Single-lined Spectroscopic Binary Star Candidates from a Combination of the Rave and Gaia DR2 surveys

Single-lined Spectroscopic Binary Star Candidates from a Combination of the Rave and Gaia DR2 surveys

[    [    [    [    [    [    [    [    [    Julio Navarro    Warren Reid    [    [    [
June 28, 2019TBD
June 28, 2019TBD
Abstract

The combination of the final version of the Rave spectroscopic survey data release 6 with radial velocities and astrometry from Gaia DR2 allows us to identify and create a catalog of single lined binary star candidates (SB1), their inferred orbital parameters, and to inspect possible double lined binary stars (SB2).

A probability function for the detection of radial velocity (RV) variations is used for identifying SB1 candidates. The estimation of orbital parameters for main sequence dwarfs is performed by matching the measured RVs with theoretical velocity curves sampling the orbital parameter space. The method is verified by studying a mock sample from the SB 9 catalogue. Studying the boxiness and asymmetry of the spectral lines allows us to identify possible SB2 candidates, while matching their spectra to a synthetic library indicates probable properties of their components.

From the RAVE catalog we select 37,664 stars with multiple RV measurements and identify 3838 stars as SB1 candidates. Joining Rave and Gaia DR2 yields 450,646 stars with RVs measured by both surveys and 27,716 of them turn out to be SB1 candidates, which is an increase by an order of magnitude over previous studies. For main sequence dwarf candidates we calculate their most probable orbital parameters: orbital periods are not longer than a few years and primary components have masses similar to the Solar mass. All our results are available via Vizier/CDS.

binaries: spectroscopic —€ surveys —€ methods: data analysis
Corresponding author: Danijela Birkodanijela.birko@gmail.com

0000-0002-5571-5981]Danijela Birko \move@AU\move@AF\@affiliationUniversity of Ljubljana, Faculty of Mathematics and Physics, Ljubljana, Slovenia

0000-0002-2325-8763]Tomaž Zwitter \move@AU\move@AF\@affiliationUniversity of Ljubljana, Faculty of Mathematics and Physics, Ljubljana, Slovenia

0000-0002-1891-3794]Eva K. Grebel \move@AU\move@AF\@affiliationAstronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr. 12–14, 69120 Heidelberg, Germany

0000-0001-6516-7459]Quentin A Parker \move@AU\move@AF\@affiliationCYM Physics Building, The University of Hong Kong, Pokfulam, Hong Kong, SAR, PRC \move@AU\move@AF\@affiliationThe Laboratory for Space Research, Hong Kong University, Cyberport 4, Hong, Kong, SAR, PRC

0000-0002-9035-3920]Georges Kordopatis \move@AU\move@AF\@affiliationUniversité Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, France

0000-0001-7516-4016]Joss Bland-Hawthorn \move@AU\move@AF\@affiliationInstitute of Astronomy, School of Physics, University of Sydney, Australia

0000-0001-6280-1207]Kenneth Freeman \move@AU\move@AF\@affiliationRSAA Australian National University, Camberra, Australia

0000-0002-1317-2798]Guillaume Guiglion \move@AU\move@AF\@affiliationLeibniz-Institut für Astrophysik Potsdam (AIP), An den Sternwarte 16, D-14482 Potsdam, Germany

0000-0003-4446-3130]Brad K. Gibson \move@AU\move@AF\@affiliationJeremiah Horrocks Institute for Astrophysics & Super-computing, University of Central Lancashire, Preston, UK

\move@AU\move@AF\@affiliation

CIfAR Fellow, University of Victoria Physics and Astronomy, Victoria, BC V8P 5C2, Canada

\move@AU\move@AF\@affiliation

Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia \move@AU\move@AF\@affiliationWestern Sydney University, Locked bag 1797, Penrith South, NSW 2751, Australia

0000-0003-4072-9536]G. M. Seabroke \move@AU\move@AF\@affiliationMullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, RH5 6NT, UK

0000-0001-6516-7459]Matthias Steinmetz \move@AU\move@AF\@affiliationLeibniz-Institut für Astrophysik Potsdam (AIP), An den Sternwarte 16, D-14482 Potsdam, Germany

0000-0002-3590-3547]Fred Watson \move@AU\move@AF\@affiliationAnglo-Australian Observatory, Sydney, Australia

1 Introduction

The majority of stars are members of multiple systems of two or more gravitationally bound stars. In the vast majority of cases these stars are coeval and have an identical chemical composition, and in favorable cases their masses and/or sizes can be determined directly. Yet, in the majority of systems with orbital periods of weeks to years it is a challenge even to identify their multiple nature. Detection of variability of radial velocities (RVs) is a very successful, though relatively time-consuming method, which has been extensively used in studies of dwarfs and sub-dwarfs (Duquennoy & Mayor, 1991; Fischer & Marcy, 1992), massive binary systems (e.g. Sana et al., 2009) and binary stars in clusters (Abt & Willmarth, 1999; Sommariva et al., 2009). There have been several surveys dedicated to the search of spectroscopic binaries (e.g. Latham et al., 2002; Griffin, 2006; Mermilliod et al., 2007). The Geneva-Copenhagen Survey (Nordström et al., 2004) marked a milestone in the size of the sample, as it presented RV measurements of 14,139 F- and G-type dwarfs drawn from a kinematically unbiased magnitude-limited sample, painstakingly observing one star at a time. A landmark result of this effort was the realization that spectroscopic binarity can be detected in 19% of the observed targets, while the fraction of binary stars of all types reached 34%, in agreement with an earlier result of Duquennoy & Mayor (1991).

