© The Authors 2025

1. Introduction

Estimates for stellar multiplicity can go from 20% up to 100% depending on the mass of the primary (see, e.g., Offner et al. 2023; Moe & Di Stefano 2017; Duchêne & Kraus 2013; Raghavan et al. 2010; Bate 2009, and references therein), making the study of binary systems of paramount importance for stellar evolution models. The properties of these systems, including mass ratio, metallicity, and the evolutionary stage of the components, among others, lead their evolution to produce different possible outcomes, including compact binaries with double degenerate components (e.g., Marsh 2011; Napiwotzki et al. 2004), rapid rotating stars (e.g., Simonian et al. 2019; Gaulme et al. 2020), semi-detached systems (such as symbiotic binaries, e.g., Podsiadlowski & Mohamed 2007; Mikołajewska 2012; cataclysmic variables, e.g., Paczynski 1985; and X-ray binaries, e.g., Bahramian & Degenaar 2023), contact binaries (e.g., Qian et al. 2020), and chemically peculiar stars such as barium and carbon-enhanced metal-poor (CEMP) stars (Jorissen et al. 2019; Escorza et al. 2019; Karinkuzhi et al. 2021). Some of these systems can eventually become the progenitors of Type Ia supernovae (SNe; Maoz et al. 2014), hypervelocity stars (Brown 2015), stellar black holes, or gravitational wave sources (see, e.g., Amaro-Seoane et al. 2012), which have a strong impact on the chemical enrichment and evolution of galaxies.

The Gaia space mission (Gaia Collaboration 2023d) has been revolutionizing the field of binary stars mostly since its third data release (DR3; see the review of El-Badry 2024, and references therein). Over ∼800 000 non-single stars and their orbital solutions were published for the first time in DR3 as part of the non_single_star (NSS) catalog (Gaia Collaboration 2023a), which is the largest all-sky collection of binaries compared to all the previous compilations (El-Badry 2024), despite it only containing a fraction of the genuine binaries that could be observed by Gaia. Unlike previous observations, binary systems observed by Gaia also have precise astrometric observations (including parallaxes and proper motions); G, G_BP, and G_RP-band photometry; and spectroscopic observations for the brightest (G_RVS < 12 mag) stars. From the epoch photometry and spectroscopy observations, the variability of the systems can be analyzed, making this dataset a unique opportunity to study different types of binary systems in a holistic approach that was not available before Gaia. Evidence of this is shown with the increasing number of studies using the Gaia NSS catalog to explore the wide-binary population (Hernandez 2023; Hollands et al. 2024) and to search for massive unseen compact companions (El-Badry & Rix 2022; Fu et al. 2022; Gomel et al. 2023; Jayasinghe et al. 2023), which includes the discovery of the most massive stellar black hole, Gaia BH3 (Gaia Collaboration 2024), as well as population studies of main-sequence and brown dwarf binaries (e.g., Bashi et al. 2023; Stevenson et al. 2023). Given the importance of radial velocity (RV) and time series epoch observations, the Gaia mission has published the variability information for classical pulsators, such as Cepheids and RR Lyrae, in its DR3 (Ripepi et al. 2023; Clementini et al. 2023) and, more recently as part of the Gaia Focused Product Release (FPR; Gaia Collaboration 2023c), for long-period variables (LPVs; which have photometric periods¹ ≳10 d to 1000 d), including Mira pulsators, semi-regular variables, and red giant binary systems.

Among red giant binaries, ellipsoidal variables are close binaries in which the primary star (usually a red giant) is tidally distorted because of the gravitational attraction of the companion (typically a main-sequence star). This distortion produces an elongated ellipsoidal shape of the primary, substantially filling the Roche lobe of the system, which leads to ellipsoidal light variations as the primary star orbits around the secondary. Therefore, the velocity variation (orbital period) is twice the light variability (photometric period). Ellipsoidal variables are known to define a linear sequence in the period-luminosity diagram of LPVs in the Large Magellanic Cloud (LMC; Soszyński et al. 2004; Nie et al. 2012; Pawlak et al. 2014). Close red giant binaries can become tidally synchronized, which is one of the mechanisms that explains the existence of rapidly rotating giants (Phillips et al. 2024; Leiner et al. 2022). As a result of the tidal influence, the giants can also present enhanced chromospheric activity due to the formation of starspots. This type of binary is commonly associated with the RS Canum Venaticorum-type (RS CVn; Hall 1976; Montesinos et al. 1988; de Grijs & Kamath 2021). Although ellipsoidal variables belong to the rotational variability class, their brightness variations are due to the changes in the orientation of the tidally distorted primary, while in the case of rotational variables such as RS CVn stars, the brightness variations are due to the rotation and starspots in the stellar surface.

In this work, we focus on the subsample of red giant binaries among the LPVs that are part of the latest Gaia FPR. Aiming to characterize this sample chemo-dynamically, we crossmatched the binary candidates from the Gaia FPR with DR3 astrometry, photometry (gaia_source table), spectroscopic atmospheric parameters (astrophysical_parameters table), and orbital (nss_two_body_orbit table) information. This paper is organized as follows. Section 2 presents the selection of the binary sample in terms of variability cuts and the properties of the sample (periods, effective temperature, surface gravity, activity level). In Sect. 3.1, the procedure to derive the stellar parameters including luminosities, masses, and radii of the primary stars and the validation of the method with external catalogs is presented. Section 4 presents the binary population properties of the sample, including the mass function distribution, period-radius-eccentricity relations, and mass estimates for the secondary component. Section 5 explores the chemical and dynamical properties of the sample, including the metallicity distribution function, Galactic velocities, velocity dispersions, and s-process [Ce/Fe] abundances. Section 6 presents the period-luminosity diagram for our sample and explores correlations between the dispersion of the PL and the mass, metallicity, and radii of the primary star. We discuss the intrinsic differences among ellipsoidal and rotational variables and summarize our results in Sect. 7.

