Gaia Data Release 2: Validation of the classification of RR Lyrae and Cepheid variables with the Kepler and K2 missions

The second data release of the Gaia mission includes an advance catalog of variable stars. The classification of these stars are based on sparse photometry from the first 22 months of the mission. We set out to investigate the purity and completeness of the all-sky Gaia classification results with the help of the continuous light curves of the observed targets from the Kepler and K2 missions, focusing specifically on RR Lyrae and Cepheid pulsators, outside the Galactic Bulge region. We crossmatched the Gaia identifications with the observations collected by the Kepler space telescope. We inspected the light curves visually, then calculated the relative Fourier coefficients and period ratios for the single- and double-mode K2 RR Lyrae stars to further classify them. We identified 1443 and 41 stars classified as RR Lyrae or Cepheid variables in Gaia DR2 in the targeted observations of the two missions and 263 more RR Lyre targets in the Full-Frame Images (FFI) of the original mission. We provide the crossmatch of these sources. We conclude that the RR Lyrae catalog has a completeness between 70-78%, and provide a purity estimate between 92-98% (targeted observations) with lower limits of 75% (FFI stars) and 51% (K2 worst-case scenario). The low number of Cepheids prevents us from drawing detailed conclusions but the purity of the DR2 sample is estimated to be around 66%.Comment: 15 pages, 12 figures, 10 tables, accepted into the Gaia DR2 Special Issue in A&A. V1: submitted version, v2: accepted version. Lists available at http://konkoly.hu/~lmolnar/gaiakepler_datafiles_R1.zi

Gaia Eclipsing Binary and Multiple Systems. A study of detectability and classification of eclipsing binaries with Gaia

In the new era of large-scale astronomical surveys, automated methods of analysis and classification of bulk data are a fundamental tool for fast and efficient production of deliverables. This becomes ever more imminent as we enter the Gaia era. We investigate the potential detectability of eclipsing binaries with Gaia using a data set of all Kepler eclipsing binaries sampled with Gaia cadence and folded with the Kepler period. The performance of fitting methods is evaluated with comparison to real Kepler data parameters and a classification scheme is proposed for the potentially detectable sources based on the geometry of the light curve fits. The polynomial chain (polyfit) and two-Gaussian models are used for light curve fitting of the data set. Classification is performed with a combination of the t-SNE (t-distrubuted Stochastic Neighbor Embedding) and DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithms. We find that approximately 68% of Kepler Eclipsing Binary sources are potentially detectable by Gaia when folded with the Kepler period and propose a classification scheme of the detectable sources based on the morphological type indicative of the light curve, with subclasses that reflect the properties of the fitted model (presence and visibility of eclipses, their width, depth, etc.).Comment: 9 pages, 18 figures, accepted for publication in Astronomy & Astrophysic

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 difficult 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 the GEV method (S\"uveges 2014), as well as a method for the direct estimation of a threshold. Three methods involve some unknown parameters, which are obtained by fitting a regression-type predictive model using easily obtainable covariates derived from observational time series. We conclude that the GEV and the Baluev methods both provide good solutions to the issues posed by a large-scale processing. The first of these yields the best scientific quality at the price of some moderately costly pre-processing. When this pre-processing is impossible for some reason (e.g. the computational costs are prohibitive or good regression models cannot be constructed), the Baluev method provides a computationally inexpensive alternative with slight biases in regions where time samplings exhibit strong aliases.Comment: 16 pages, 14 figures, 1 tabl

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

We propose a robust principal component analysis (PCA) framework for the exploitation of multi-band 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 Delta Scuti variables. We found also 129 new RR Lyrae variables, complementary to the catalogue of Sesar et al., 2010, extending the halo area mapped by Stripe 82 RR Lyrae stars towards the Galactic bulge. The sample comprises also 25 multiperiodic or Blazhko RR Lyrae stars.Comment: 23 pages, 17 figure

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&

Gaia's Cepheids and RR Lyrae Stars and Luminosity Calibrations Based on Tycho-Gaia Astrometric Solution

Gaia Data Release 1 contains parallaxes for more than 700 Galactic Cepheids and RR Lyrae stars, computed as part of the Tycho-Gaia Astrometric Solution (TGAS). We have used TGAS parallaxes, along with literature ($V, I, J, {K_\mathrm{s}}, W_1$) photometry and spectroscopy, to calibrate the zero point of the Period-Luminosity and Period-Wesenheit relations of classical and type II Cepheids, and the near-infrared Period-Luminosity, Period-Luminosity-Metallicity and optical Luminosity-Metallicity relations of RR Lyrae stars. In this contribution we briefly summarise results obtained by fitting these basic relations adopting different techniques that operate either in parallax or distance (absolute magnitude) space.Comment: 5 pages, 4 figures, proceedings for the 22nd Los Alamos Stellar Pulsation Conference Series Meeting "Wide field variability surveys: a 21st-century perspective", held in San Pedro de Atacama, Chile, Nov. 28 - Dec. 2, 201

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

Pulsating star research and the Gaia revolution

In this article we present an overview of the ESA Gaia mission and of the unprecedented impact that Gaia will have on the field of variable star research. We summarise the contents and impact of the first Gaia data release on the description of variability phenomena, with particular emphasis on pulsating star research. The Tycho-Gaia astrometric solution, although limited to 2.1 million stars, has been used in many studies related to pulsating stars. Furthermore a set of 3,194 Cepheids and RR Lyrae stars with their times series have been released. Finally we present the plans for the ongoing study of variable phenomena with Gaia and highlight some of the possible impacts of the second data release on variable, and specifically, pulsating stars.Comment: 12 pages, 4 figures, proceedings for the 22nd Los Alamos Stellar Pulsation Conference Series Meeting "Wide field variability surveys: a 21st-century perspective", held in San Pedro de Atacama, Chile, Nov. 28 - Dec. 2, 201