The last decade has been marked by much larger ground-based spectroscopic surveys, which use wide field coverage and fibre optics to obtain spectra of a hundred or more stars at a time. The result are not only RVs but also spectroscopically determined values of stellar parameters, including chemistry. On the other hand, the scientific focus is shifting from stellar kinematics to Galactic archaeology, so the goal is to observe as many stars as possible. This means that most targets are observed only during a single night, with the majority of repeated observations consisting of two visits per target scheduled days to years apart. So any statement on binarity from these spectroscopic surveys is based on a large number of targets with a small number of visits. These properties are typical for the Rave (Radial Velocity Experiment) survey (Steinmetz et al., 2006), but also for Gaia-ESO (Gilmore et al., 2012), Apogee (Apache Point Observatory Galactic Evolution Experiment) (Holtzman et al., 2015), Lamost (The Large Sky Area Multi-Object Fibre Spectroscopic Telescope) (Liu et al., 2017), and Galah (The GALactic Archaeology with HERMES) (De Silva et al., 2015) surveys.

Here we focus on spectroscopic binaries that can be identified in the Rave survey. Double lined binaries (SB2) where we identify both sets of spectral lines are quite rare (Matijevič et al., 2012), as they imply a very similar mass of both components. Another major reason why SB2 are rare is that the geometry needs to be rather favourable for us to see the line split. So our primary goal is to identify single-lined binaries (SB1), binaries where only spectral lines of primary component can be detected, which are much more common. We base our approach on an earlier study (Matijevič et al., 2011), but with two important upgrades: (i) our analysis is based on the final and complete set of Rave spectra (Steinmetz et al., 2019) which approximately doubles the considered sample, (ii) RVs derived by Rave are matched to those of ESA’s Gaia space mission (Gaia Collaboration et al., 2018a) which increases the sample with multiple measurements by an order of magnitude. A Monte-Carlo approach is used to infer physical properties of the identified SB1 binaries. Their spectra are also searched for the presence of light from a secondary component.

We start with a sample based on Rave observations only. In Sec. 2 we present the data and in Sec. 3 we summarize the method to select SB1 candidates. Next, we present basic properties of the SB1 sample, statistical inference of values of fundamental parameters, and results of the search for absorption lines from a secondary component. In Section 7 we repeat the whole process, now including also RV observations from the Gaia satellite which are, however, different enough from Rave observations to keep their analysis separate from the one using Rave observations only. Finally we add some discussion of the results and an outline for the future.

2 Rave observations and sample selection

The RAdial Velocity Experiment (Steinmetz et al., 2006; Zwitter et al., 2008; Siebert et al., 2011; Kordopatis et al., 2013; Kunder et al., 2017; Steinmetz et al., 2019) is a medium resolution (R 7500) spectroscopic survey of the Milky Way. It used the UK Schmidt telescope at the Australian Astronomical Observatory to obtain over half a million stellar spectra over the period of 12 April 2003 to 4 April 2013. These cover wavelength range of 8410 – 8795 Å. The survey properties as well as all its data products and analysis are described in detail in its final data release paper (Steinmetz et al., 2019). Here we provide just a brief summary as a service to the reader.

Rave is the first systematic (wide field coverage) spectroscopic Galactic archaeology survey. While the survey was ongoing its goals were gradually surpassing its original name by supplementing determination of radial velocity with estimates of effective temperature, surface gravity, and chemical properties, including abundances of aluminum, iron, magnesium, silicon, titanium and nickel in the stellar photospheres (these abundances are quoted in order of increasing uncertainties, which generally range from 0.14 to 0.23 dex). An inclusive approach has been used, where information obtained from observed spectra was supplemented with complementary photometric and astrometric information, as it became available.

The final Rave data release contains 518,392 spectra of 451,788 stars, which present a magnitude limited sample with 9  I  12. The typical signal-to-noise ratio (S/N) of the measured spectra is  40 per pixel. The Rave wavelength range matches that of the Gaia mission. This wavelength range includes a lot of spectral lines; most importantly the singly ionized calcium triplet ( = 8498, 8542, 8662 Å), the Paschen series of hydrogen, and Fe I multiplets. In the measured part of the spectrum, contributions from telluric lines can be neglected and the only significant spectral signature of the interstellar medium is the diffuse interstellar band at 8620 Å (Munari et al., 2008; Kos et al., 2014).

