Gaia Data Release 2
Free Access
Issue
A&A
Volume 620, December 2018
Gaia Data Release 2
Article Number A127
Number of page(s) 16
Section Galactic structure, stellar clusters and populations
DOI https://doi.org/10.1051/0004-6361/201833514
Published online 07 December 2018

© ESO 2018

1 Introduction

RR Lyrae stars are large-amplitude pulsating stars with easily recognisable light-curve shapes. They can be used to measure distances, to trace structures in the Milky Way and other galaxies, and to investigate stellar pulsation and evolution. Large sky surveys have mapped the distribution of RR Lyrae stars in particular to large numbers and depths (see e.g. Drake et al. 2013; Sesar et al. 2013; Beaton et al. 2016; Hernitschek et al. 2016; Minniti et al. 2017, for some examples).

Cepheids, an umbrella term used to describe the classical δ Cephei stars, the Type II Cepheids, and the anomalous Cepheids, are even more important tools for mapping the structure of the cosmos and individual galaxies: although they are less frequent than RR Lyrae stars, they are more luminous, and hence more easily detectable. The OGLE survey has very thoroughly searched both the Galactic bulge and the Magellanic Clouds for all members of the Cepheid and RR Lyrae families. According to Soszyński et al. (2017), their collection of classical Cepheids is now nearly complete, concluding the work started a century ago by Leavitt (1908).

The Gaia Data Release 2 (DR2; Gaia Collaboration 2018) represents a new step forward in mapping the distribution of RR Lyrae and Cepheid stars, as well as other variable stars in the Milky Way and its vicinity. However, these classifications are based on sparse photometry, and those classifications can be affected by poor phase coverage and/or confusion between variable types. Space photometric missions, such as MOST, CoRoT, Kepler, or BRITE, provide dense, continuous photometry of variable stars that might in principle be used to validate the results from other surveys. However, most missions have either small apertures or very limited sample sizes or both, therefore their use for validation purposes is very limited. The only exception is the Kepler space telescope, which observed hundreds of thousands of targets so far, including thousands of RR Lyrae and hundreds of Cepheid stars (Szabó et al. 2017; Molnár 2018). Our preliminary studies with the PanSTARRS PS1 survey by Hernitschek et al. (2016) indicate that a comparison with data from Kepler is feasible, but the first results indicate that eclipsing binary stars may contaminate the RR Lyrae sample in the Galactic disc in that survey (Juhász & Molnár 2018).

These findings led us to use the observations of Kepler to provide an independent validation of the classifications of the various RR Lyrae and Cepheid-type variables in Gaia DR2. Conversely, input from Gaia DR2 will allow us in the future to correctly identify as RR Lyrae or Cepheid stars targets that hide in the Kepler and K2 databases.

The paper is structured as follows: in Sect. 2 we introduce the variable star observations made by Gaia and Kepler, respectively; in Sect. 3 we describe the classification of the Kepler light curves into the various subclasses; in Sect. 4 we present the results of the validation, and in Sect. 5 we provide our conclusions.

2 Observations

2.1 Variable stars in Gaia DR2

Holl et al. (2018) summarized the results for the more than half a million variable stars published in Gaia DR2, which include candidates of RR Lyrae stars, Cepheids, long-period variables, rotation modulation (BY Draconis) stars, δ Scuti & SX Phoenicis stars, and short-timescale variables.

Different techniques were employed in the variability pipeline depending on the variability type. Here, we focus on the Cepheids and RR Lyrae stars identified by the all-sky classification (Rimoldini et al. 2018), available in the gaiadr2.vari_classifier_result table of the Gaia archive. Such classifications are normally verified by a subsequent pipeline module dedicated to the RR Lyrae and Cepheid variables (Clementini et al. 2018), but only for sources with at least 12 field-of-view (FoV) transits in the G band. The variable classes that we use are the four RR Lyrae subtypes, RRAB, RRC, and RRD/ARRD (corresponding to fundamental-mode, first-overtone, and double-mode stars with either normal or anomalous period ratios), and various Cepheid types, CEP, T2CEP, and ACEP (corresponding to classical or δ Cephei stars, Type II Cepheids, and anomalous Cepheids). Throughout the paper, we refer to the variable classifications in Gaia DR2 in all capitals (RRAB, RRC, RRD), and use the regular RRab, RRc, RRd notations for our classifications based on the Kepler and K2 light curves.

Our goal is to provide an independent assessment of the completeness and purity rates of the all-sky classification results of RR Lyrae and Cepheid candidates based on the fine light-curve sampling of Kepler and K2 targets, regardless of the number of observations and other features or limitations related to the Gaia data. We define completeness here as the fraction of sources with properly identified classes in Gaia DR2 against all RR Lyrae stars observed in the Kepler and K2 missions. Purity is defined here as the fraction of sources with properly identified variable classes compared to all sources in those classes in Gaia DR2.

Kepler is superior in terms of photometric precision and duty cycle to all ground-based surveys. The OGLE survey comes close as a result of the decade-long coverage, but it is limited to the Galactic bulge, disc, and the Magellanic Clouds (Udalski et al. 2015), whereas Kepler observed several halo fields. We note that Holl et al. (2018) presents some completeness and purity estimates based on the OGLE survey results for the RR Lyrae and Cepheid candidates. The only other program similar to Kepler is the Transiting Exoplanet Survey Satellite space telescope (TESS; Ricker et al. 2016): it has already started collecting continuous photometry from nearly the whole sky, but it will not reach the depth of either Gaia or Kepler or ground-based surveys.

In this study, we used the following information available in the Gaia DR2 archive (fields and table names specified in footnotes): celestial coordinates1, median G brightnesses2, the number of FoV transits in the G band3, classification classes4 and scores5 ranging between 0 and 1, provided by the all-sky classification pipeline (Rimoldini et al. 2018).

2.2 Kepler and K2 missions

The Kepler space telescope was designed to detect transiting exoplanets and determine the occurrence of Earth-like, temperate rocky planets around Sun-like stars (Borucki et al. 2010; Borucki 2016). To achieve this, it collected quasi-continuous photometry of approximately 170 000 stars in a field between Lyra and Cygnus, spanning about 115 deg2. The majority of stars were observed with a 29.4 min sampling, called long cadence (LC), and the telescope was rolled by 90 deg every quarter year. Not all stars were continuously observed: the target list was updated for every quarter. The prime mission lasted for four years, until the breakdown of two reaction wheels on board.

