© ESO, 2016

1. Introduction

Easy to recognise thanks to their characteristic light variation, Cepheids and RR Lyrae stars are radial pulsating variables that trace stellar populations with different age and chemical composition: classical Cepheids (hereafter DCEPs) trace a young (t ≲ 300 Myr) stellar component; anomalous Cepheids (ACEPs) can trace stars of intermediate age (t ~ 1−5 Gyr) and metal poor content ([Fe/H] < −1.5 dex), although it is still matter of debate whether they might also arise from coalescence of binary stars as old as about 10 Gyr; finally, the RR Lyrae stars and the Type II Cepheids (T2CEPs) trace an old (t> 10 Gyr) stellar population.

They are primary standard candles in establishing the cosmic distance ladder because Cepheids conform to period-luminosity (PL), period-luminosity-colour (PLC), and period-Wesenheit (PW) relations, whereas the RR Lyrae stars follow a luminosity-metallicity relation in the visual band (M_V–[Fe/H]) and a period-luminosity-metallicity (PLZ) relation in the infrared.

With its multi-epoch monitoring of the full sky, Gaia will discover and measure position, parallax, proper motion and time series photometry of thousands of Cepheids and RR Lyrae stars in the Milky Way (MW) and its surroundings down to a faint magnitude limit of G ~ 20.7 mag. The spacecraft is expected to observe from 2000 to 9000 MW Cepheids, about 70 000 RR Lyrae stars in the Galactic halo, from 15 000 to 40 000 RR Lyrae in the MW bulge (see Table 3 in Eyer et al. 2012, and references therein), and according to the most recent estimates (Soszynski et al. 2015b, 2016) over 45 500 RR Lyrae stars and 9500 Cepheids in the Magellanic Clouds. Gaia will revise upwards these statistics as ongoing surveys such as OGLE-IV (Soszynski et al. 2015a,b,c, 2016), Catalina Sky Survey (CSS, Drake et al. 2013; Torrealba et al. 2015), Pan-STARRS (Hernitschek et al. 2016), LINEAR (Sesar et al. 2013), and PTF (Cohen et al. 2016) are constantly reporting new discoveries and increased numbers of RR Lyrae stars and Cepheids both in the MW and in its neighbour companions.

Gaia’s complete census of the Galactic Cepheids and RR Lyrae stars will allow a breakthrough in our understanding of the MW structure by tracing young and old variable stars all the way through from the Galactic bulge, to the disk, to the halo, and will likely reveal new streams and faint satellites that bear witness to the MW hierarchical build-up (see e.g. Clementini 2016). But most importantly, Gaia will measure the parallax of tens of thousands of Galactic Cepheids and RR Lyrae stars, along with milli-mag optical spectrophotometry (G broad-band white-light magnitude, blue and red spectro-photometry) and radial velocities and chemistry for those within reach of the Radial Velocity Spectrometer (RVS; G ≲ 17 mag). The unprecedented accuracy of Gaia measurements for local Cepheids and RR Lyrae stars will allow the absolute calibration via parallax of the Cepheid PL, PLC, PW and of the M_V −[Fe/H] and infrared PLZ relations for RR Lyrae stars, along with a test of the metallicity effects through simultaneous abundance measurements. This will enable re-calibration of “secondary” distance indicators probing distances far into the unperturbed Hubble flow and a total re-assessment of the whole cosmic distance ladder, from local to cosmological distances, in turn significantly improving our knowledge of the Hubble constant. The physical parameters of Cepheids and RR Lyrae stars will be constrained by Gaia photometry, parallax, metallicity, and radial velocity (RV) measurements, which will in turn constrain the input physics of theoretical pulsation models. This will further improve the use of Cepheids and RR Lyrae stars as standard candles and stellar population tracers.

In this paper we describe the Specific Objects Study (SOS) pipeline developed within the Coordination Unit 7 (CU7) of the Data Processing and Analysis Consortium (DPAC), the coordination unit in charge of the processing and analysis of variable sources observed by Gaia, to validate and fully characterise Cepheids and RR Lyrae stars observed by the spacecraft. A detailed description of the Gaia mission, its scientific goals and performance, as well as a comprehensive illustration of the Gaia DPAC structure and activities can be found in Gaia Collaboration (2016c). A summary of the astrometric, photometric, and survey properties of Gaia Data Release 1 (Gaia DR1) and a description of scientific quality and limitations of this first data release are provided in Gaia Collaboration (2016a). The photometric dataset and the processing of the G-band photometry released in Gaia DR1 are thoroughly discussed in van Leeuwen et al. (2016), Carrasco et al. (2016), Riello et al. (in prep.), and Evans et al. (2016).

We note that a rather strict policy has been adopted within DPAC for the processing and dissemination of Gaia data. Specifically, it was decided to be consistent in how DPAC does the processing and what is published in Gaia releases. That is, we do not release results which are based on Gaia data that is not published. For instance, since no G_BP, G_RP photometry is released in Gaia DR1, only the G-band time series photometry was used for processing and classification of the variable sources released in Gaia DR1. Furthermore, characterisation and classification of Gaia variable sources rely only on Gaia data. That is, we do not complement Gaia’s time series with external non-Gaia data to increase the number of data points or the time-span of the Gaia observations. Literature published data are used once the processing is completed, but only to validate results (i.e. characterisation and classification of the variable sources), which are, however, purely and exclusively based on Gaia data. Whether – and how – this may have limited the efficiency of the Gaia pipeline for Cepheids and RR Lyrae stars is extensively discussed in the paper, most specifically in Sect. 3.2. On the other hand, we are also sure that the next Gaia data releases will significantly improve both census and results for variable stars, and will also emend misclassifications if and where they have occurred.

The SOS pipeline for Cepheids and RR Lyrae stars, hereafter referred to as SOS Cep&RRL pipeline, is one of the latest stages of the general variable star analysis pipeline. Steps of the processing prior the SOS Cep&RRL pipeline are fully described in Eyer et al. (2016), to which the reader is referred to for details.

Validation of the classification provided by the general variable star analysis pipeline is necessary, since Cepheids and RR Lyrae stars overlap in period with other types of variables (binary systems, long period variables, etc.). SOS Cep&RRL uses specific features such as the parameters of the light curve Fourier decomposition and diagnostic tools like the Gaia colour−magnitude diagram (CMD), the amplitude ratios, the period-amplitude (PA), PL, PLC, and PW relations, and the Petersen diagram (Petersen 1973) to check the classification, to derive periods and pulsation modes, and to identify multi-mode pulsators. Radial velocity measurements obtained by the RVS are also planned for use to identify binary/multiple systems as soon as they become available.

The main tasks of the SOS Cep&RRL pipeline are i) to validate and refine the detection and classification of Cepheids and RR Lyrae stars in the Gaia data base, provided by the general variable star analysis pipeline, by cleaning the sample from contaminating objects, i.e. other types of variables falling into the same period domain; ii) to check and improve the period determination and the light curve modelling; iii) to identify the pulsation modes and the objects with secondary and multiple periodicities; iv) to classify RR Lyrae stars and Cepheids into subtypes (fundamental mode RRab, first overtone RRc, and double-mode RRd) according to the pulsation mode for the RR Lyrae stars, and DCEPs, ACEPs, and T2CEPs for the Cepheids, along with identification of pulsation modes for the first two, and subclassification into W Virginis (WVIR), BL Herculis (BLHER), and RV Tauri (RVTAU) types for the last; v) to identify and flag variables showing modulations of the light curve that are due to a binary companion or to the Blazhko effect (Blazhko 1907) that may falsify both the star brightness and the derived trigonometric parallax; vi) to use the pulsation properties and derive physical parameters (luminosity, mass, radius, effective temperature, metallicity, reddening, etc.) of confirmed bona fide RR Lyrae stars and Cepheids to be ingested into the Gaia main database by means of a variety of methods specifically tailored to these types of variables.

The paper is organised as follows. Section 2 provides a description of the whole architecture of the SOS Cep&RRL pipeline, its diagnostic tools, and their definition in the Gaia passbands. Sect. 3 presents the dataset and source selection on which the SOS Cep&RRL pipeline was run and describes how the pipeline was specifically tailored and simplified to analyse the Gaia SEP G-band time series data of candidate Cepheids and RR Lyrae stars. Section 4 presents the results of the SOS Cep&RRL analysis that are published in Gaia DR1. Finally, the main results and future developments of the pipeline are summarised in Sect. 5.