The selection of the Rave targets was very close to a random magnitude-limited sample of southern stars, but avoiding fields closer than degrees from the Galactic plane and those in the direction of the Galactic bulge. Details of the selection function are discussed in Wojno et al. (2017). A random selection implies that some of the stars belong to rare spectral types or brief evolutionary stages. Local linear embedding was shown to be an efficient morphological classification technique to pinpoint such peculiar cases and has been applied to Rave (Matijevič et al., 2012). While morphological classification proved efficient in detecting SB2 objects and chromospherically active stars it is clear that it cannot identify SB1 stars which are hidden among the vast majority of 90-95% of stars with morphologically normal spectra.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefHistogram of the number of observations for stars observed more than once.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefCumulative plot of a time-span between the first and the last observations of the same object within the Rave survey (left line) and for a combination of Rave data with RV measurements of Gaia (right line). In the latter case the assumed epoch for the Gaia observation is 15 June 2015.

The derivation of RVs is the main result of interest to us here. Velocities are derived as described in Siebert et al. (2011). A two stage process is used. First a rough estimate of RV, with a typical precision better than 5 km s, is obtained using a subset of 10 template synthetic spectra covering a wide range of stellar parameters. Next, a best-matching template is constructed using the full template database with a penalized chi-square technique described in Zwitter et al. (2008). This template then allows us the determination of the final, more precise RV, which is corrected for possible zero-point shifts (due to thermal instabilities of the instrument) and reported in the inertial frame of the Solar barycenter. As discussed in Steinmetz et al. (2019), typical error of the derived RV in the Rave survey is  km s.

SB1s can be identified from multiple RV measurements of good quality, so we used the following selection criteria:

  1. to safeguard against systematic problems with measurements of noisy spectra we used only those with a SNR_avg_SPARV in Rave DR6;

  2. only stars that have all their spectra classified as normal (flag1 with the value ’n’) were used in Rave DR6;

  3. only stars with at least two RV determinations were considered;

The first criterion is fulfilled for 414,637 (91.8 %) stars and the second further narrows selection to 395,919 (87.4 %) stars in RAVE DR6. The third criterion is more selective, though unavoidable in a search of SB1 candidates. In total 47,360 stars (9.1 %) have multiple observations. When applying the other two criteria we end up with a sample of 37,661 stars with repeated observations. Some of the targets have been observed up to 13 times (Figure 2). Most of the stars with at least 6 visits are located at Galactic latitude and are part of a logarithmic cadence with observations separated by approximately 1, 4, 10, 40, 100, and 1000 days. But a vast majority of stars have only two spectra, form a random sub-sample of the RAVE survey and are of primary interest to us here. Some of the repeats were made only days apart but about half have a time-span longer than 2 years (Figure 2).

3 The Method

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Table 0. \Hy@raisedlink\hyper@@anchor\@currentHrefNumber and fraction of SB1 candidates for different values of . is the number of objects with observations per object. Fraction of SB1 is higher for higher number of observations. Longer time span between re-observations of objects with higher results in a higher percentage of SB1s.

% % % 2 31059 2384 7.7 1694 5.5 1183 3.8 3 2744 394 14.4 273 10.0 166 6.0 4 943 182 19.3 107 11.3 61 6.5 5 1269 276 21.7 166 13.1 102 8.0 6 1015 326 32.1 210 20.7 106 10.4 7 345 120 34.8 76 22.0 43 12.5 8 131 60 45.8 39 30.0 24 18.3 9 53 23 43.4 16 30.2 8 15.1 10 60 33 55.0 28 46.7 16 26.7 11 35 19 54.3 16 45.7 8 22.9 12 7 3 42.9 2 28.6 0 0.0 2 37661 3838 10.2 2627 7.0 1717 4.6

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The identification of SB1 candidates is based on the detection of their RV variability. So we need a quantitative criterion for considering changes in RV as significant. Following the method and reasoning from Matijevič et al. (2011), one can write the probability that is larger than as

(1)

where RV and RV are radial velocities and and errors measured for the same star at the two different observations. The squares of the RV errors can be treated as variances of the Gaussian distribution with the RV as the mean value. If we would pick two samples from each of these distributions, (21) represents the probability that the pick from the second sample is greater than the pick from the first one. If the RVs are the same, the numerator of the error function will be zero and the probability will equal 1/2. For a pair of very different RVs and comparably small errors, the error function approaches 1, and consequently the complete probability goes to 1. For stars with a significant RV variability the value of should be close to 1, so we introduce a new function that includes a logarithm of

(2)

For objects with very significant variability the argument of the logarithm can be very small and cause floating point errors, so we limit the value of to 14. Pourbaix et al. (2005) use = 2.87 as a lower limit indicating a significant RV variability, assuming equal RV errors. Such a limit on corresponds to RV values that are apart. Similarly, corresponds to RV values less than apart, so the variability is questionable. And implies RV differences smaller than , so an insignificant RV variability.