Afterwards, Kepler was reoriented to observe in shorter, 60- to 80-day-long campaigns along the ecliptic, using only the two remaining reaction wheels. The new mission, named K2, had no core science program, and the space telescope has been utilized as a space photometric observatory instead, carrying out a very broad science program that extends beyond exoplanets and stellar physics (Howell et al. 2014). Coordination and target selection is managed by the Kepler Guest Observer Office6. Stellar physics studies are coordinated by the Kepler Asteroseismic Science Consortium (KASC), which has a dedicated RR Lyrae and Cepheids Working Group.

During the original mission, Kepler observed about 50 RR Lyrae stars, one classical Cepheid, V1154 Cyg, and a Type-II Cepheid of the RVb subtype, DF Cyg (see e.g. Benkő et al. 2010; Nemec et al. 2013; Bódi et al. 2016; Derekas et al. 2017; Vega et al. 2017, and references therein). The K2 mission greatly expanded the spatial coverage of the telescope, and propelled the numbers of observed RR Lyrae and Cepheid stars into several thousands and hundreds, respectively, greatly exceeding the observations of previous space photometric missions (Szabó et al. 2017).

An important aspect of the Kepler space telescope that sets it apart from other space photometricmissions is the large optical aperture (95 cm), allowing us to reach targets fainter than Kp ~ 20 mag (where Kp refers to brightness in the wide passband of Kepler). In case of RR Lyrae stars, this translates into the distance of the nearest dwarf galaxies (Molnár et al. 2015). Kepler is the only space telescope that is able to deliver continuous time-series photometry while matching the depth of Gaia DR2. Ground-based, deep, but sparse surveys such as Catalina (Drake et al. 2009) and PanSTARRS PS1 (e.g. Chambers et al. 2016) can also be useful to identify faint RR Lyrae candidates and have been used to select targets for the K2 mission. These surveys lack the potential of continuous light curves to unambiguously distinguish pulsating stars from other sources, however, like eclipsing binaries that could be confused with them in sparse data sets (Juhász & Molnár 2018). We exploit the properties of the Kepler sample mentioned above (depth, coverage, and FoV size) to verify and validate the classification of RR Lyrae and Cepheid variables in Gaia DR2.

It is important to note that only pre-selected targets have been observed in the Kepler and K2 missions. Data storage and download bandwidth limitations meant that only a low percentage of pixels were used to gather data in any given observing quarter or campaign. Full-frame images (FFI) were rarely stored, but a sparse sample is available for the original mission7. In the K2 mission, targets were exclusively proposed through the Guest Observer program. RR Lyrae candidates from large sky-surveys were revised and the weakest candidates were not proposed (Plachy et al. 2016). The target list was then cut by the Guest Observer Office, especially in the early campaigns. Therefore, the observed sample is neither a complete sample of the potential RR Lyrae stars nor fully representative of the populations of stars within a FoV. However, these data still represent the largest sample of space-based photometry available to us. At the time of this study, data from Campaigns 0 to 13 were processed and released.

The resolution of Kepler at 4"/px is much poorer than that of Gaia. This could potentially lead to source confusion. However, RR Lyrae and Cepheid light curves are easily recognisable even if a target is blended with another star nearby. Therefore, if photometric variation was detected at the target coordinates, we accepted it as a confirmed variable. Multiple stars of the same variable type could still be confused, but we found no such examples. Given the limited angular resolution, we decided to avoid the Galactic bulge areas. The OGLE survey provides superior coverage for classification and validation purposes in the bulge, and was already used in this manner by Holl et al. (2018). The K2 Campaigns 9 and 11 (C9 and C11) targeted the Galactic bulge: we omitted C9 entirely, and only used stars on C11 below –6 deg Galactic latitude, that is, excluding the region covered by the OGLE survey. Only a small fraction of the OGLE RR Lyrae targets were included in the K2 observations in C11, and their inclusion would not have been representative for the bulge population. We note that even with these cuts, blending and confusion hindered the detection and classification of some targets in C11 and C7; the latter targeted the Sagittarius (Sgr) stream and the outskirts of the bulge.

3 Target identification and classification

We cross-matched the Gaia DR2 sources that were classified as RR Lyrae or Cepheid variables around the original Kepler Lyra-Cygnus field with the Kepler Input Catalog (KIC, Brown et al. 2011). The results of the cross-match are presented in Appendix A. We did not use the DR2 parallax and GBPGRP colour data for classification and relied only on the light-curve shape information provided by Kepler. For the original mission, we searched for observed targets and classifications within the literature (Benkő et al. 2010, 2014; Nemec et al. 2013; Moskalik et al. 2015) or visually inspected the light curves available at MAST8.

During the original Kepler mission, 52 FFIs were recorded: 8 during commissioning, and a further 44 during the mission, each taken before the monthly data downlink period. The integration time was the same as for LC exposures. Although these images only provide sparse photometry, they were obtained at completely different epochs with respect to the Gaia observations, and are numerous enough to provide acceptable phase coverage and a more representative stellar sample that is not affected by selection bias. We used the f3 code developed by Montet et al. (2017) to extract the photometry of the stars, then folded the light curves with the most likely period based on the FFI data. A comparison of LC and FFI light curves of an RRab star is illustrated in Fig. 1, which also shows the agreement of the periods recovered from the two light curves. We compared the FFI periods to the periods determined from normal light curves for all RR Lyrae-type stars that Kepler observed, and they agree in all cases. The low number of data points in FFI light curves effectively reduces the faint limit of this data set to G ~ 20 mag.