2. SOS Cep&RRL pipeline

In this section we present the SOS Cep&RRL pipeline in its complete form, briefly describing all its algorithms and tools, only part of which could actually be applied due to the specific characteristics of the dataset published in Gaia DR1 (see Sect. 3.2 for details).

In order to validate and refine the classification of Cepheids and RR Lyrae stars provided by the general variable star analysis pipeline, and be able in the future to make comparisons with the parameters measured for these stars by other DPAC processing tasks, different procedures are implemented in the SOS Cep&RRL pipeline as described in the following sections. The whole processing of the SOS Cep&RRL pipeline is presented schematically in Figs. 1−3 and described in detail in Sects. 2.1, 2.3 and 2.4. For each candidate confirmed as a bona fide RR Lyrae star or Cepheid, SOS Cep&RRL returns the most probable period, pulsation mode, multiple periodicities, if any, associated amplitudes, intensity-averaged magnitudes and mean radial velocities (if RVS data are available) as well as flagging of binary or multiple systems, to be published in the Gaia main data base.

The main input of SOS Cep&RRL is the calibrated Gaia time series photometry (G-magnitudes and integrated G_BP, G_RP photometry) processed by CU5, the DPAC coordination unit charged with the photometric processing of Gaia data, for all sources pre-classified as candidate Cepheids and RR Lyrae stars by the general variability Characterization and Classification processing, along with general information on the data, such as number of transits per source (after outlier removal), typical errors, time span of the observations, mean and median magnitude values, etc., computed by the Statistical Parameters module in the general pipeline (Eyer et al. 2016) prior SOS Cep&RRL.

Additional information will be progressively added in future releases: RV time series for sources within the RVS magnitude limit, Gaia’s parallaxes (distances), and astrophysical parameters such as effective temperature (log T_eff), gravity (log g), and absorption (A_λ) inferred by combining Gaia’s astrometry, photometry, and spectroscopy. This information can be used to optimise the SOS Cep&RRL processing.

2.1. Initial processing: characterisation of the light curves (period search and Fourier fitting)

The SOS Cep&RRL processing starts by characterising the G-band light curve (as well as the G_BP and G_RP light curves and the RVS RV curve if/when available) of sources classified as candidate Cepheids and RR Lyrae stars by the Supervised Classification module of the general variable star analysis pipeline. This part of the SOS Cep&RRL processing is common to both Cepheids and RR Lyrae stars and its main steps are shown in Fig. 1. The first step is the derivation of the source periodicity independently and with a different method to that used in the general pipeline Characterization module. We used the Lomb-Scargle algorithm (Lomb 1976; Scargle 1982) as opposed to the least-squares method used in Characterization (see Eyer et al. 2016). Tests performed on Cepheids and RR Lyrae stars in the Hipparcos catalogue showed that the Lomb-Scargle method reduces the number of large deviating period values for these specific types of variables. The period derived by SOS Cep&RRL is used to fold the light curve, which is then modelled with a truncated Fourier series in the form: (1)Zero-point (zp), period (1/ν_max), harmonic number (i), amplitudes (A_i), and phases (φ_i) of the harmonics for the G-band light curve are first computed with a linear fitting procedure. They provide initial trial values for the non-linear modelling of the light curve which is performed using the Levenberg-Marquardt (Levenberg 1944; Marquardt 1963) non-linear fitting algorithm (module NonLinearFourierAnalysis in Fig. 1). The non-linear fitting refines both the period and model of the light curve. In Gaia DR1 only the G-band time series photometry is available for the sources, hence the period resulting from the non-linear fitting of the G-band light curve is the final period adopted for the source, and module LcMeasurements directly measures the source intensity-averaged G mean magnitude, peak-to-peak G-amplitude, and epoch of maximum light from the G-band light curve modelled with the non-linear fitting algorithm¹. The peak-to-peak G-amplitude [Amp(G)] is calculated as the (maximum) − (minimum) values of the model which fits the folded light curve best. An estimate of the error on this quantity is provided by . The epoch of maximum light is computed as the Baricentric Julian day (BJD) of the maximum value of the G-band light curve model which is closer to the BJD of the first observations minus 3 times the period of the source. This procedure ensures that the time of maximum light precedes the time of the first observation. The mentioned BJD is offset by JD 2 455 197.5 d (= J2010.0). Adopting the results of the non-linear modelling amplitude ratios (R_ij = A_i/A_j), the phase differences (φ_ij = j × φ_i−i × φ_j) and related errors of the Fourier decomposition of the G-band light curve are computed by the module FourierDecomposition². Errors for all the parameters (period, amplitude, zp, etc.) derived with the non-linear Fourier modelling are estimated via Monte Carlo simulations³ according to the following procedure:

• a new light curve is generated where (value of each phase point) = (value of the original phase point) + (random number) × (±error of the original phase point value). Random numbers range between 0 and 1;

• a new model is computed with the non-linear modelling procedure, using as trial values the model parameters of the original light curve;

• the first two steps are iterated 100 times;

• for each parameter of the model, average and standard deviation are computed over the 100 simulations;

• the standard deviations derived in the previous step are assigned as uncertainties of the parameters resulting from the non-linear modelling.

The final step in the general part of the SOS Cep&RRL pipeline is the detection of possible secondary periodicities in the source periodogram. This is the task of the SecondaryPeriodicities module. For RR Lyrae stars we look for one additional frequency and for Cepheids for two beyond the first periodicity. Following the procedure adopted in the NonLinearFourierAnalysis module, the residuals (observed − model phase points) are searched for secondary periodicities. If a significant secondary frequency is found the procedure is iterated twice. The steps of the SecondaryPeriodicities algorithm are as follows:

• 1.

  residuals are computed as (observed) − (corresponding model) phase points;

• 2.

  the Lomb-Scargle period search method is run on the residual time series.

This module will be revised in preparation for the Gaia second data release (Gaia DR2) in order to properly take into account the actual significance of the detected secondary periodicities (see Sect. 5).

After this common part the analysis proceeds in two separate branches each specifically tailored to the processing of RR Lyrae stars and Cepheids. This is summarised in the flow charts in Figs. 2 and 3. Sources classified as candidate Cepheids by the general Classification pipeline will be sent first to the Cepheid branch. Conversely, sources classified as candidate RR Lyrae stars will first be processed through the RR Lyrae branch. However, for the processing of the Gaia DR1 data we followed a different approach to decide which branch a source should be sent to (see Sect. 3.2).

2.2. Conversions to the Gaia passbands

A number of tools specifically applicable for the characterisation of RR Lyrae stars and Cepheids are adopted in the different modules of the Cepheid and RR Lyrae branches (see Figs. 2 and 3). They include the CMD; the G-band PA diagram (for RR Lyrae stars also known as the Bailey diagram; Bailey 1902); the PL, PLC, and PW relations for Cepheids; the different planes in the Fourier parameter space; and the Petersen diagram (Petersen 1973) for double-mode Cepheids and RR Lyrae stars. All limits and loci of these tools are defined for the Johnson photometric system. We have converted them to the Gaia photometric system in order to apply them directly to Gaia sources. We have used the passband transformations provided in Jordi et al. (2010) and subsequent updates (Jordi, priv. comm.) to compute conversion formulae appropriate for the colour and metallicity ranges of Cepheids and RR Lyrae stars (V−I< 2.5 mag and −2.5 < [Fe/H] < 0.5 dex) and to transform the Johnson-Cousins V, I to the Gaia G, G_BP, G_RP passbands. The conversion formula for the G band is provided in Appendix A and shown in Fig. A.1. We then used a sample of 128 RR Lyrae stars belonging to the Galactic halo and bulge, to the Galactic globular clusters M 3 and M 68, and to the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) and also 77 classical Cepheids in the MW, LMC, and SMC, for which excellent light curves in the Johnson V and I passbands have been published by Soszynski et al. (2008a, 2009, 2010a,c, 2011a), Cacciari et al. (2005), Walker (1994), Moffett & Barnes (1984), Gieren (1981), Coulson & Caldwell (1985), Coulson et al. (1985), and Berdnikov & Turner (1995), Berdnikov et al. (2012, 2014). The two samples cover entirely the parameter space of pulsation modes, periods and metallicities for RR Lyrae stars and Cepheids. We used Eq. (A.1) to transform the V, I light curves of these selected samples to the Gaia G passband and fitted both original V, I, and Gaia-transformed G-band light curves with truncated Fourier series obtaining R₂₁, R₃₁, φ₂₁, φ₃₁ parameters and peak-to-peak amplitude in each band. Finally, we used the quantities obtained with the above procedure to derive relationships and transform the Fourier parameters and peak-to-peak amplitudes from the Johnson-Cousins to the Gaia G band. The relations obtained with this procedure are described by Eqs. (2) to (19)⁴.