Detection of RV variability is not a sufficient criterion to identify a SB1 object. We want to check if RV variability is not caused by surface activity and if the object shows photometric variability that is unlikely considering long orbital periods of a majority of SB1 stars. Although we required that spectra of SB1 candidates are morphologically classified as those of normal single stars we made additional cross-checks. In particular, Žerjal et al. (2013) made a catalog of chromospherically active stars, and photometric variability can be identified using the Rave DR5 Gaia DR2 photometic variability flag (plot_variable_flag). These checks do not change our results significantly. Among the 3838 candidates discussed in the next section only 3 are known to be chromospherically active and 17 have a flag for photometric variability, most of them are red giants. Also, we checked RV variability as a function of time span. Close or semi-detached binaries that fill their Roche lobe, with periods usually shorter than one day, have large RV variability. Among SB1 candidates the majority of objects have low RV variability, and 23 objects have RV variability greater than 140 km/s for different time spans, from one day up to a few years.

4 SB1 candidates in the Rave -only sample

SB1s were searched for in Rave using the method described above. This is similar to Matijevič et al. (2011) but we applied it to a larger sample. Instead of considering only data obtained up to the third data release we use the sixth and final Rave data release. This increases the number of SB1 candidates from 1333 to 3838 and keeps their percentage at 10 of the stars with repeated observations. We note that the fraction of SB1 candidates reaches  % for objects with a large number of observations (Table 3). In Table 4 we report the basic properties of our 3838 SB1 candidates. Their individual RV measurements are published by Steinmetz et al. (2019).

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Table 0. \Hy@raisedlink\hyper@@anchor\@currentHrefRepresentative extract from full list of SB1 candidates, reporting the number of observations (), their time-span in days, and the epoch of the first and the last observation by Rave. The whole list of 3838 objects is published electronically.

Object Time-span Epoch(first) Epoch(last) J000107.9-412208 4.38 2 1862 2005-08-06 2010-09-11 J000349.3-405352 4.10 3 1564 2003-08-09 2007-11-20 J114037.8-260605 3.05 6 123 2009-01-27 2009-05-30 J114110.6-320837 6.47 7 1167 2006-03-18 2009-05-28 J114155.8-235143 7.00 4 100 2009-02-19 2009-05-30

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefLeft panel: Kiel diagram of SB1 candidates, color coded according to values. The dashed line separates main sequence dwarfs from giant stars. The Padova isochrones plotted as solid lines have solar metallicity and ages of 1 - 4 Gyr with steps of 1 Gyr. Right panel: Histograms of effective temperature (MADERA pipeline), metallicity (MADERA pipeline), magnitude, and signal to noise ratio show distributions that are generally different for the complete Rave sample (black), for objects with multiple observations (green), and for SB1 candidates (red).

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefCumulative histogram of maximum radial velocity changes between measurements for red giant (RG), red clump (RC) and main sequence (MS) SB1 candidates. This diagram shows that RV variability is the largest for MS stars and the lowest for RG stars. MS stars have statistically lower masses, smaller orbits, and consequently larger RV variability in comparison to RG and RC stars.

Next we study the physical properties of the primary stars in SB1 candidate systems. Figure 4 shows two peaks in the distribution of the effective temperature, one at 4500 K for the red clump and giant stars with masses larger than 1.5 M and another at 6000 K for the main-sequence dwarfs with masses 1 - 1.2 M. SB1 candidates have a slightly lower metallicity than general population, maybe due to a contribution from the secondary star spectrum. The S/N of the re-observed stars and SB1s is higher than in the general population because brighter stars are re-observed more frequently than the faint ones in Rave (so observation time was used more efficiently). The same properties can be seen also in an apparent magnitude histogram. Objects with repeated observations and SB1 candidates have lower magnitudes than the general Rave sample. As shown in Figure 2, the time-span between the first and the last observation of a given object is around 10 years, so systems with significantly larger orbital periods cannot be detected. This is demonstrated also by Figure 4, which shows that the most probable maximum RV differences are  km s, which at our limit of corresponds to a pair measurements with uncertainties  km s, a typical value for Rave . A slight dependence of the position of the most probable RV differences on stellar type is therefore driven by the fact that giants tend to have their RVs measured with a greater precision, as their spectral lines are numerous and sharper. The maximal RV differences can reach 60 or even 100 km s, which should correspond to rather close systems with short orbital periods.

5 Orbital parameters for main sequence dwarfs

The radial velocity of a binary star is given by the following equation:

(3)

where i is the orbital inclination, e the eccentricity, P the orbital period, the true anomaly, the longitude of periastron, the radial velocity of the center of mass, and a the semi-major axis. The latter relates to the mass of the primary star (M) and the mass ratio q = M/M as

(4)

All 6 parameters cannot be determined from the small number of re-observations of a given object obtained by Rave. But for objects with at least 4 RV determinations well distributed over time one can attempt a probabilistic approach, with the goal of obtaining approximate estimates for their orbital periods. To do so one should adopt a grid of parameter values that are to be tested. These are given in (Table 5). We limit our analysis to primary stars on the main sequence, so that we could infer their mass from their spectroscopically determined effective temperature.