For the K2 observations, we selected the sources near the campaign fields from the Gaia DR2 RR Lyrae and Cepheid classifications. The selection of RR Lyrae candidates is described in this section, while the one related to Cepheids is discussed in Sect. 4.4. Cross-match results for both groups are listed in Appendix A. We used the K2FoV tool to determine which stars fell on the CCD modules of Kepler in each campaign (Mullally et al. 2016). Overall, 11 361 stars were potentially observable during the selected campaigns, that is, about 5% of the RR Lyrae variables identified in Gaia DR2. Most of these are near the bulge or the Sgr stream (9843 stars for Campaigns 2, 7, and 11), and only 1518 fell into the halo FoVs. We cross-matched these sources with the K2 Ecliptic Plane Input Catalog (EPIC) and with the list of targets selected for observation in the mission (Huber et al. 2016).

The K2 observations contain various systematics caused by the excess motion of the space telescope, and multiple solutions were developed to correct for these. We generated an initial classification list by selecting the best light curves created by the various photometric pipelines. For the majority of the stars, we used the official pipeline-produced pre-search data conditioned simple aperture photometry (PDCSAP) products (Stumpe et al. 2012). Where PDCSAP was not available or was of inferior quality, we used data from the K2 extracted light-curves (or K2SFF), the EPIC Variability Extraction and Removal for Exoplanet Science Targets (EVEREST), and, in a few cases, the K2 Planet candidates from OptimaL Aperture Reduction (POLAR) light curves (Vanderburg & Johnson 2014; Luger et al. 2016; Barros et al. 2016). For a few stars, none of the light curve solutions provided by MAST were useful, and we applied the PyKE software to generate customised extended aperture photometry to obtain better data (Still & Barclay 2012; Plachy et al. 2017; Vinícius et al. 2017). The distribution of the RR Lyrae stars from the Kepler and K2 missions cross-matched with the Gaia DR2 candidates are plotted in Fig. 2 in equatorial coordinates.

For the K2 observations, our validation procedure was based on visual inspection and quantitative properties of the light-curve shapes. Our criteria for the visual inspection were the following. Fundamental-mode RR Lyrae and classical Cepheid stars have very distinct, almost sawtooth-like light curves with short, sharp rising branches and long descending branches that repeat (almost) regularly, or vary smoothly if they are modulated. Characteristic bumps or humps, generated by shockwaves appearing at the surface of the star, also show up at distinct pulsation phases. Hump- or bump-like features can also appear in rotating variables, but in these cases, they drift in phase because of differential rotation.

Double-mode stars can be harder to identify as they have less asymmetric light curves. They usually still have steeper rising branches, often with prominent humps before maximum light. Scatter in the light curve extrema may indicate beating with additional modes. In contrast, regular or smoothly varying alternations in the minima or maxima can be attributed to differences in the components and/or appearance and evolution of spots in eclipsing binaries. Nevertheless, classification of nearly sinusoidal light curves can remain ambiguous.

Overtone stars show distinct beating patterns in the light curve, which unlike beating caused by spot patterns in rotating stars, repeat very regularly. Given the small number of double-mode stars, we examined all candidates in more detail before accepting them (see below).

thumbnail Fig. 1

Left panel: phased long-cadence light curve of a modulated RRab star, KIC 5559631, from the original Kepler mission, using the customised light curve of Benkő et al. (2014). Right panel: light curve from the full-frame image of the same star, extracted by the f3 code (Montet et al. 2017). Pulsation periods were determined independently for the two data sets. Different colours and symbols denote data from different CCD modules.

thumbnail Fig. 2

Distribution of the Gaia DR2 RR Lyrae candidates confirmed by the Kepler (targeted and FFI) and K2 measurements in the sky, mapped in a Mollweide projection of equatorial coordinates. The thick line in light blue marks the Galactic equator, and the colour-coding shows the number of Gaia FoV transits in the G band per star. The original Kepler field is the northernmost group of stars at RA ≈ 300 deg.

3.1 Fourier parameters

For a quantitative analysis, we calculated the Fourier fits of the five strongest frequency components in the light curve using the LCFit code (Sódor 2012). Then we calculated the relative Fourier parameters, comparing the ith and the first harmonics with amplitude ratios Ri1 = AiA1 and phase differences (where c refers to cosine-based Fourier fits), as defined by Simon & Lee (1981) and Simon & Teays (1982). These terms are frequently used to classify pulsating variables and to separate various subclasses. We plot them as a function of period for i = 2, 3 in Fig. 3. The stars clearly separate into the RRab and RRc loci, with very few outliers (for comparison, we refer to Soszyński et al. 2009). We discuss some of the outliers in Sect. 4.2.2. The low quality of light curves in the densestellar field of the Sgr stream prevented us from calculating Fourier parameters in only six cases. Because hints of RRab variability can be visually confirmed in them, however, we included these stars as positive detections.

To validate double-mode candidates, we also computed the period ratios of the two main modes of the RRd stars: these give strong constraints if the star is a normal or anomalous RRd star (Soszyński et al. 2016). These values, along with the analysis of all RRd stars observed in the K2 mission, will be published in a separate paper (Nemec, priv. comm.).

thumbnail Fig. 3

Fourier parameters of the light curves of cross-matched K2–Gaia RR Lyrae-type sources. The ith and the first Fourier harmonics are compared by the , relative phase differences (in radians, using cosine-based Fourier fits) and the R21, R31 amplitude ratios, as a function of the periods (P). The colour-coding shows the respective and pairs. Triangles show RRc stars, dots represent RRab stars, and crosses show potential anomalous Cepheid stars (see Sect. 4.2.2).

3.2 Brightness comparison

We compared the Gaia DR2 median G brightnesses with the values obtained from the K2 data. The passbands of the two missions are similar, with Kepler spanning a 420–900 nm and Gaia a slightly wider 350–1000 nm wavelength range, both peaking around 600–700 nm (Van Cleve & Caldwell 2016; Evans et al. 2018).

We computed the flux-calibrated brightnesses (Kpfc) of the K2 stars from the PDCSAP light curves, using the zero-point of 25.3 mag, as determined by Lund et al. (2015). The two measurements generally agree well (see Fig. 4), with 60% of the stars below 0.1 mag difference, although it exceeds 1 mag for about 10% of the targets. The flux-calibrated magnitudes provide a better agreement with Gaia than the values found in EPIC (KpEPIC) up to about G ≈ 18 mag. For G > 18, as the colour-coding in Fig. 4 illustrates, the flux-calibrated values appear to be systematically fainter than the EPIC values. These issues probably come from the properties of the PDCSAP pipeline (poor background correction for dense fields and small pixel apertures for faint targets). This is especially pronounced for the population of the Sgr stream stars, marked with crosses in Fig. 4.

