The analysis of an illustrative sample of ~400,000 candidates with significant parallaxes shows properties in the observational HR diagram as expected for eclipsing binaries. The subsequent analysis of a sub-sample of detached bright candidates provides further hints for the exploitation of the catalogue. The orbital periods, light curve model parameters, and global rankings are all published in the catalogue with their related uncertainties where applicable.Comment: Submitted to A&A. Main text: 23 pages, 35 figures. Four appendices (17 pages) with 38 figure

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 data base of photometric time series. The methods are based on multivariate Bayesian statistics and use a multistage approach. We applied our method to the ground-based data of the Trans-Atlantic Exoplanet Survey (TrES) Lyr1 field, which is also observed by the Kepler satellite, covering ∼26 000 stars. We found many eclipsing binaries as well as classical non-radial pulsators, such as slowly pulsating B stars, γ Doradus, β Cephei and δ Scuti stars. Also a few classical radial pulsators were foun

Gaia Data Release 2: All-sky classification of high-amplitude pulsating stars

Out of the 1.69 billion sources in the Gaia Data Release 2 (DR2), more than half a million are published with photometric time series that exhibit light variations during 22 months of observation. An all-sky classification of common high-amplitude pulsators (Cepheids, long-period variables, Delta Scuti / SX Phoenicis, and RR Lyrae stars) is provided for stars with brightness variations greater than 0.1 mag in the G band. A semi-supervised classification approach was employed, firstly training multi-stage Random Forest classifiers with sources of known types in the literature, followed by a preliminary classification of the Gaia data and a second training phase that included a selection of the first classification results to improve the representation of some classes, before the application of the improved classifiers to the Gaia data. Dedicated validation classifiers were used to reduce the level of contamination in the published results. A relevant fraction of objects were not yet sufficiently sampled for reliable Fourier series decomposition, so classifiers were based on features derived from statistics of photometric time series in the G, BP, and RP bands, as well as from some astrometric parameters. The published classification results include 195,780 RR Lyrae stars, 150,757 long-period variables, 8550 Cepheids, and 8882 Delta Scuti / SX Phoenicis stars. All of these results represent candidates, whose completeness and contamination are described as a function of variability type and classification reliability. Results are expressed in terms of class labels and classification scores, which are available in the vari_classifier_result table of the Gaia archive

Automated classification of periodic variable 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.Comment: 11 pages, 6 figures Accepted for publication in MNRA