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Table 0. \Hy@raisedlink\hyper@@anchor\@currentHrefRanges of parameters for main sequence dwarfs.

Parameter Range Step or Values Angle of inclination (i) 10 … 90 deg random selection of its sin i value Eccentricity (e) 0.0 … 0.8 0.05 Orbital period (P) 1 … 3600 days 220 logarithmic steps Longitude of the periastron () 0 … 360 random selection Mass ratio (q) 0.1 … 0.85 0.05

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Table 0. \Hy@raisedlink\hyper@@anchor\@currentHrefRepresentative sample extracted from the full list showing the most probable values of parameters: mass of the primary star (M), mass ratio (q), orbital period (P) in days, system velocity () in kms, and eccentricity (e). See text for a discussion of typical errors. The whole table is published in electronic form only.

Object MM q P e J143128.8-292205 1.17 0.4 181 3 0.6 J101329.8-200252 0.98 0.5 515 3 0.35 J101211.5-200052 1.05 0.25 317 50 0.65 J162232.0-063353 1.27 0.2 139 -9 0.5 J100305.0-111032 1.05 0.3 174 -3 0.6 J143206.2-302751 0.97 0.3 903 28 0.55 J093202.1-083428 1.05 0.25 535 31 0.38

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefExamples of radial velocity curves for a few binary systems. Black dots are RVs measured by Rave and the curve is calculated with orbital parameters obtained with our method. The objects are J154304.9-122933 (a), J115256.0-161543 (b), J142501.1-290222 (c), and J021532.1-363260 (d).

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefLeft panel: Cumulative diagram of estimated orbital periods. Most of the SB1 systems have periods shorter than 2 years. Right panel: Cumulative period dispersion distributions for different trends in radial velocity changes.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefComparison of true period values for objects in the 9th Catalogue of Spectroscopic Binaries and for periods calculated with the method described in Section 5. The grey area represents offsets from unity of 40 of the period value. The left panel is color coded by the number of observations and the right panel by the primary star’s temperature. It seems that neither temperature nor the number of observations have a significant impact on our results.

All combinations of these parameters do not occur in nature. Following Duquennoy & Mayor (1991) and Raghavan et al. (2010) we adopt the following constraints:

  1. main sequence systems with  days are assumed to have circular orbits due to tidal interaction in close binaries;

  2. systems with a period  days have a flat distribution in eccentricity that varies from 0.0 to , independent of period;

  3. short-period systems ( days) have .

There are 406 SB1 candidates with primaries that are main sequence dwarfs and that have at least 4 RVs measured by Rave . This makes them suitable objects to attempt an approximate determination of their orbital periods. To do so, we first split them into 4 groups according to the sign of their RV changes: in the first group are objects where the RV derivative is either positive or negative throughout (n = 0), and in the other three groups are objects with one, two, or more changes in the sign of their RV derivative (n = 1, 2, ). The first two groups are well populated while there are only a handful of objects in the last two groups. These groups can be used to roughly infer what are likely values of . For the first two groups (n = 0, 1) we assumed that cannot be longer than 8 times the time-span between the first and the last observation, for the third group (n = 2) we lower the maximum period to 3 times the time-span and for the last group (n ) to within the time-span. Next we use these limits on to compare observed RVs to the calculated ones by marginalizing over other parameters. In particular, for each object we generate 500 sets of randomized values of inclination, longitude of periastron and initial orbital phase and for each of these sets we check on all allowed combinations of period, eccentricity, and mass ratio as quoted in Table 2. Table 3 reports parameter values for the best fit to the observed RVs and Figure 5 illustrates solutions for a few objects.

An SB1 with a very high eccentricity can be very hard to identify. Such a binary spends only a very short time close to periastron at high orbital velocities, but most of the time their RVs are nearly constant and close to the velocity of the center of mass. Rave objects generally have a small number of observations (Figure 2), so it is quite likely to miss the RV spike around the periastron passage and the object might not be identified as a binary at all.

Most of the SB1 candidates have orbital periods shorter than a year, and only 10 of the objects have orbital periods larger than 2 years (Figure 5, left panel). As already mentioned, orbital periods cannot be very long as observations span only a few years or less, but they cannot be very short either as large RV variations are quite rare. The right panel of Figure 5 shows that the orbital period is determined to within 50% for about half of the objects. Similar uncertainties are true also for , while is determined to within 10% using the effective temperature of the primary and its assumed position on the main sequence.