For about 1% of the stars, the Gaia brightness differs significantly from the two nearly identical Kp values (|KpfcKpEPIC| < 0.1 mag, while |GKpfc | > 1.0 mag). The cause of discrepancy in most of these cases is that the cross-matched EPIC refers to a close-by (within 1–3 Kepler pixels) brighter star that is blended with the faint RR Lyrae variable. In these cases, the light curve also consists of the combined flux of the two stars. Many of these G-Kp discrepant stars are also members of the Sgr stream.

thumbnail Fig. 4

Comparisons of the Gaia DR2 median G magnitudes and the flux-calibrated Kp magnitudes from the K2 mission, with the inset showing the distribution of the absolute differences. Colour-coding marks the absolute differences between the flux-calibrated Kp values and those found in EPIC: there is a clear systematic difference between the two Kp values towards, the faint end. Red outliers indicate agreement between the Kp values, but difference from the Gaia brightnesses. Crosses mark the Sgr stream stars in Field 7. The black line marks equality.

4 Results

The two quantities we are most interested in are the purity, defined as the fraction of bona fide variable stars of the appropriate class in the sample, and the completeness, defined as the fraction of the sources that are (properly) identified in Gaia DR2 compared to all (known) RR Lyrae stars within the FoVs. We investigated the distribution of stars according to the classification score, the number of Gaia FoV transits in the G band, and the median G brightness.

4.1 RR Lyrae stars in the original Kepler field

We identified 48 Gaia DR2 targets that were observed by Kepler, and we were able to confirm 44 of them as RR Lyrae variables, suggesting a purity of 92%. Beyond these 44 stars, 12 additional RR Lyrae stars have been identified by the KASC Working Group in the Lyra-Cygnus field, not all of which are published yet, indicating a completeness of 78% (44/56). One of the stars that is missing from the Gaia DR2 RR Lyrae sample is RR Lyr itself (as explained in Rimoldini et al. 2018), which was observed in the original FoV of Kepler (Kolenberg et al. 2011). (RR Lyr is present in DR2, but with an erroneous mean G brightness and parallax values (Gaia Collaboration 2018).)

After checking the data from the targeted observations, we then generated FFI-based light curves for a further 267 stars. We were able to classify 147 and 38 as (potential) RRab or RRc variables. The photometry of a further 10 targets was not successful as they were either near the edges of a CCD module or were blended with bright stars: we did not include them in our statistics. Combined with the LC targets discussed above, we can provide a lower-limit estimate of at least 75% for the purity of the Gaia DR2 RR Lyrae candidates within the original Kepler field, although the low value can partially be attributed to the sparse FFI data we used. The completeness of the sample rises to 96% when we include the stars confirmed by the FFI light curves. A more detailed analysis of the FFI sample will be published elsewhere (Molnár & Hanyecz, in prep.).

The distribution of the stars in the original Kepler field against the classification scores, the number of Gaia G-band FoV transits, and the median G brightnesses are shown in Fig. 5. There is very little cross-contamination between the RRAB and RRC classes (stars that we classified into a different type). Contamination from sources that we could not confirm as RR Lyrae variables is significant among stars that have low coverage and/or are faint (G >18 mag). However, this can be partially attributed to the FFI photometry pipeline that was not developed to handle very faint Kepler targets. The purity of the FFI sample is 90% or 85% when we limit the targets to G < 18 or G < 19 mag, respectively.

thumbnail Fig. 5

Histograms for the Gaia DR2 RRAB- and RRC-classified objects in the original Kepler field. The light hues (light green and orange) mark stars that were confirmed as RRab or RRc variables based on the Kepler light curves. Dark hues are RR Lyrae stars that we reclassified into the other group (dark green: RRc variables found in the RRAB class; brown: RRab stars in the RRC class). White indicates stars that we could not confirm as RR Lyrae variables.

4.2 RR Lyrae stars in the K2 fields

Overall, we were able to inspect the light curves of 1395 cross-matched K2 targets from Campaigns 0–8 and 10–13. The distribution of the Gaia DR2 candidates observed in the K2 mission is not uniform: the 601 stars from Campaigns 2, 7, and 11 represent only 6% of the 9843 observable targets in those fields, whereas for the rest, the halo fields the ratio is 52% (787/1518).

Of these 1395 stars, we confirmed the RR Lyrae-type variability of 1371 stars (1243 RRAB, 141 RRC, and 10 RRD sources). No data were available for the five ARRD-type stars that were within the K2 FoVs. The remaining 24 observed stars turned out to be different types of variables. These numbers lead to a Gaia DR2 purity of 98%, in agreement with those of the targeted observationsof the original Lyra-Cygnus field, and the findings of Holl et al. (2018). However, we emphasize again that the observed stellar samples of the K2 campaigns are not necessarily representative of the true stellar populations within those fields, therefore wetreat the purity value as an upper limit. We discuss the range of possible purity values in Sect. 4.3 in more detail.

Although the K2 photometric data are superior to data from other surveys, the observed sample is not exhaustive, so we can only providean estimate for the completeness of the Gaia DR2 classifications. Targets proposed for observation in the K2 campaigns were cross-matched from various surveys, and vetted based on the available photometry in the literature, and they are therefore more complete than any single catalogue (Plachy et al. 2016). Light curves gathered by Kepler based on these proposals were also checked visually, and they revealed very low level of contamination by other variables. Therefore, we considered the number of proposed and observed stars to be a good estimate for the number of true RR Lyrae stars in the FoVs. We then collected all stars that were proposed and observed during the mission, but had no counterparts in Gaia DR2 RR Lyrae classifications. We ended up with 445 targets, leading to a completeness estimate of 75% for the K2 fields. This is somewhat higher than the values computed for the OGLE fields (Holl et al. 2018), but agrees with our estimate for targeted observations in the original Kepler field. We plot the brightness distribution of the confirmed and missed RR Lyrae stars from the K2 mission in Fig. 6. The two distributions are fairly similar, but the maximum is shifted towards fainter magnitudes for the stars that are not classified as RR Lyrae in the Gaia DR2 classification table, by about 0.6 mag (the medians of the two groups are 16.6 and 17.2 mag).