Formulae to convert the literature peak-to-peak amplitudes of RR Lyrae stars to the Gaia G band are provided by Eqs. (2) and (3): We show in Fig. 4 the PA diagram in the Gaia G band of RR Lyrae stars in the LMC, the SMC, and the Galactic bulge and halo, obtained by converting the literature V and I amplitudes using Eqs. (2) and (3). We used literature amplitudes from Soszynski et al. (2009, 2010c, 2011a) for the RR Lyrae stars in the Magellanic Clouds, and from Pojmanski (1997) for the Galactic variables. In the figure a black solid line is drawn to separate RRab from RRc types. Also shown in the figure are ACEPs (filled circles) and T2CEPs (crosses) in the LMC and SMC taken from Soszynski et al. (2008b, 2015a). Their amplitudes were also transformed to the G band using Eqs. (2) and (3), since colours and amplitudes of ACEPs and T2CEPs are similar to those of RR Lyrae stars. The diagram in Fig. 4 is the main tool used to separate RR Lyrae stars into RRab and RRc types (see Sect. 3). However, since mixing of the pulsation modes occurs close to the separation line and further contamination is also caused by ACEPs, we also used the Fourier parameters to separate different pulsation modes and variable types.

Equations (4) to (11) provide formulae to convert the literature values of the Fourier parameters R₂₁, R₃₁, φ₂₁, and φ₃₁ of RR Lyrae stars to the Gaia G band: (11)Figures 5 and 6 show the G-band Fourier parameters φ₂₁ and R₂₁ of RR Lyrae stars computed using Eqs. (4), (5), (8), and (9) plotted versus period (P). The φ₂₁ vs. P plot was used along with the PA diagram to distinguish RR Lyrae stars from ACEPs and to better separate the RRab and RRc types (see Sect. 3).

Finally, Eqs. (12) to (19) provide formulae to convert the literature values of the Fourier parameters R₂₁, R₃₁, φ₂₁, and φ₃₁ of Cepheids to the Gaia G band: (12)(13)(14)(15)(16)(17)(18)(19)Figures 8 and 9 show the G-band Fourier parameters φ₂₁ and R₂₁ of Cepheids computed using Eqs. (12), (13), (16), and (17) plotted versus period. These diagrams were used to distinguish different Cepheid modes and to separate Cepheids from RR Lyrae stars (see Sect. 3).

2.3. RR Lyrae branch

The different steps of the processing for sources classified as RR Lyrae stars by the general Classification pipeline are summarised in Fig. 2. However, only some modules of the RR Lyrae branch were activated for the analysis of the Gaia DR1 data.

2.3.1. Identification of double-mode RR Lyrae stars: RRLyraeDoubleModeSearch module

For RR Lyrae stars for which a secondary periodicity was detected by the SecondaryPeriodicities module of the initial SOS Cep&RRL processing (see Fig. 1), the RRLyraeDoubleModeSearch module sets the shorter and the longer periodicities to first overtone period (P_1O) and fundamental mode period (P_F), respectively. Then if both P_1O and P_F are longer than 0.3 d, it checks whether the star locates within the regions of the P_1O/P_F vs. P_F plane (generally known as the Petersen diagram; Petersen 1973) allowed for RR Lyrae double-mode pulsation. The allowed loci in the Petersen diagram were defined using the P_1O, P_F, and P_1O/P_F values of 1335 RRd variables observed by the OGLE and ASAS surveys of the LMC, SMC, Galactic bulge, and halo. Their Petersen diagram is shown in Fig. 7. A lower limit of 0.3 d for the P_1O, P_F values was also inferred from Fig. 7, which shows that no RRd pulsators are known with P_F< 0.3 d. Schematically, the RRLyraeDoubleModeSearch algorithm performs the following steps:

• computing the P_1O/P_F ratio;

• if the source falls in the region defined as 0.724 <P_1O/P_F< 0.752 and 0.30 <P_F< 0.62 days, then the RR Lyrae star is identified as RRd.

The light curve modelling of a confirmed double-mode RR Lyrae star is then refined in the NonLinearDoubleModeModeling module by applying the non-linear fitting procedure with the proper truncated Fourier series and simultaneously fitting the two pulsation modes. In a similar way, the period, the epoch, the peak-to-peak amplitudes, and the Fourier decomposition are recomputed and refined. The RRLyraeDoubleModeSearch module of SOS Cep&RRL was tested, but its results have not yet been included in Gaia DR1.

2.3.2. Blazhko effect search, position in the CMD, and amplitude ratios

There are three modules in the RR Lyrae branch (BlazhkoEffectSearch, PositionInTheCMD, and AmplitudeRatios) that could not be activated because in the Gaia DR1 we lack the information to properly operate them. They are briefly described in the following.

The BlazhkoEffectSearch module searches for RR Lyrae stars affected by the Blazhko effect (Blazhko 1907), a periodic modulation of the amplitude and/or the phase of the main pulsation that occurs on timescales typically varying from a few days to hundreds of days. This phenomenon is shown by some 25−30% of the Galactic RRab and 5% of the RRc stars. However, recent detections of Blazhko stars with very small amplitudes suggest that these numbers may be underestimated (an occurrence rate as high as 50% follows from the studies by Jurcsik et al.; Jurcsik, priv. comm.). Using data from future releases, Gaia may provide accurate and updated occurrence rates. Radial velocity measurements and multi-band photometric data, to be obtained by Gaia with the foreseen long time base of observations, are fundamental to identify irregular and Blazhko variables among the RR Lyrae stars, and can help to understand whether they are due to non-radial modes excited during pulsation.

The PositionInTheCMD module verifies that sources classified as RR Lyrae stars fall inside the RR Lyrae instability strip (IS) in the CMD, by checking whether the colours of the targets are compatible with the IS for RR Lyrae stars. Gaia CMD is a fundamental tool used to clean the sample of RR Lyrae stars from possible contaminating objects, since other types of variables falling in the same period domain, for instance eclipsing binaries (ECLs), should lie predominantly outside the RR Lyrae IS in this diagram. Knowledge of the source absolute magnitude (via parallax) and colour (or effective temperature) are needed to use this tool. Parallaxes are published in Gaia in DR1 only for Cepheids and RR Lyrae stars with G ≲ 13.5 mag as part of the Tycho-Gaia Astrometric Solution (TGAS; Lindegren et al. 2016). Cepheids and RR Lyrae stars for which results of the SOS Cep&RRL processing are published in Gaia DR1 are fainter than this limit (see Sect. 3.1), hence parallaxes are not yet available for them. This limited the use of the CMD tool (see Sect. 3).

The AmplitudeRatios module uses the peak-to-peak amplitude ratios between Gaia’s three different photometric bands to check whether the observed periodicity is due to a contact binary system mimicking an RR Lyrae-like light curve (this may be the case especially for RRc pulsators). In fact, amplitude ratios between different photometric bands are expected to be close to unity in the case of ECLs. Lacking G_BP, G_RP time series, this tool could not be activated for Gaia DR1.

2.3.3. PA diagram and mode identification: ModeIdentification module

RRab and RRc types occupy different locations in the G-band peak-to-peak amplitude vs. period diagram (see Fig. 4) and in the P–R₂₁, and P–φ₂₁ planes (see Figs. 5 and 6). The ModeIdentification module combines results from these three diagnostics to identify the pulsation mode of candidate RR Lyrae stars and/or recognise misclassified objects. According to Fig. 4, RR Lyrae stars are confined within 0.2 d ≤ P ≤ 1.0 d in period and within 0.05 mag ≤ Amp(G) ≤ 2.0 mag in G-band amplitude. Sources outside these ranges will be flagged as possible misclassified objects. Furthermore, RRc and RRab types can then be separated with a line described by the equation Amp(G) = −4.0 × P + 2.2. Mixing of RRc and RRab pulsators occurs close to the separation line, and significant contamination also exists in Fig. 4 between RR Lyrae stars and ACEPs. However, they can both be reduced by using the star position in the Fourier R₂₁ and φ₂₁ vs. P planes (Figs. 5 and 6) where the two types are located in separate regions whose borders we define in Sect. 4.