In order to better evaluate the precision and reliability of our orbital period determinations we constructed a mock sample of RV measurements using orbital solutions of SB1 binaries as reported in the Catalogue of Spectroscopic Binaries (Pourbaix et al., 2004). For each Rave SB1 candidate we selected its counterpart in the catalogue, matching the effective temperature and dwarf nature of its primary. The orbital phase of the first Rave observation was picked randomly, with subsequent velocities generated from the orbital solution at the same time-offsets as in the actual Rave observations. The set was processed in the same way as the Rave observations, so that the derived orbital period could be compared to the actual one from the catalogue (Figure 5). 50 of all objects are in the gray area, where the dispersion is 40 around the true value, while 90 of all objects have periods determined to within a factor of 2. The results do not depend on the effective temperature of the primary (see right panel in Figure 5). The results are generally acceptable but we note some systematics: our periods tend to be overestimated for short period binaries and underestimated for long-period ones.

6 SB2 candidates

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefAsymmetry and boxiness of the calcium triplet for single stars (black dots), SB1 candidates (gray dots), and 8 SB2 candidates, each in a different color. SB1 candidates with at least one spectrum outside the marked circle with a radius of 0.05 centered on (0.01, 0.3) were visually inspected for the presence of secondary light in their spectra.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefTop panel: spectra of the SB2 candidate J154304.9-122933 with its orbital phases labelled. The RV curve of this object is shown in Figure 5a. Middle panel: Fitted calcium triplet lines for the orbital phase 0.72. Bottom panel: Fitted spectra for the same phase, using  km/s,  km/s,  K,  K, , [FeH].

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefAbsolute magnitude - color diagram for single, SB1, and SB2 candidate stars. The blue lines are 2 and 4 Gyr Padova isochrones (Marigo et al., 2017) with a metallicity set to the Solar value. Gray dots are Rave single stars, red ones are SB1 candidates, and black ones SB2 candidates. The black solid line is the median value of the J magnitude for single stars and the gray area indicates the around median. Similarly, red solid line and shaded area are medians for SB1 candidates.

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Table 0. \Hy@raisedlink\hyper@@anchor\@currentHref Most probable values of parameters for double lined binary candidates: mass ratio (q), temperature of primary (), temperature of secondary star (), and metallicity [FeH].

Object q [FeH] J120432.1-203723 0.5 7250 6750 0.5 J203415.1-201303 0.6 6750 6500 -0.5 J090701.4-142256 0.65 4750 4500 0.0 J125113.4-202156 0.5 7500 6750 -0.5 J154304.9-122933 0.55 7500 6750 -0.5 J161301.0-130342 0.65 5000 4750 -0.5 J100235.9-093818 0.55 7000 6250 -0.5 J045419.4-030709 0.55 6750 6000 -0.5

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SB1 candidates in Rave have been labelled as normal single stars by a morphological classification scheme (Matijevič et al., 2012). This is understandable, as the primary star is usually much brighter than the secondary one in such systems. But a close inspection of their spectra sometimes reveals a contribution of the light from the secondary, thus moving the object to the SB2 category. The signature of the secondary can be searched for in spectral lines. Due to the limited S/N ratios of the Rave spectra the strongest lines turn out to be the most appropriate ones. So we focused on the calcium triplet lines and measured their boxiness and asymmetry indices (Figure 6). Boxiness is defined as the ratio of line widths at three quarter and one quarter of the line depth, while asymmetry is the shift of the centroid at half maximum in units of full width at half maximum (FWHM). The reported values are averages over the three calcium lines. For a symmetric Gaussian line the boxiness equals 0.456 and the asymmetry is zero. Calcium triplet lines have broad wings, so one expects somewhat smaller values of boxiness, but the asymmetry should still be very close to zero for a spectrum of a single star, with an exception of hot stars where the presence of Paschen lines of hydrogen contaminates wings of the calcium lines.

The combination of these values points to spectra with unusual shapes of spectral lines that could be double lined binaries (colored dots on Figure 6). Visual inspection of those spectra confirmed the existence of several double lined binaries where a chi-square fit with two spectra gave a much better representation of the observed spectrum than a single spectrum.

An example is given in Figure 6. The top panel shows five spectra of the same star, where only the last one, observed at orbital phase 0.72, shows obvious double components in the Calcium triplet and also in other spectral lines. The RV curve of the same object is presented in Figure 5a. The first four spectra in Figure 6 were obtained in 2009, while the last one which shows double-lined spectral lines was obtained in 2006. The bottom two panels show results of a least-square fit to this double-lined spectrum using both RVs, temperatures, mass ratio, and metallicity as free parameters, with surface gravity constrained by the assumption that both stars are on the main sequence. We note that the same solution presents a good fit also for the other four spectra, though one would expect more pronounced double-lined profiles also at the other quarter phase. This may be explained by the fact that we adopted orbital periods and phases as calculated in the SB1 fit, even though a contribution from a secondary component in SB2s may alter these values. The goal of this analysis is to point to possible SB2 candidates, but the number of multiple Rave spectra is too small to attempt a complete solution anyway. We also note that our list of SB2 candidates contains only 8 objects – these are the ones that escaped detection by the automated morphological classification algorithm (Matijevič et al., 2012). On the other hand, Steinmetz et al. (2019) lists 2861 objects with (some) spectra in the SB2 category, with physical properties of 123 of them discussed already by Matijevič et al. (2010).