We alsocompared the brightness distributions of all Gaia DR2 candidates falling into the K2 fields to all confirmed RR Lyrae stars therein (including the missed 445 stars) in Fig. 7 to see how different the selection function of the two missions are. Based on their capabilities alone, Kepler is only limited by source confusion, but it is able to observe stars below the faint limit of Gaia (see e.g. the RR Lyrae stars in Leo IV; Molnár et al. 2015). However, the sample observed by Kepler was limited by the input catalogues used for target selection. The large difference in the upper panel of Fig. 7 comes from the large number of bulge stars that were not observed in the K2 mission. The comparison of the halo fields only (i.e. excluding Campaigns 2, 7, and 11) shows a much better agreement in the lower panel. For stars brighter than 16.5 mag (here we used either G or Kp magnitudes for stars, given the good agreement between the two), the K2 observations and the input catalogues we used provide a sample more complete than that of Holl et al. (2018). Interestingly, the Gaia DR2 sample shows another excess below 18.5 mag. Since most of these stars have no K2 light curves, we cannot decide if these stars are contaminants or bona fide RR Lyrae stars that were not detected by other surveys before. Unfortunately, this brightness range will not be accessible to the TESS space telescope either.

thumbnail Fig. 6

Brightness distributions of the K2 targets stars that are classified as RR Lyrae variables both in Gaia DR2 and based on their K2 light curves (blue), vs. those that were missed as variable candidates in Gaia DR2, but their K2 light curves show RR Lyrae variation (grey). The blue solid and black dashed lines indicate the median values. These histograms are overlaid, not stacked.

thumbnail Fig. 7

Brightness distributions of the Gaia DR2 candidates (blue) by Holl et al. (2018) in the K2 fields vs. all known confirmed RR Lyrae stars within in the same fields, including stars not in the DR2 variability catalogue. The upper panel shows all fields; the spike at 18 mag is the Sgr stream. The lower panel shows the halo fields only.

4.2.1 RRLyrae subclass statistics

Based on their K2 light curves, we identified 1371 objects as RR Lyrae stars, 1211 (88%) RRab, 142 (10%) RRc, and 17+1 RRd and anomalous RRd stars (1%). Our classifications do not always agree with those of Gaia DR2. We found the Gaia DR2 RRAB class to be nearly pure, with only 1% (14/1243) of contamination from the other classes (stars that turned out to be RRc- or RRd-type pulsators instead). The contamination in the RRC and RRD classes was 8% (12/142) and 50% (5/10), respectively. While contamination rises significantly for these classes, they are much less numerous, therefore the overall rate is only about 2% for the RR Lyrae stars in general.

Moreover, of the 24 stars that we could not confirm as RR Lyrae variables, K2 light curves of 5 RRAB candidates revealed Cepheid variations (1 anomalous and 4 Type II Cepheids). This indicates a low level of cross-contamination between the RR Lyrae and Cepheid classes. We reclassify two of these, V1637 Oph (EPIC 234649037, PK 2 = 1.327 d), previously classified as an RR Lyrae, and FZ Oph (EPIC 251248334, PK 2 = 1.500 d), an under-observed variable, as short-period Type II Cepheids, also known as BL Her-type stars, based on their K2 light curves. The results are summarised in the confusion matrix in Table 1.

Figure 8 shows the distribution of the classification scores for the various RR Lyrae subclasses. The left panels group the stars according to their Gaia DR2 classification types. We indicate the portion of stars that we reclassified into different classes with darker hues. The right panels show the variability types based on the K2 light curves, with the same colours denoting the number of stars that we reassigned a different RR Lyrae subclass. The difference between the classification score distributions of RRab and RRc/RRd stars is striking: half of the RRab stars have scores above 0.8, while the distribution of the RRc and RRd stars is essentially flat, and for RRc stars the score falls off near 1.0. The flat distribution suggests that the RRC and RRD classes were harder to identify, likely because of the competition with the dominant RRAB class. Figure 8 also confirms that the RRab sample is nearly pure (almost all stars are from the RRAB class), while the RRd sample includes Gaia classifications of all three subclasses. For the RRc stars, the sample appears to be nearly pure above classification score 0.6, and about 15% of RRc stars with scores < 0.6 ended up in the RRAB or RRD classes of the Gaia DR2 classification.

The distributions of the median brightnesses in the G band of the three RR Lyrae subclasses are shown in Fig. 9. In contrast to the distribution from the original Kepler field, we do not see an increase of unconfirmed variables toward the faint end, as they appear rather evenly spread. Interestingly, RRc stars brighter than G ~ 15 mag seem to be missing from our particular selection of Gaia DR2 classifications (centre left panel), although we reclassified a few of them from the other subclasses (centre right panel). However, the number of RRab stars also decreases rapidly from 14–15 mag towards the bright end. Therefore, the apparent lack of a few RRc stars most certainly stems from small number statistics here.

Finally, Fig. 10 shows the distribution of stars according to the number of G-band observationsper RR Lyrae subclass. Here, the unconfirmed variables are clearly grouped at the low end, especially for the RRAB class. For stars with 20 or fewer FoV transits, the contamination is about 3%, and for the few stars with fewer than 12 FoV transits, it rises to 8%. These numbers indicate that the Gaia DR2 sample of RR Lyrae classifications is relatively pure even for stars with only a few observations.

These estimates illustrate that the classifications of Gaia DR2 are already well suited to identifying single-mode pulsators, even at low numbers of FoV transits, but multiperiodic objects like RRd stars will need more extended observations.

Table 1

Confusion matrix of the Gaia and K2 results.

thumbnail Fig. 8

Distribution of the various classification scores of the RR Lyrae subtypes. Left panels: Gaia DR2 classification type; right panels:as classified based on the K2 data. The distribution is skewed towards score values of 1.0 for RRab stars but is flat for RRc and RRd stars. Light green, orange, and pale violet mark bona fide RRab, RRc, RRd stars, respectively. Dark green, brown, and dark lilac denote stars that we classified into a different subclass (which are distributed in different panels on the right-hand side). White bars refer to the counts of stars for which the RR Lyrae variability was not confirmed or was rejected.

thumbnail Fig. 9

Distribution of the median G magnitudes per RR Lyrae subtype. The colour-coding is the same as in Fig. 8.

thumbnail Fig. 10

Distribution of the number of FoV transits in the G band per RR Lyrae subtype. The colour-coding is the same as in Fig. 8.