2.3.4. RR Lyrae star classification

This module performs the final assignment of a source to the RR Lyrae class based on results of the previous SOS Cep&RRL modules. If the source is confirmed to be an RR Lyrae star, thus validating the initial class assignment provided by the general Classification pipeline, the analysis proceeds with the derivation of the stellar parameters⁵ and the final export of the source attributes (period, mean magnitude, peak-to-peak amplitude, Fourier parameters, secondary periodicity, pulsation mode, and any other relevant quantities) to the Main Data Base. Conversely, if the source is not confirmed as an RR Lyrae star, it is sent for analysis through the Cepheid branch (green box in Fig. 2) unless it was already analysed in that branch and not found to be a Cepheid either, in which case it will be definitively rejected as an RR Lyrae star and/or Cepheid and fed back to the general variable star analysis pipeline for processing through other SOS modules.

2.4. Cepheid branch

The processing of sources classified as Cepheid candidates by the general Classification pipeline occurs in the Cepheid branch first, the steps of which are schematically shown in Fig. 3. As with the RR Lyrae stars only some modules of the Cepheid branch could be used for the analysis of the Cepheids in Gaia DR1. In particular, the first step of the Cepheid branch processing would be the identification of Cepheids in binary or multiple systems using RV measurements obtained by the RVS and the ratios of photometric amplitudes in the different passband. Since neither RVs nor G_BP, G_RP photometry is available in Gaia DR1, this module was not activated. Similarly, we could not use the PositionInTheCMD module to check whether the candidate Cepheids fell inside the DCEP, ACEP, and TCEP instability strips in the CMD. Analysis in the Cepheids branch starts from the search for multi-mode variables performed by the CepMultModeSearch module.

2.4.1. Identification of multi-mode Cepheids: CepMultiModeSearch module

The CepMultiModeSearch module identifies Cepheids pulsating simultaneously in different modes by checking the period ratios of the different periodicities found by the SecondaryPeriodicities module of the general trunk (Fig. 1). The relevant period ratios are 1O over F (P_1O/P_F), second-overtone (2O) over F (P_2O/P_F), and so on (P_2O/P_1O; P_3O/P_1O; P_3O/P_2O). The typical values for these ratios are known both from empirical and theoretical studies. Allowed periods and period ratios for multi-mode DCEPs, following Soszynski et al. (2008a), are reported in Table 1.

The following different cases are considered, depending on the number of secondary periodicities found by the SecondaryPeriodicities module of the SOS Cep&RRL general trunk:

• case 1: two periodicities are found

  • The algorithm sets the shorter and the longer periodicities toP_1O and P_F, respectively. Then it checks whether the ratio P_1O/P_F falls within the allowed ranges listed in Table 1.

  • The algorithm sets the shorter and the longer periodicities to P_2O and P_F, respectively. Then it checks whether the ratio P_2O/P_F is within the allowed ranges, as listed in Table 1.

  • The algorithm sets the shorter and the longer periodicities to P_2O and P_1O, respectively. Then it checks whether the ratio P_2O/P_1O is within the allowed ranges, as listed in Table 1.

  • The algorithm sets the shorter and the longer periodicities to P_3O and P_1O, respectively. Then it checks whether the ratio P_3O/P_1O is within the allowed ranges, as listed in Table 1.

If none of the above conditions is satisfied the source is rejected as a multi-mode Cepheid.

case 2: three periodicities are found

• The algorithm sets the shortest, the intermediate, and the longestperiodicity to P_2O, P_1O, and P_F, respectively. Then it checks whether the P_1O/P_F, P_2O/P_F, and P_2O/P_1O ratios are within the allowed ranges, as listed in Table 1.

• The algorithm sets the shortest, the intermediate, and the longest periodicity to P_3O, P_2O, and P_1O, respectively. Then it checks whether the P_3O/P_1O, P_3O/P_2O, and P_2O/P_1O ratios are within the allowed ranges, as listed in Table 1.

If none of the above conditions is satisfied the source is rejected as a multi-mode Cepheid.

The light curve modelling of a confirmed multi-mode Cepheid is refined in the NonLinearDoubleModeModeling module by applying the non-linear fitting procedure with the proper truncated Fourier series and fitting simultaneously all pulsation modes (generally two). Periodicities, epoch of maximum light, intensity-averaged mean magnitude, peak-to-peak amplitudes of the two/three pulsation modes, and the parameters of the Fourier decomposition are also recomputed and refined taking into account all periodicities. The CepMultiModeSearch module of SOS Cep&RRL was tested, but its results have not yet been included in Gaia DR1.

2.4.2. Identification of Cepheid type (DCEP, ACEP, T2CEP): CepTypeIdentification module

The CepTypeIdentification module combines pulsation and photometric characteristics (in the future also spectroscopic characteristics) of the candidate Cepheids computed in the previous modules of the SOS Cep&RRL processing (both in the general trunk and in the Cepheid branch) to subdivide them into DCEP, ACEP, and T2CEP types. The module foresees the use of two main diagnostics: (i) the source metallicity that will be derived by the DPAC processing of RVS measurements as DCEP and T2CEP/ACEP types in general show different metallicity content, being the DCEPs typically more metal-rich than the T2CEPs and ACEPs, and (ii) the PL and PW relations, which are different for the three types of Cepheids. However, for Gaia DR1 the identification of the Cepheid types could rely only on the use of the G-band PL relations, for which we used the following set of equations (20)(21)(22)(23)(24)where M_G is the absolute magnitude in the G band. These relations were defined using Cepheids in the LMC for which light curves and pulsation characteristics have been published by Soszynski et al. (2008a,b), and adopting an absolute de-reddened distance modulus for the LMC of DM_LMC = 18.49 mag from Pietrzynski et al. (2013). They are shown in Fig. 10.

Candidate Cepheids that fall within 4σ of any of the above relations are assigned the Cepheid type and pulsation mode of the closest PL. Conversely, candidate Cepheids falling beyond 4σ will be rejected as misclassified sources. T2CEPs are further subdivided into three separate classes: the BLHER class, the WVIR class, and the RVTAU class, depending on the pulsation period. The three different subclasses of the T2CEP group follow different PL and PW relations and populate different period ranges. The T2CEPSubclassification module identifies the T2CEPs with periods in the range 1 ≤ P< 4 d as BLHER, the T2CEPs with periods in the range 4 ≤ P< 20 d as WVIR, and the T2CEPs with periods equal to or longer than 20 days as RVTAU (Soszynski et al. 2008b).

Single-mode DCEPs are known to pulsate in the F, 1O, and 2O modes. Since F, 1O, and 2O DCEP subclasses occupy different loci in the R₂₁ vs. Period diagram, the DCEPModeIdentification module assigns the pulsation mode to a DCEP using the R₂₁ parameter of the light curve Fourier decomposition. Specifically, considering the Fourier decomposition of the G-band light curve, and the R₂₁ vs. P diagram, a DCEP will be pulsating in the 1O mode if the following conditions are verified,

R₂₁<−0.13 × P(d) + 0.53 and

P< 2.34 d or R₂₁< 0.214 and

0.234 d <P< 7 d,

otherwise it is assigned the F mode. These limits were inferred from the PL relations of DCEPs based on OGLE-III data.

In Sect. 4 we discuss and illustrate graphically the regions we specifically defined in the φ₂₁ and R₂₁ vs. Period diagrams to separate Cepheids from RR Lyrae stars and to identify the Cepheid pulsation mode.

Similarly, ACEPs are known to pulsate in the F and 1O modes. The ACEPModeIdentification module assigns the pulsation mode to an ACEP by combining results from the classification in types based on the PL relations (CepTypeIdentification module) and the source period, as 1O ACEPs have periods in the range 0.35 <P ≤ 1.20 d, whereas F ACEPs have periods in the range 1.20 <P ≤ 2.5 d. These limits were inferred from PL relations of ACEPs based on OGLE-III data.