For an object on the main sequence one could expect a moderate increase of luminosity if the object is not single but a SB1 binary system, with an effect even more pronounced for SB2s. This is an obvious consequence of an increasing contribution of light from the secondary. Indeed, the SB1s in Figure 6 are about 0.2 magnitudes brighter than single stars, but the dispersion around the median value is the same. The data pool of SB2s is too small to make the same statistics, but it can be seen that they are brighter than single stars and some of them approach a 0.75 mag limit, which corresponds to the joint luminosity of two equal stars instead of one. The positions of evolutionary tracks of Solar-type stars in Figure 6 demonstrate, however ,that many of the single or binary objects may be actually evolving off the main sequence, which also makes these objects brighter. This matter is discussed in Čotar et al. (2019).

7 Combining Rave with Gaia

\H@refstepcounter

figure \hyper@makecurrentfigure

Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefMaximum RV variability for groups of objects identified as single stars or SB1 candidates by Rave DR6 survey alone (label R), or by a combination of the Rave and Gaia DR2 (label RG) surveys. The red line denotes RV differences between Rave and Gaia for all objects that have only one Rave observation. The green line shows that the RVs of single stars match to  km s across the surveys, so one can use a combination of RVs from both surveys to search for SB1 candidates. The black solid line demonstrates that a combination of the two surveys can use its long time-span to identify SB1s with the lowest RV amplitude.

\H@refstepcounter

figure \hyper@makecurrentfigure

Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefCumulative histogram of the relative dispersion of period median values for SB1 candidates with Rave DR5 Gaia DR2 velocities combined. The results are similar to the ones with Rave DR6 data only (Figure 5). About 70% of the objects have determined to within 50%.

\H@refstepcounter

table \hyper@makecurrenttable

Table 0. \Hy@raisedlink\hyper@@anchor\@currentHrefRepresentative sample from full on-line list of SB1 candidates obtained by a combination of Rave and Gaia RV measurements. The table is similar to Table 4 but it contains a much larger list of 27,716 SB1 candidates. The complete table will be published only electronically. An epoch of 15 June 2015 for the Gaia observations was adopted (see Section 7 for an explanation).

Object Time-span Epoch(first) Epoch(last) J012955.0-623622 5.99 3 2462 2008-09-17 2015-06-15 J135416.6-222607 4.30 3 3758 2005-03-01 2015-06-15 J004904.6-222139 8.91 3 4262 2003-10-14 2015-06-15 J070727.9-480148 11.56 4 3126 2006-11-23 2015-06-15 J051516.8-324737 5.53 3 3423 2006-01-30 2015-06-15

\twocolumngrid

The Gaia satellite was launched on 19 December 2013 and started with scientific observations in July 2014 (Gaia Collaboration et al., 2016). Its main objective are astrometric measurements of parallax and proper motion, but here we focus on results from an on-board RV spectrometer. It has a resolving power of  11 500 covering the near infra-red wavelength range at 845 - 782 nm, with an expected precision of 1 km s for GK stars brighter than (Cropper et al., 2018; Katz et al., 2019). In April 2018 the Gaia Collaboration et al. (2018b) published median RVs for 7.2 million sources with effective temperatures in the range of 3550–6900 K that are brighter than . These medians were obtained over 22 months of observations (July 25 2014 - May 23 2016), they have a typical overall precision of 1.05 km s. Most of the stars observed also by Rave lie at the faint end of objects accessible for Gaia RV measurements. For such objects () the precision of Gaia RVs is 1.4 and 3.7 km s for an effective temperature of 5000 K and 6500 K, respectively. We note that these errors are not significantly larger than for the Rave survey, so the two sets of measurements can be efficiently combined. The small offset of the RVs reported by Gaia with a typical value of 0.3 km s (Steinmetz et al., 2018) is negligible, when our relatively stringent limits on used to search for SB1 candidates are considered. Objects with a pronounced RV variation or SB2s were not included in Gaia DR2. Still, a combination of Rave and Gaia DR2 allows for an efficient search of SB1s with an orbital period of a few years.

Gaia obtained its RV measurements after completion of the Rave survey, so combining the two datasets increases the time-span of RV measurements and thus allows a detection of SB1 systems with longer orbital periods. More importantly, most of its targets have been observed with Rave only once (Figure 2), but Gaia is adding another observation and so allows to test for variability of their RVs. In fact, Gaia itself observed each object several times, but these observations will be published only in one of the next data releases and they do not reach the combined timespan of Rave  Gaia, which stretches up to over a decade (Figure 2).