4.2.2 Ambiguous identifications

As mentioned in Sect. 3, the Fourier parameters in Fig. 3 mostly separate the stars into two groups corresponding to RRab- and RRc-type stars, but we found a few stars that we could not classify unambiguously. We flagged four stars as potentially anomalous Cepheids: three fundamental-mode candidates and one first-overtone candidate. We must emphasize, however, that the Fourier parameters of anomalous Cepheids overlap with those of RRab stars for certain period ranges, and therefore we could not rule out that these four objects are RRab stars based on their light-curve shapes alone. These four stars are identified in K2 as EPIC 206010651, 206175324, 212459957, and 234523936 (the last is the overtone candidate), corresponding to Gaia DR2 source_id 2600030303142307968, 2614960399737036672, 3606980678405498368, and 4134356134978875904, respectively.

Some outliers of the distribution of in Fig. 3 can be attributed to a peculiar group of modulated RRab stars that exhibit a strong Blazhko effect, with a full rotation in the parameters during the minimum-amplitude cycle (Guggenberger et al. 2012; Bódi et al. 2018). This phenomenon could shift the average value of the parameters when the duration of the light curve is comparable to the modulation period. This is the case, for example, for EPIC 245954410, with log Pd = −0.29 and rad, and for EPIC 212545143, an extremely modulated RRab star with logPd = −0.27 and rad. We note that two other stars at low but with shorter periods are not flagged as outliers. Although most RRc stars appear in a tight group, others spread out from 0 to 2π, and these two stars represent that subgroup of RRc stars.

4.3 RR Lyrae completeness and purity ranges

The observations of the two missions of Kepler provide different samples that are not straightforward to combine. Here we discuss the various samples and statistics obtained. We can focus on the original Kepler field where the combination of the targeted, continuous light curves and the FFI photometry provides a sample that is not biased by prior selection of targets, but hindered by the sparse nature of the FFI light curves. Alternatively, we can gather all targeted observations from the two missions, resulting in a larger sample that is based on the same data acquisition method. Finally, we can calculate purity and completeness values for all three samples (Kepler, Kepler FFI, and K2) combined. Through these combinations we provide a range of estimates, which are summarised in Table 2.

Overall, we were able to identify 0.9% of the RR Lyrae variables classified by Rimoldini et al. (2018) over the whole sky in the observations of the two missions of Kepler, outside the bulge. Inside the Kepler and K2 FoVs, light curves were collected for 15% of the DR2 targets (1706 stars out of 11 702 potential, observable targets from the two missions). As stated above, however, the actual coverage is much higher for the original Kepler FoV (near-complete) and the halo fields in the K2 mission (52%).

For the Kepler and/or K2 targeted observations, we derived a purity rate between 92 and 98% (with lower limits at 51% and 75%), and a completeness in the range of 70–78%. The completeness is estimated by simply comparing the number of cross-matched and confirmed Gaia sources to those also in the fields but not classified as RR Lyrae variables in Gaia DR2. The lowest completeness value of 70% here is reached if we only use the targeted observations but count the FFI stars amongthe missed ones (even though they were not known before DR2). The DR2 classifications have a completeness of 75% within the K2 fields, while the combination of all data sets leads to an overall completeness rate of 78%.

We obtain a very high completeness ratio of 96% for the original Kepler field when the FFI stars are included. The lack of further sources here can be attributed to the fact that the field is at low Galactic latitudes and thus was largely avoided by deep surveys thatcould have identified faint RR Lyraes there. Therefore, the high completeness in this field reflects our limited knowledge that has now been expanded by the Gaia DR2 identifications, so we consider this value as an upper limit.

Even more diverse limits can be derived for the purity. The estimate of 92% originates from the targeted Kepler observations, but that sample alone is much smaller than the rest. Both the K2 and combined Kepler+K2 observationsshow 98% purity. This is in broad agreement with the findings of Holl et al. (2018). We conclude that the single-mode group RRAB is nearly pure, whereas the RRC group suffers from some contamination, but most of the confusing sources are RRd stars, and not eclipsing binaries. Gaia DR2 all-sky classifications are not well suited yet to identifying double-mode (RRd) stars, but as these are intrinsically rare, they have little effect on the overall population statistics.

The inclusion of the FFI stars into the statistics of the original field, however, warns us that the Kepler and K2 samples might include some bias against contaminating sources in Gaia DR2 that have not been proposed for observation in the Kepler and K2 missions. The combined statistics from the original field gives us a lower limit of 75% for purity, although this value is likely affected by faint RR Lyrae sources whose FFI photometry was of insufficient quality.

Of course, the Kepler+FFI sample is disjunct from the K2 FoVs, but it is the only one without prior selection bias. The excess of faint unobserved stars in the selection function (Fig. 7) suggests that the DR2 RR Lyrae sample might be less pure than our statistics suggests. In absence of these light curves, only a simple lower limit can be estimated for K2, considering that in halo fields, 52% of the Gaia sources were observed with 98% purity. Even if all the remaining 48% were false positives, this sets an absolute lower limit of 51% for the purity in the Galactic halo. The combination of halo and original-field stars raises that limit slightly to 55%.

Table 2

Completeness and purity values for the RR Lyrae and Cepheid stars in Gaia DR2 based on the Kepler and K2 light curves.

4.4 Cepheids in the Kepler and K2 data

Cepheids are much less numerous than RR Lyrae stars, and many of them populate the Galactic bulge, the Magellanic Clouds, and the discof the Milky Way. The Kepler and K2 missions largely avoided these areas to prevent source confusion and blending, therefore the overlap between these missions and the Cepheids in Gaia DR2 is much more limited than for the RR Lyrae stars. Because of the low number of targets, we decided to also include the Bulge stars in our statistics. Since Cepheids are intrinsically luminous, their variations can be recognised even when blended with other stars in the Kepler observations.