2.4.3. Cepheid classification

This module performs the final assignment of a source to the Cepheid class and its subclasses based on results of the previous SOS Cep&RRL modules. If the source is confirmed to be a Cepheid, thus validating the initial class assignment provided by the general Classification pipeline, the analysis proceeds with derivation of the stellar parameters⁶ and the final export of the source attributes (period, mean magnitude, peak-to-peak amplitude, Fourier parameters, secondary periodicity, classification in Cepheid types, pulsation mode, and any other relevant quantities) to the Main Data Base. Conversely, if the source is not confirmed to be a Cepheid, it will be sent for analysis through the RR Lyrae branch (green box in Fig. 3), unless it was already analysed in that branch and not found to be an RR Lyrae star, in which case, it will be definitely rejected as a Cepheid and/or RR Lyrae star and fed back to the general variable star analysis pipeline for processing through other SOS modules.

3. Application of the SOS-Cep&RRL pipeline to Gaia DR1 dataset

Results on Cepheids and RR Lyrae stars published in Gaia DR1 are based only on the application of the SOS Cep&RRL pipeline to Gaia G-band time series photometry calibrated to the Vega magnitude system as no G_BP/G_RP photometry is published in the Gaia DR1, and parallax and RV information are not yet available for these Cepheids and RR Lyrae stars which are fainter than the TGAS sample (Lindegren et al. 2016). This made it necessary to rearrange and specifically tailor the SOS Cep&RRL pipeline to cope with the limited information available for the analysis of the Cepheid and RR Lyrae star candidates.

Processing of Gaia photometry takes place in an iterative manner organised through cycles (Evans et al. 2016). As detailed in Eyer et al. (2016), two datasets with different photometric calibration, time extent, and source number were used exceptionally in order to be able to publish Cepheids and RR Lyrae stars in advance of schedule for the Gaia DR1. The first dataset included Cycle 0 (C0) photometry of millions of objects observed in the first three months after commissioning (from July 25, 2014), which were reduced by the general variable star processing to a sample of under 20 K potential candidate Cepheids and RR Lyrae stars. This selection of sources was further analysed with the Gaia DR1 calibration photometry of Cycle 1 (C1), which spanned almost 14 months of observations.

The global variable star analysis performed for the Gaia first data release is schematically summarised in Fig. 11, which shows both the initial processing on the C0 dataset and the final processing of the C1 photometry released in Gaia DR1. The SOS Cep&RRL actual processing is detailed in Fig. 12 and specifically discussed in Sect. 3.2.

3.1. Dataset, source selection, and initial processing

The dataset processed by the SOS Cep&RRL pipeline to produce results published in Gaia DR1 consists of G-band time series photometry⁷ of candidate Cepheids and RR Lyrae stars, observed by Gaia during 28-day ecliptic pole scanning law (EPSL) from the end of July to the end of August 2014, followed by over a year of nominal scanning law (NSL). We refer the reader to Sect. 5.2 in Gaia Collaboration (2016c) for a detailed description of Gaia’s scanning law. Source selection and steps of the preliminary analysis carried out on the C0 photometry (Evans et al. 2016) are summarised in the upper portion of Fig. 11. Sources were then reprocessed using the C1 photometry, producing the final results for Cepheids and RR Lyrae stars in the south ecliptic pole (SEP) footprint, which were published with the Gaia first data release. Only sources having 20 or more data points in the G-band time series were analysed as this was deemed to be the minimum number of epochs allowing a reliable estimate of the period and other (pulsation) characteristics of the confirmed variables. However, the actual number of epochs per source is <20 in some cases owing to the subsequent removal of outliers. As detailed in Eyer et al. (2016) and schematically summarised in Fig. 11, after applying the initial cut according to the number of epochs, the Statistical Parameters of the general variability pipeline computes the statistics of the time series data for all sources without any prior information on variability. Sources showing variability are then identified by the General Variability Detection module, characterised in terms of periodicity and modelling of the light variation by the Characterization workpackage, and are finally sent to the Supervised Classification module to determine the variability type. The SOS Cep&RRL pipeline received sources classified as candidate Cepheids and RR Lyrae stars by the three classifiers (Gaussian Mixtures − GMs; Bayesian Networks − BNs, and Random Forests − RFs) operated by the Supervised Classification module of the general variable star analysis pipeline (see Eyer et al. 2016, and references therein for details). A sample of 19 923 source were initially classified as candidate RR Lyrae stars and Cepheids by applying the BN, RF, and GM classifiers to the C0 photometry of Gaia SEP region. Their distribution on sky is shown in Figs. 13 and 14. This rather large number of candidates included all probability levels and the candidates flagged as class outliers in order to maintain a high level of completeness and not lose potentially valid candidates.

The characteristic geometric shape of the area covered by Gaia SEP observations is mainly due to the way the spacecraft scanned the sky during the first 28 days of science operation in EPSL when Gaia was set to repeatedly monitor the two ecliptic poles. Therefore, sources very close (~1 deg) to the ecliptic poles may have time series data with more than 200 observations, though quickly dropping off at distances further away. Gaia SEP footprint intercepts a peripheral portion of the LMC, offset by about 3 degrees to the north and 4 degrees to the east of the LMC centre, which contains several Cepheids and RR Lyrae stars (as well as other types of variable stars) with characteristics known from the studies by the OGLE (Soszynski et al. 2012, 2015a,b,c, 2016, and references therein) and EROS-2 (according to Kim et al. 2014) surveys. They are shown as grey (RR Lyrae stars) and red (Cepheids) filled circles in Figs. 13 and 14.

Candidate Cepheids and RR Lyrae stars in the Gaia SEP most likely belong to the LMC, hence, to a first approximation, they are all the same distance from us. Due to the lack of parallaxes/distances to support the variability analysis of these sources at this early stage of the Gaia mission, this occurrence, along with the high cadence of the EPSL observations, were important assets that helped the SOS Cep& RRL processing for the first Gaia data release, which specifically focused on the 19 923 Cepheids and RR Lyrae star candidates within the Gaia SEP marked in blue in Figs. 13 and 14.

The scanning law determines the cadence of Gaia multi-epoch observations and, in turn, has a bearing on the alias patterns we may expect to show up in the power spectrum of Gaia time series data. Particularly strong is the 6 h alias caused by the spacecraft rotation around its axis, which during EPSL was always kept in the ecliptic plane and fixed with respect to the Gaia-Sun axis (see Sect. 3 in Eyer et al. 2016). This is clearly seen in the two panels of Fig. 15, which show the period −G-band amplitude distribution of the 19 923 candidate RR Lyrae stars and Cepheids in the Gaia SEP. Sources are plotted using the period computed by the Characterization workpackage of the general variability pipeline for Cepheid and RR Lyrae star candidates and OGLE’s period for the known variables. The figure also shows that only very few of the known Cepheids and RR Lyrae stars in this region of the LMC have G-band amplitude smaller than 0.1 mag, hence suggesting that the vast majority of candidates with such small amplitudes are misclassifications, lending support to the choice of not considering them any further (see Sect. 3.2). Test runs of the SOS Cep&RRL pipeline along with visual inspection of a randomly selected sample of the 19 923 SEP Cepheid and RR Lyrae star candidates during this initial stage of the processing helped to provide a general overview of the dataset, improve the global analysis, and fine-tune the classifiers’ predictions. The visual inspection also confirmed five candidates that were later added to the final counts.

By excluding sources flagged as RR Lyrae star and Cepheid outliers in the predictions of the used classifiers the sample of automatically identified Cepheid and RR Lyrae star candidates reduces to 9347 sources. Then, by further rejecting sources with G-band amplitudes smaller than 0.1 mag (more than 3800) but including the above-mentioned candidates identified by visual inspection, the number of SEP Cepheid and RR Lyrae star candidates drops to 6714 sources, 6053 of which were recovered by cross-matching the C0 and C1 photometries. This forms the sample finally processed through the SOS Cep&RRL pipeline.

Statistical properties (time sampling, number of observations, time series duration, mean/median G magnitudes, magnitude uncertainties, etc.) of the G-band C0 time series photometry out of which the initial 19 923 enlarged sample of Cepheid and RR Lyrae star candidates analysed by the SOS Cep&RRL pipeline was extracted are described in great detail in Sect. 5.2 and Figs. 14−17 of Eyer et al. (2016). Instead, the characteristics of the G-band C1 time series photometry of the sample of 6053 sources finally processed through the SOS Cep&RRL pipeline and turned into the 3194 confirmed Cepheids and RR Lyrae stars released in Gaia DR1 are described in Sect. 6.2, Figs. 27, 28, 30, 31 and Table 3 of Eyer et al. (2016).