Median Gaia RVs have been calculated from several observations over 22 months. Individual measurements are not available, so we adopted an epoch of 15 June 2015, which is at the middle of the observed timespan. Note that the true median epoch of Gaia RV measurements could be up to a few months earlier or later. But this has little influence on our analysis, as the closest Rave observations were obtained at least 2.1 years earlier. The combination of Rave and Gaia RVs extends the maximum time span from 8 to 12 years, while the median value is extended from 2 to 7 years (Figure 2). We note that the use of median velocity of Gaia favours an analysis which is separate from the one based on Rave data only.

There are 450,646 stars with RVs measured in both surveys. This is a remarkable increase by over 37,661 stars suitable for SB1 search in the Rave-only survey. After conducting the same analysis as before (Section 3) we obtained the following results. 7.7% of the stars with observations in both datasets are SB1 candidates. This is close to a the fraction of 10.2% that was obtained based on Rave data only, even though the time-span is much longer. Among Rave stars with multiple observations that were labeled as single stars ( 2.87) we found almost 10 % new binary candidates after we included Gaia velocities in calculations. Overall, we were able to identify 27,716 SB1 candidates in the Rave  Gaia sample, compared to 3838 from the Rave-only analysis.

The black dashed line in Figure 7 shows the radial velocity variability for stars that were classified as normal single stars, according to their Rave radial velocities. For the vast majority of objects the RV changes are less than 5 km s, so we can assume those objects are long period binaries, impossible to detect without observations over a longer time-span. After we added Gaia velocities, the resulting RV variability became significant for some of these stars and we identified new SB1 candidates. Future Gaia data releases will probably reveal even more binary candidates.

Next we repeated the computation of orbital parameters (Section 5), now adding Gaia velocities. The results are shown in Figure 7. The results are very similar as for the Rave-only dataset. This is a consequence of the similar accuracy of RV measurements in both samples.

8 Conclusions

This paper presents a complete list of SB1 candidate stars in the Rave survey based on the requirement that their RV measurements differ by at least apart (). Using the probability function described in (Matijevič et al., 2011) we detected 3838 single lined spectroscopic binary candidates. This almost triples the number of candidates known so far and corresponds to % of all normal stars observed multiple times by Rave. Most of the primary stars of these systems belong to main-sequence dwarfs with temperatures around 6000 K and masses around 1 - 1.2 M, or red clump stars and red giant stars with temperatures 4500 - 5000 K and masses larger than 1.5 M. The secondary stars contribute only a small fraction of the total light of an SB1 candidate. Still, the spectral lines in the combined spectrum are somewhat shallower, so this may be the reason why SB1 candidates appear to be more metal poor than the general Rave population.

Even though most of the stars with repeated observations in Rave have been observed only a few times, it is possible to make a rough estimate of the orbital parameters for systems with primary components on the main sequence. We focused on systems with at least 4 observations. Being limited by the time span between re-observations, our results showed that most systems have an orbital period shorter than one year, and only a few of them have orbital periods of around three years.

Our sample of SB1 candidates includes stars morphologically classified as normal single stars. But at least in some cases one may hope to identify a contribution of the secondary component to the total light of the system. In the spectra this is revealed by unusual shapes of the spectral lines, which were measured through the boxiness and asymmetry of calcium triplet lines. A visual inspection of their spectra revealed some compelling cases with a mass ratio around 0.8. We also note that both SB1 and SB2 candidates tend to be somewhat brighter than their single-star counterparts, which is consistent with a contribution of light from a secondary component.

Gaia DR2 is supplementing the Rave dataset with another RV observation for 450,646 stars. It also observed at an epoch after Rave observations were concluded, so the combined dataset has a larger time-span of up to 12 years and with a median of 7 years. The analysis of the combined datasets allows us to identify 27,716 stars as single lined binary candidates, which presents an order of magnitude increase over earlier studies. The orbital and physical properties of these systems are similar to the ones from the Rave-only dataset, but an accurate knowledge of their spatial position and velocity vectors provided by Gaia DR2 allows us to calculate their Galactic orbits and to further characterize their physical parameters.

The contents of Tables 4, 5, and 7 are available via the Vizier/CDS service.


Funding for Rave  has been provided by: the Leibniz-Institut für Astrophysik Potsdam (AIP); the Australian Astronomical Observatory; the Australian National University; the Australian Research Council; the French National Research Agency; the German Research Foundation (SPP 1177 and SFB 881); the European Research Council (ERC-StG 240271 Galactica); the Istituto Nazionale di Astrofisica at Padova; The Johns Hopkins University; the National Science Foundation of the USA (AST-0908326); the W. M. Keck foundation; the Macquarie University; the Netherlands Research School for Astronomy; the Natural Sciences and Engineering Research Council of Canada; the Slovenian Research Agency (core funding No. P1-0188); the Swiss National Science Foundation; the Science & Technology Facilities Council of the UK; Opticon; Strasbourg Observatory; and the Universities of Basel, Groningen, Heidelberg and Sydney. TZ thanks the Research School of Astronomy & Astrophysics in Canberra for support through a Distinguished Visitor Fellowship.

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, in particular the institutions participating in the Gaia Multilateral Agreement.

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