In the Lyra-Cygnus field of the original Kepler mission, Gaia DR2 classifications correctly include V1154 Cyg as CEP and HP Lyr as T2CEP (which is a potential RV Tau star; Graczyk et al. 2002), while it missed DF Cyg and misclassified V677 Lyr as T2CEP (known to be a longer-period semi-regular variable; Gorlova et al. 2015).

In the K2 fields, 73 stars classified as Cepheids in Gaia DR2 were observable (Fig. 11). Of these, we found data for 38 from the three subclasses (3 ACEP, 13 CEP, and 22 T2CEP stars), of which we were able to confirm 20 as a members of the Cepheid family, and 5 more as likely Cepheid stars. Given the small sample size, we did not separate the stars further into subclasses. With the inclusion of the stars from the RRAB class that we classified as Cepheids, the number of Cepheid variables common between Kepler/K2 and Gaia is 32 stars (2 from Kepler and 25+5 from K2).

The stars we were not able to confirm as Cepheids include four eclipsing binaries and/or rotational variables, five long-period variables, and four stars with unidentified variations. We classified one star as an RRab variable, further confirming a low level of cross-identification between Cepheids and RR Lyrae stars. This star was included in a K2 proposal as an RR Lyrae target, and thus it has been accounted for in our completeness estimate.

We were able to inspect the light curves of 54% (41/76) of the stars that fell into the FoVs of the two missions. The stars identified in the two Kepler missions account for only 0.9% (observable)and 0.5% (observed) of the 8550 Cepheid variables identified by Rimoldini et al. (2018). However, most of the DR2 detections are concentrated in the Magellanic Clouds, therefore our results are more relevant for the Cepheid population in the Milky Way. The findings indicate a purity on the order of 66% for this size-limited sample. Considering the very low number of sources available to us and the limited temporal coverage of the K2 data, this result is more or less in agreement with the 15% contamination in the sky-uniform test results of Holl et al. (2018).

thumbnail Fig. 11

Distribution in the sky of various Cepheid-type stars from the Gaia DR2 classifications cross-matched with Kepler and K2 measurements. Crosses mark stars that we rejected or were not able to confirm: half of them are at high Galactic latitudes. The notation is the same as in Fig. 2.

5 Conclusions

RR Lyrae and Cepheid stars are used for many purposes, such as mapping the substructures and stellar populations of the Milky Way and the Magellanic Clouds. The Gaia Data Release 2 features a large collection of RR Lyrae and Cepheid candidates (among others) over the entire sky that can be exploited for such studies. However, many of the identifications are based on a low number of observations. The Kepler space telescope observed a selection of these targets in great detail during the Kepler and K2 missions. The fact that Kepler is able to provide continuous light curves for the entire brightness range of the Gaia DR2 targets provides a great opportunity to validate these classifications. We investigated the targets in common between the missions, consisting of0.9% of both the RR Lyrae and Cepheid candidates from the all-sky classification of DR2 (Rimoldini et al. 2018). Within the areas of the Kepler and K2 FoVs (between Campaigns 0–8 and 11–13), 15% and 54% of the DR2 RR Lyrae and Cepheid candidates, respectively, had LC data recorded by Kepler. For the original FoV we also extracted sparse photometry from the full field images to obtain a sample more complete than the targeted observations alone.

We found that the photometry in Gaia DR2 is already suitable to properly identify single-mode pulsators. The RRAB class was found to be nearly pure, with very few contaminants. The RRC class and the various Cepheid classes are somewhat more contaminated. The few RRD (double-mode) stars we found included single-mode pulsators as well, and bona fide RRd stars have Gaia DR2 classifications from all RR Lyrae subclasses, indicating that reliable identification of multimode pulsators will require more observations. Overall, we found the purity to be in the 92–98% range, based on the targeted observationsof the Kepler space telescope, with lower limits of 75% (FFI stars) and 51% (worst-case scenario for the halo K2 fields). For the classification of Cepheids in Gaia DR2, we provide a purity estimate in the order of 66%.

Based on the visual examination of the contaminating sources (stars that were not found to be RR Lyrae or Cepheid stars), we conclude that contaminants are more likely to be pulsators or rotational variables than eclipsing binaries.

We estimate the completeness of the Gaia DR2 RR Lyrae classifications in the Kepler and K2 fields to be around 70–78% for the targeted observations with an upper limit of 96% for the original field, if we included the FFI stars as well.

All of the estimates presented here are summarised in Table 2, and they are in agreement with the limited validation tests presented in Holl et al. (2018), indicating that the observations of the Kepler space telescope can indeed be used to validate surveys that collect sparse photometry.

Acknowledgements

This research received funding from the Hungarian Academy of Sciences through the Lendület grants LP2014-17 and LP2018-7, and the János Bolyai Research Scholarship (L.M. and E.P.); the Hungarian National Research, Development, and Innovation Office through the NKFIH grants K-115709, PD-116175, and PD-121203; and the ÚNKP-17-3 program of the Ministry of Human Capacities of Hungary (Á.L.J.). L.M. has been supported by the Premium Postdoctoral Research Program of the Hungarian Academy of Sciences. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, some of which participate in the Gaia Multilateral Agreement, which include, for Switzerland, the Swiss State Secretariat for Education, Research and Innovation through the ESA Prodex program, the “Mesures d’accompagnement”, the “Activités Nationales Complémentaires”, and the Swiss National Science Foundation. This paper includes data collected by the Kepler mission. Funding for the Kepler and K2 missions are provided by the NASA Science Mission Directorate. The Kepler/K2 data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. We thank Carolyn Doherty for proofreading the manuscript, and Benjamin Montet for the fruitful discussions about the f3 code.

Appendix A Gaia DR2 and KIC/EPIC cross-match

In the following tables, we provide the cross-match of the sources in common between Gaia DR2 classifications and the Kepler and K2 observations. Tables A.1A.3 list stars from the original Kepler FoV that we classified as RRab, RRc, or likely RRab/RRc variables. Tables A.4A.6 include the RRab, RRc, and RRd stars identified in the K2 observations, respectively. Longer tables are available at the CDS in full length. Table A.7 lists the cross-matched Cepheid-type stars. Finally, stars that we rejected as RR Lyrae or Cepheid stars based on their K2 data are presented in Tables A.8 and A.9.