We briefly note here that the latter sample spans the G-band magnitude range 12 ≲ ⟨ G ⟩ ≲ 20.3 mag with typical errors on the order of a few millimag and ≳0.02 mag per individual data point at the bright and faint ends, respectively, G-band amplitudes in the range from ~0.1 and 1.5 mag, and between 15 and over 200 phase-point sampling of the light curves (see text and figures in Sect. 4 for details).

Integrated blue (G_BP) and red (G_RP) spectrophotometry from the blue and red photometers on board Gaia was not released in Gaia DR1. This additional limitation of the Gaia DR1 dataset means we could not build the Gaia CMD of the SEP Cepheid and RR Lyrae star candidates. However, we built a G-band vs. V−I CMD, shown in Fig. 16, using the OGLE-IV GSEP catalogue of LMC RR Lyrae stars (Soszynski et al. 2012) and the OGLE-IV catalogues of LMC Cepheids published by Soszynski et al. (2015b,c). The mean V magnitudes published by OGLE were transformed to the Gaia G-band using Eq. (A.1). This gave us some insight into the range in G magnitude spanned by RR Lyrae stars and Cepheids in the Gaia SEP (see Sect. 3.2).

The C1 time series photometry of the 6053 Cepheid and RR Lyrae star candidates, selected as described in Sect. 3.1, was fed into the SOS Cep&RRL pipeline. As a first step sources were cross-matched against catalogues of known RR Lyrae stars and Cepheids existing in the literature. We primarily used the OGLE-III (Soszynski et al. 2009) catalogue for RR Lyrae stars⁸ OGLE-IV catalogue (Soszynski et al. 2015a,b,c) for Cepheids and the EROS-2 catalogue of Kim et al. (2014). We also used RR Lyrae stars and Cepheids identified in the SEP region by the Catalina (Torrealba et al. 2015,) and ASAS (Pojmanski 1997) surveys and also checked the online version of the GVCS⁹ and the Simbad catalogue¹⁰.

3.2. Tailoring the SOS Cep&RRL pipeline for the analysis of the SEP data

Given the limitations of the first Gaia data, the SOS Cep&RRL pipeline had to be properly tailored to successfully process the Gaia DR1 data. This occurred through the following assumptions and simplifications which had a significant impact on the pipeline effectiveness and enhanced the need for visual inspections and manual intervention to check and adjust results (see Fig. 12):

• Lacking parallaxes (distances) for the stars in the sam-ple, we assumed that the SEP sources were all the samedistance from us, which is an acceptable first approxima-tion given that they are located primarily in the LMC, andwe adopted a cut in apparent magnitude to initially sep-arate Cepheids from RR Lyrae stars. Athreshold was set using the CMD in Fig. 16by which we assumed that candidates with⟨ G ⟩ > 18.5 mag are more likely RR Lyrae stars and after the general trunk (Fig. 1) they were sent to the RR Lyrae branch (Fig. 2) of the SOS Cep&RRL pipeline. Conversely, candidates with ⟨ G ⟩ < 18.5 mag were sent to the Cepheid branch (Fig. 3). However, since the SEP sample might also include Galactic RR Lyrae stars projected against the LMC, candidates brighter than 18.5 mag, with P< 1 d, and G-band amplitudes larger than 0.5 mag were analysed in both Cepheid and RR Lyrae branches as the two types overlap in this region of the parameter space. A fine-tuning of the Fourier parameters and definition of strict loci in the φ₂₁ vs. P and R₂₁ vs. P planes (see Sect. 4) were adopted to distinguish bright MW RR Lyrae stars from Cepheids.

• Lacking source colours, the classification of Cepheids in different types and pulsation modes could only rely on the PL relations, complemented by visual inspection of the Fourier planes. Furthermore, without colours, the contaminations by ECLs (both for Cepheids and RRc) and by δ Scuti (particularly at the faint end of the LMC RR Lyrae star distribution, ⟨ G ⟩ ≳ 20.0 mag) were issues that only a visual inspection of the light curves could resolve.

• The limited time span covered by the Gaia DR1 data, whose bulk spans roughly 28 d, made the measure of period most reliable only for Cepheids with periods shorter than about 10 d. In addition, the strong aliases affecting the SEP data required visual inspection of the light curves and manual intervention (period or type tagging of sources) to solve ambiguous cases.

When G_BP, G_RP colours, parallaxes, and an increasingly complete dataset becomes available in next Gaia releases, the need for visual inspection and manual intervention will definitely decrease.

For known Cepheids and RR Lyrae stars the periods measured by the SOS Cep&RRL pipeline (hereafter, P_SOS) were compared with the literature values. Agreement was deemed satisfactory if differences were within 0.01 d for the Cepheids and 0.001 d for RR Lyrae stars. When differences excede these limits, visual inspection of the light curve folded according to the two different periods helped to decide which periodicity to adopt¹¹. Figure 17 shows the comparison with the literature of the periods finally adopted for the known RR Lyrae stars and Cepheids released in Gaia DR1. The flattening of RR Lyrae stars/Cepheids around ΔP = 0.001/0.01 d occurs because we have assumed that P_SOS and the literature period are in agreement if they differ by less than 0.001 and 0.01 d for the RR Lyrae stars and Cepheids, respectively. A few sources above these limits in Fig. 17 are variables for which ΔP> 0.001/0.01 d and P_SOS produce a better folding of the light curve than the literature period. Visual inspection of all light curves during final assessment of the SOS Cep&RRL results confirms that the comparison procedure described above worked well for the present dataset which does not contain many long period Cepheids (above 10 d).

Type and mode classification of the known RR Lyrae stars and Cepheids assigned by the SOS Cep&RRL pipeline were also cross-checked against literature. A number of obvious type misclassifications were emended by manual adjustment.

After processing through the SOS Cep&RRL pipeline the light curves of all 6063 candidates were visually inspected for data quality assurance, validation of the modelled light curve and quantities thereby derived (period, peak-to-peak amplitude, mean magnitude, etc.), and final assessment of the Cepheids and RR Lyrae stars to be published in Gaia DR1.

The run of the SOS Cep&RRL pipeline on the 6053 candidates combined with visual inspection of the resulting light curves produced a final sample of 3602 confirmed Cepheids and RR Lyrae stars and the rejection of a total number of 2451 sources. There are various reasons for this high number of rejections, including candidates identified in C0 which are not present in C1 photometry and photometry issues in the time series data among which very large outliers and/or systematically noisy light curves. However, the most important reason for rejection was incomplete sampling of the light curves resulting in unreliable values for the source period, peak-to-peak amplitude, and mean magnitude. Finally, further rejections were also due to contamination of the sample by ECLs and other types of variables (δ Scuti, LPVs, etc.). We explicitly note that a large fraction of these rejections (over 50%) are in fact bona fide RR Lyrae stars and Cepheids for which unambiguous determinations of period and/or type classification could be obtained, or are RR Lyrae stars and Cepheids that did not pass the strict quality control criteria we have adopted to validate these first variability results from Gaia. During quality assessment, it was also decided not to release results for double- or multi-mode sources (239 in total between RR Lyrae stars and Cepheids) as they were not fully compliant with our internal validation criteria. These criteria are quite strict to ensure a high reliability of the information for variable sources released in Gaia DR1, notwithstanding the actual limitations of the available dataset. By rejecting double-mode RR Lyrae stars and multi-mode Cepheids the sample was reduced to 3363 sources. Finally, 169 additional sources were rejected during the final validation process which was meant to achieve consistency on the total number of sources released by different tasks of the DPAC processing contributing results for Gaia DR1. This further trimming lead to a final sample of 3194 Cepheids and RR Lyrae stars.

4. Results

Position, G-band time series photometry, and final results of the SOS Cep&RRL pipeline were published in Gaia DR1 for a total of 3194 sources. They comprise 599 Cepheids (of which 43 are new from Gaia) and 2595 RR Lyrae stars (of which 343 are new discoveries). The subdivision of the 3194 sources according to type, subtype, and pulsation mode is summarised in Table 2.