Table A.1

Cross-match of RRab-type stars in the original Kepler observations.

Table A.2

Cross-match of RRc-type stars in the original Kepler observations.

Table A.3

Stars with uncertain but likely classifications from the original Kepler observations.

Table A.4

Cross-match of RRab-type stars in the K2 observations.

Table A.5

Cross-match of RRc-type stars in the K2 observations.

Table A.6

Cross-match of RRd-type stars in the K2 observations.

Table A.7

Cepheid cross-match.

Table A.8

Cross-match of stars that turned out not to be RR Lyrae stars.

Table A.9

Cross-match of stars that turned out not to be Cepheid variables.

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1

ra and dec from gaiadr2.gaia_source

2

median_mag_g_fov from gaiadr2.vari_time_series_ statistics

3

num_selected_g_fov from gaiadr2.vari_time_series_ statistics

4

best_class_name from gaiadr2.vari_classifier_result

5

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7

52 FFIs were recorded in the original Kepler mission, and one or two per campaign in the K2 mission.

8

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All Tables

Table 1

Confusion matrix of the Gaia and K2 results.

Table 2

Completeness and purity values for the RR Lyrae and Cepheid stars in Gaia DR2 based on the Kepler and K2 light curves.

Table A.1

Cross-match of RRab-type stars in the original Kepler observations.

Table A.2

Cross-match of RRc-type stars in the original Kepler observations.

Table A.3

Stars with uncertain but likely classifications from the original Kepler observations.

Table A.4

Cross-match of RRab-type stars in the K2 observations.

Table A.5

Cross-match of RRc-type stars in the K2 observations.

Table A.6

Cross-match of RRd-type stars in the K2 observations.

Table A.7

Cepheid cross-match.

Table A.8

Cross-match of stars that turned out not to be RR Lyrae stars.

Table A.9

Cross-match of stars that turned out not to be Cepheid variables.

All Figures

thumbnail Fig. 1

Left panel: phased long-cadence light curve of a modulated RRab star, KIC 5559631, from the original Kepler mission, using the customised light curve of Benkő et al. (2014). Right panel: light curve from the full-frame image of the same star, extracted by the f3 code (Montet et al. 2017). Pulsation periods were determined independently for the two data sets. Different colours and symbols denote data from different CCD modules.

In the text
thumbnail Fig. 2

Distribution of the Gaia DR2 RR Lyrae candidates confirmed by the Kepler (targeted and FFI) and K2 measurements in the sky, mapped in a Mollweide projection of equatorial coordinates. The thick line in light blue marks the Galactic equator, and the colour-coding shows the number of Gaia FoV transits in the G band per star. The original Kepler field is the northernmost group of stars at RA ≈ 300 deg.

In the text
thumbnail Fig. 3

Fourier parameters of the light curves of cross-matched K2–Gaia RR Lyrae-type sources. The ith and the first Fourier harmonics are compared by the , relative phase differences (in radians, using cosine-based Fourier fits) and the R21, R31 amplitude ratios, as a function of the periods (P). The colour-coding shows the respective and pairs. Triangles show RRc stars, dots represent RRab stars, and crosses show potential anomalous Cepheid stars (see Sect. 4.2.2).

In the text
thumbnail Fig. 4

Comparisons of the Gaia DR2 median G magnitudes and the flux-calibrated Kp magnitudes from the K2 mission, with the inset showing the distribution of the absolute differences. Colour-coding marks the absolute differences between the flux-calibrated Kp values and those found in EPIC: there is a clear systematic difference between the two Kp values towards, the faint end. Red outliers indicate agreement between the Kp values, but difference from the Gaia brightnesses. Crosses mark the Sgr stream stars in Field 7. The black line marks equality.

In the text
thumbnail Fig. 5

Histograms for the Gaia DR2 RRAB- and RRC-classified objects in the original Kepler field. The light hues (light green and orange) mark stars that were confirmed as RRab or RRc variables based on the Kepler light curves. Dark hues are RR Lyrae stars that we reclassified into the other group (dark green: RRc variables found in the RRAB class; brown: RRab stars in the RRC class). White indicates stars that we could not confirm as RR Lyrae variables.

In the text
thumbnail Fig. 6

Brightness distributions of the K2 targets stars that are classified as RR Lyrae variables both in Gaia DR2 and based on their K2 light curves (blue), vs. those that were missed as variable candidates in Gaia DR2, but their K2 light curves show RR Lyrae variation (grey). The blue solid and black dashed lines indicate the median values. These histograms are overlaid, not stacked.

In the text
thumbnail Fig. 7

Brightness distributions of the Gaia DR2 candidates (blue) by Holl et al. (2018) in the K2 fields vs. all known confirmed RR Lyrae stars within in the same fields, including stars not in the DR2 variability catalogue. The upper panel shows all fields; the spike at 18 mag is the Sgr stream. The lower panel shows the halo fields only.

In the text
thumbnail Fig. 8

Distribution of the various classification scores of the RR Lyrae subtypes. Left panels: Gaia DR2 classification type; right panels:as classified based on the K2 data. The distribution is skewed towards score values of 1.0 for RRab stars but is flat for RRc and RRd stars. Light green, orange, and pale violet mark bona fide RRab, RRc, RRd stars, respectively. Dark green, brown, and dark lilac denote stars that we classified into a different subclass (which are distributed in different panels on the right-hand side). White bars refer to the counts of stars for which the RR Lyrae variability was not confirmed or was rejected.

In the text
thumbnail Fig. 9

Distribution of the median G magnitudes per RR Lyrae subtype. The colour-coding is the same as in Fig. 8.

In the text
thumbnail Fig. 10

Distribution of the number of FoV transits in the G band per RR Lyrae subtype. The colour-coding is the same as in Fig. 8.

In the text
thumbnail Fig. 11

Distribution in the sky of various Cepheid-type stars from the Gaia DR2 classifications cross-matched with Kepler and K2 measurements. Crosses mark stars that we rejected or were not able to confirm: half of them are at high Galactic latitudes. The notation is the same as in Fig. 2.

In the text

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