For these 3194 sources the following parameters, computed by the SOS Cep&RRL pipeline, have been released in Gaia DR1 along with the related errors:

− source pulsation period; − intensity-averaged mean G magnitude; − epoch of maximum light; −φ₂₁ and R₂₁ Fourier parameters; − peak-to-peak G-band amplitude [Amp(G)]; − RR Lyrae star subclassification into RRab and RRc types; − Cepheid classification into DCEP, ACEP, T2CEP types; − DCEPs and ACEPs pulsation mode (F, 1O); − T2CEPs subclassification into BLHER, WVIR, RVTAU types.

Gaia’s sourceids, coordinates, values of the above quantities and associated statistics, along with the G-band time series for each of the 3104 sources can be retrieved from the Gaia first data release archive¹² and other distribution nodes. The archives also provide tools for queries and to cross-match Gaia data with other catalogues available in the literature.

We provide in Table 3 specific links to the archive tables, and summarise the names of the parameters computed by SOS Cep&RRL that can be retrieved from the archive tables. In Appendix B we provide queries to retrieve the various quantities and parameters listed in Table 3.

The PA and PL distributions of the total sample of 3194 sources are shown in Figs. 18 and 19, whereas Figs. 21 and 22 show their distribution in the Fourier φ₂₁ vs. P and R₂₁ vs. P planes, respectively, according to the period determined by the SOS Cep&RRL pipeline (P_SOS). The MW RR Lyrae stars are clearly recognised in Fig. 19 for P< 1 d. This figure also shows the overlap between RR Lyrae stars, DCEPs, and ACEPs, occurring in the short period regime (P< 1d). Of the 3194 Cepheids and RR Lyrae stars published in Gaia DR1, 2808 are already known. Figure 20 shows the comparison with the literature. The comparison is done primarily with OGLE, for which there is the largest number of sources in common (2659 out of the 2808 known RR Lyrae stars and Cepheids). Other surveys among those listed at the end of Sect. 3.1 were considered in case an OGLE classification was not available. Since contrasting classifications were manually checked during the processing, the number of sources in Fig. 20 for which the SOS Cep&RRL classification differs from the literature is limited and reflects actual differences resulting from the analysis based on Gaia data.

Examples of light curves for RR Lyrae stars and Cepheids released in Gaia DR1 are presented in Figs. 23 and 24. Light curves are folded according to period and epoch of maximum light determined by the SOS Cep&RRL pipeline. The full atlas of light curves is available at http://davide2.bo.astro.it/~felix/. Samplers are shown in Appendices C and D, for Cepheids and RR Lyrae stars, respectively. New discoveries by Gaia are labelled.

Classical Cepheids with periods ranging from about 6 to 16 d show a secondary maximum (bump) in their light and RV curves, whose position varies with the pulsation period (see Bono et al. 2000 for details). This phenomenon is called the Hertzsprung progression (Hertzsprung 1926; Ledoux & Walraven 1958).

In the case of Galactic DCEPs the bump appears on the descending branch of the light and RV curves for P< 9 d, close to maximum light for 9 <P< 12 d, and along the rising branch for longer periods. The period at the centre of the Hertzsprung progression varies with metallicity moving to longer periods as metallicity decreases (Marconi et al. 2005; Soszynski et al. 2011a). Figure 25 shows the G-band light curves for a subset of DCEPs that exhibit the Hertzsprung progression. The centre of the progression for these DCEPs is close to 9 days, as it is for the MW DCEPs, thus possibly suggesting that their metallicity is higher than for the bulk of the LMC Cepheids.

Figures 26 and 27 show, respectively, the number of observations available for the 2595 SEP RR Lyrae stars and the 599 Cepheids in Gaia DR1. The distribution peaks between 40 and 70 with a maximum of around 50 transits for the RR Lyrae stars and between 60 and 80 with a maximum of around 70 transits for the Cepheids, which means that these SEP sources provide a reasonably realistic representation of the typical number of observations per source that will be available on average at the end of the five-year nominal lifetime of the Gaia mission, although with a totally different cadence. However, we note that for the specific case of regular, periodic objects with typical periods of RR Lyrae stars and Cepheids and over a large time interval (e.g. the five-year time span), the sparser NSL cadence being less prone to aliasing than the EPSL cadence, whose sampling is too regular, may turn into an advantage for period derivation.

Figures 28 and 29 show the period distributions of the RR Lyrae stars and Cepheids in Gaia DR1. In both figures the light blue shaded areas correspond to new discoveries by Gaia. New and known variables follow very similar distributions. The RR Lyrae stars show the typical bimodal distribution corresponding to RRc and RRab pulsators. The period distribution of the RRab stars peaks at P ~ 0.59 d and confirms a predominantly Oosterhoff-intermediate nature of the LMC RR Lyrae stars (Oosterhoff 1939; Catelan 2009, and references therein). However, a minor component of Oosterhoff type II RRab stars is also present, which defines a second less populated sequence in the PA diagram shown in Fig. 30.

Figure 31 shows the PL distribution of the 2595 SEP RR Lyrae stars. The LMC RR Lyrae stars in the Gaia SEP typically appear to have ⟨ G ⟩ ~ 19.0 mag with a dispersion of about ±0.5 mag. This rather large dispersion is due to the combination of PL intrinsic width, reddening, metallicity effects, LMC geometric depth, and also to the extended throughput of Gaia G-band (330−1050 nm), which means that the RR Lyrae star PL relation has a significant span in the G-band (Gaia Collaboration 2016b). On the other hand, the over six magnitudes scatter seen in Fig. 31 for G ~ 18 mag is largely due to Galactic RR Lyrae stars that fall within the Gaia SEP footprint and contaminate the LMC sample.

Figure 32 shows the spatial distribution of the 2595 RR Lyrae stars in Gaia DR1 overlaid on the sample of LMC RR Lyrae stars recently released by OGLE-IV (Soszynski et al. 2016, orange filled circles). Marked in green are the RR Lyrae stars observed by Gaia that are in common with other surveys listed at the end of Sect. 3.1. About 700 of them were new discoveries by Gaia that were in the meantime also identified by OGLE (Soszynski et al. 2016). Red filled circles are 343 new RR Lyrae stars discovered by Gaia; they mainly belong to the LMC and allow a first glance at the very extended halo of this galaxy. Also particularly interesting is the distribution in average magnitude of the 2595 RR Lyrae stars in the Gaia SEP. This is shown in Fig. 33, where we have sliced the sample into three magnitude bins. The top panel shows 73 RR Lyrae stars with ⟨ G ⟩ < 18.5 mag, sixty-three of them have ⟨ G ⟩ < 17.5 mag and 24 in this brighter sample are new discoveries by Gaia. All RR Lyrae stars in this panel likely belong to the MW halo in front of the LMC. The central panel shows 2375 RR Lyrae stars with 18.5 < ⟨ G ⟩ < 19.5 mag. The average apparent magnitude of this sample is ⟨ G ⟩ = 19.13 mag, with σ = 0.16 mag; this value is typical of the LMC RR Lyrae stars. They are quite homogeneously distributed and trace the LMC halo (see Fig. 32). The bottom panel shows 147 RR Lyrae stars with ⟨ G ⟩ > 19.5 mag; they follow the clumped distribution of the LMC Cepheids in this area (see Fig. 35) and are fainter than the average of LMC RR Lyrae stars likely because they are more affected by reddening, which is expected to be higher in the dusty regions populated by Cepheids. This figure very nicely showcases the potential of Gaia and variable stars for studying galactic structure.

Finally, Figs. 34 and 35 show, respectively, the PL relation and the distribution on the sky of the 599 Cepheids in Gaia DR1. The various types of Cepheids in the sample clearly define different PL relations. They will be used to identify and classify different types of Cepheids in future Gaia data releases (see Sect. 5). Red filled circles in Fig. 35 mark 43 new Cepheids discovered by Gaia. This sample comprises 25 DCEPs, 10 ACEPs, and 8 T2CEPs which are located outside the OGLE-IV footprint and at increasing distance from the LMC. According to the position on the PL relation shown in Fig. 34 they belong to the LMC. However, it is premature to draw any conclusions on the LMC structure from this fairly small sample of new Cepheids, which might also be contaminated at the 3% level by ECLs (see Moretti et al. 2014), and by other types of variables (e.g. ellipsoidals or spotted stars) that populate the same period, period-luminosity, period-amplitude, and Fourier parameter domain. Whether some of these misclassifications may have actually occurred cannot be judged from the Gaia DR1 data alone. This will become possible and checks will certainly be done, if and where appropriate, now that we have started the re-processing of all sources in preparation of Gaia DR2. For Gaia second data release our analysis will also be easier because other parts of the CU7 pipeline will be activated, those specifically devoted to binaries of different types (among which also ellipsoidals) and to spotted stars in particular. Furthermore, for Gaia DR2 we will also have G_BP, G_RP time series available to help us disentangle Cepheids and RR Lyrae stars from other types of variables. We leave any further discussion of this sample for Gaia DR2 when the analysis of Cepheid and RR Lyrae candidates extends beyond the SEP footprint and G_BP,G_RP photometry is used to help with the Cepheid classification.

5. Conclusions and future developments

We have presented an overview of the Specific Objects Study (SOS) pipeline SOS Cep&RRL, developed in the context of Coordination Unit 7 (CU7) of the Gaia Data Processing and Analysis Consortium (DPAC) to validate and fully characterise Cepheids and RR Lyrae variables observed by the spacecraft. The SOS Cep&RRL pipeline was specifically tailored to analyse the Gaia G-band time series photometry of sources in the SEP footprint, which covers an external region of the LMC, and to produce results for confirmed RR Lyrae stars and Cepheids to be released with Gaia Data Release 1 (Gaia DR1).

The results presented in this paper were obtained by applying the whole variable star analysis pipeline on the time series photometry collected by Gaia during 28 days of ecliptic pole scanning law (EPSL) and 13 months of nominal scanning law (NSL). In addition to positions and G-band time series photometry, for confirmed Cepheids and RR Lyrae stars in the Gaia SEP, Gaia DR1 contains the following outputs of the SOS Cep&RRL pipeline: period of pulsation, classification in type and pulsation mode, intensity-averaged mean magnitude, peak-to-peak amplitude, and Fourier decomposition parameters R₂₁ and φ₂₁. All quantities are provided with related uncertainties. The variable star inventory of Gaia DR1 includes 3194 variables which comprise 599 Cepheids and 2595 RR Lyrae stars, 386 of them (43 Cepheids and 343 RR Lyrae stars) are new discoveries by Gaia.

The published sources are distributed over an area extending 38 degrees on either side of 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 sample also includes 63 bright RR Lyrae stars that belong to the MW halo, of which 24 are new Gaia discoveries.

A number of improvements of the SOS Cep&RRL pipeline are planned in view of Gaia forthcoming releases. They include the following:

• 1.

  Passband transformations will be checked. In preparation for Gaia DR2, all tools and relations used by SOS Cep&RRL to classify and characterise the Gaia sources will be re-derived directly from Cepheids and RR Lyrae stars released in DR1, overcoming the need for transforming quantities that are generally known in the Johnson-Cousins system to Gaia passbands. This will definitely allow the PL relationships adopted to identify and classify different types of Cepheids to be refined. On the other hand, as shown by Fig. A.2, the G-band transformation (Eq. (A.1)) worked rather well for the colour range spanned by the Cepheids and RR Lyrae stars in Gaia DR1.

• 2.

  Gaia G_BP, G_RP colours will become available with Gaia DR2. This will allow PW relations to be used; the reduced scatter, compared to the PL relations, will allow further improvement of the classification of Cepheids.

• 3.

  Double-mode RR Lyrae stars and multi-mode classical Cepheids (F/1O, 1O/2O, etc.) will be identified and fully characterised for Gaia DR2 by improving the detection algorithm to properly take into account the scatter in the folded light curve, thus reducing the number of false positives.

• 4.

  Estimate of the error in period, mean magnitude, peak-to-peak amplitude, etc., will be refined. In particular, errors in the Fourier parameters φ_ij and R_ij, which are currently computed by propagation of the errors in φ_i, φ_j, R_i, and R_j, will be entirely computed via Monte Carlo simulations.

• 5.

  A classifier will be developed to optimise the type and subtype classification of Cepheids and RR Lyrae stars performed by the SOS Cep&RRL pipeline.

The results for Cepheids and RR Lyrae stars shown in this paper demonstrate the excellent quality of Gaia photometry despite all the limitations in the dataset and processing for Gaia Data Release 1. They nicely showcase the potential of Gaia and the promise of Gaia Cepheids and RR Lyrae stars for all areas of the sky in which an appropriate light curve sampling will be achieved.

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Acknowledgments

This work has made use of data from the ESA space mission Gaia, processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC has been provided by national institutions participating in the Gaia Multilateral Agreement. In particular, the Italian participation in DPAC has been supported by Istituto Nazionale di Astrofisica (INAF) and the Agenzia Spaziale Italiana (ASI) through grants I/037/08/0, I/058/10/0, 2014-025-R.0, and 2014-025-R.1.2015 to INAF (PI M. G. Lattanzi), the Belgian participation by the BELgian federal Science Policy (BELSPO) through PRODEX grants, the Swiss participation by the Swiss State Secretariat for Education, Research and Innovation through the ESA Prodex program, the “Mesures d’accompagnement”, the “Activités Nationales Complémentaires”, the Swiss National Science Foundation, and the Early Postdoc. Mobility fellowship, and the Spanish participation by the Spanish Ministry of Economy MINECO-FEDER through grants AyA2014-55216, AyA2011-24052. UK community participation in this work has been supported by funding from the UK Space Agency, and from the UK Science and Technology Research Council. The Gaia mission website is: http://www.cosmos.esa.int/gaia.

References

Appendix A: Conversion formula

In this section we present the conversion formula, appropriate for the colour and metallicity ranges of Cepheids and RR Lyrae stars (V−I< 2.5 mag and −2.5 < [Fe/H] <0.5 dex), that we have used to transform the Johnson-Cousins V, I to the Gaia G passband. This formula was computed using passband transformations provided in Jordi et al. (2010) and subsequent updates (Jordi, priv. comm.): (A.1)The relation is shown by the red solid line in Fig. A.1.

It should be noted that the above conversion formula between the Gaia G and Johnson-Cousins V, I passbands is based on the pre-launch nominal Gaia G passband, hence it might not be perfect. Nevertheless, Fig. A.2 shows this transformation to have worked rather well for Cepheids and RR Lyrae stars that are published in Gaia DR1. In the figure we have plotted the ⟨ G ⟩ mean magnitude computed by the SOS Cep&RRL pipeline for 2659 sources (510 Cepheids and 2149 RR Lyrae stars) in common with OGLE-IV vs. the source V−I colours from OGLE. The differences are, on average, within ±0.1 mag.

New transformations have now been computed using Gaia real data (van Leeuwen et al. 2016). The reader is advised to use the new formulae to make passband transformations. As far as future Gaia releases are concerned, Cepheids and RR Lyrae stars published in Gaia DR1 will be used to compute directly in the Gaia G-band the PA and PL relations used in the SOS Cep&RRL pipeline to classify these types of variable stars.

Appendix B: Examples of Gaia archive queries

Appendix C: Atlas of the G-band light curves for Cepheids

In this appendix we present the G-band light curves of 599 Cepheids observed by Gaia in the SEP region. The light curves are folded according to the period and epoch of maximum light computed by the SOS Cep&RRL pipeline and are plotted grouping the Cepheids by type and pulsation mode according to the following order: DCEPs 1O (230 in total), DECPs F (313), DCEPs NoMode (15 DCEPs for which we did not identify the pulsation mode); ACEPs 1O (7 sources), ACEPs F (6), ACEPs NoMode (3); T2CEPs BLHER (11 sources), T2CEPs WVIR (10), T2CEPs RVTAU (2), and T2CEPs NoMode (2). In each group the sources are displayed in order of increasing period.

Appendix D: Atlas of the G-band light curves for RR Lyrae stars

In this appendix we present the G-band light curves of 2595 RR Lyrae stars observed by Gaia in the SEP region. The light curves are folded according to the period and epoch of maximum light computed by the SOS Cep&RRL pipeline and are plotted grouping the RR Lyrae stars according to the pulsation mode: the 685 RRc stars are first, followed by the 1910 RRab stars. In each group the sources are displayed in order of increasing period.

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