2. Long-period binary candidates in Gaia DR3

2.1. Photometric and radial velocity variability

Long-period variable candidates were selected from the gaiafpr.vari_long_period_variable table, following the criteria in Gaia Collaboration (2023c). In particular, non-pulsating binary sources were isolated by making cuts in the photometric G-band amplitude, Amp_G, and the RV amplitude, A_VR:

$$\begin{array}{c}\hfill {\mathrm{Amp}}_G<0.3\mathrm{mag}\mathrm{and}\frac{{\mathrm{Amp}}_G}{\mathrm{mag}}<2.5·{10}^{-3}·{\left(\frac{A_{V_R}}{{\mathrm{km}\mathrm{s}}^{-1}}\right)}^2\text{.}\end{array}$$(1)

From this sample, only those stars in the “top-quality sample” (TQS, flag_rv = True) were selected. The TQS consists of stars with compatible RV and photometric variability, having (P_VR≃ P_ph or P_VR≃ 2 P_ph) for all P_ph ∈ {P_G, P_GBP, P_GRP}. There were 881 sources that pass these cuts.

To characterize the physical properties of the sample, a good estimate of their distance and atmospheric parameters is needed. Therefore, we also imposed a cut in parallax to select sources with reliable astrometry: 0.0 < ϵ_ϖ/ϖ < 0.15, and Renormalized Unit Weight Error (RUWE) < 1.4 (see, e.g., Lindegren et al. 2021, and the discussion on its impact on the analysis of single-line spectroscopic binaries in Gosset et al. 2025), obtaining 636 sources. The cut in RUWE aims to remove partially resolved binaries in which the astrometric solution has large uncertainties. This cut therefore removes true binaries from our sample (28 sources) for which the RV determination and photogeometric distances can be highly affected by their binary nature. The 636 sources were crossmatched to have an entry in the gaiadr3.astrophysical_parameters table, leading to an initial sample of 434 sources (hereinafter, the input sample). Their distribution in the period-luminosity diagram is shown in Fig. 1, in which the photometric period based on the G-band time series, P_ph, and the Gaia Wesenheit index (W_BP, RP; see Lebzelter et al. 2018, 2019) are used. The distance modulus μ of each star was estimated using the parallax. The stars are color coded according to the ratio of the RV and photometric variability (P_VR/P_ph), and those sources included in the NSS catalog (Gaia Collaboration 2023a), having a binary solution SB1 (single line spectroscopic binary, 154 sources) are marked with empty black squares. In this diagram, the brightest sequence is composed of stars with W_BP, RP − μ ≥ −3.0 mag, 20.0 ≤ P_ph (days) ≤ 400.0 days, and P_VR/P_ph ≃ 2, consistent with the sequence of ellipsoidal binaries (Nicholls et al. 2010; Gaia Collaboration 2023c), also known as the sequence E for ellipsoidal variables in the LMC (see, e.g., Soszyński et al. 2007).

Fig. 1. Photometric period versus the absolute Wesenheit magnitude, WBP, RP − μ, for the long-period binary candidates. The color code corresponds to the ratio between the period derived based on the RV curve and the photometric period. Stars having binary solutions in the Gaia NSS catalog are marked with empty squares. Two sequences are recovered: a sequence composed of brighter stars with PVR/Pph ≃ 2, and a tidally locked population having lower luminosities and shorter periods.

The second sequence is restricted to shorter periods, P_ph≤ 150.0 days, having P_VR ≃ P_ph. The nature of this sequence is uncertain, although it is mostly composed of binaries according to the NSS solutions, which does not favor the scenario of pulsating stars. Their period ratio is consistent with (almost) tidally locked binaries, in which the orbital period is the same as the photometric period. This sequence resembles the secondary, although ∼1 mag fainter, sequence found for contact binaries (including ellipsoidal binaries) for the LMC reported in Muraveva et al. (2014). It is worth mentioning that, when using the RV period P_VR, the sequence of ellipsoidal variables is shifted and both sequences merge into one. Most of these stars have a variability type “Rotational” in the compilation of Gavras et al. (2023); therefore, we would refer to them as “rotational” binaries from now on. In this variability class, the rotation of a star with a spotted surface produces the observed photometric variability, which is enhanced in close binary systems compared to a single red giant star with a similar rotation period (Yadav et al. 2015; Gehan et al. 2022).

To confirm the difference between the two groups, the Gaia photometric periods were compared to those from the literature (see Appendix A). Based on the overall good agreement, we can conclude that the two sequences seen in the period-luminosity diagram in Fig. 1 are not due to an incorrect photometric period estimate, but rather to an intrinsically different variability phenomenon. We visually inspected the phase-folded G-band light curves using the period obtained based on the RV curve. For ellipsoidal binary candidates, two minima of different depth are recovered, while for the rotational candidates, only one minima is obtained. Figure 2 shows two photometric and RV light curves for one ellipsoidal (left) and one rotational (right) star candidate. From this inspection, we discarded 19 ellipsoidal candidates (P_VR/P_ph ≲ 2.0) having light curves with one single minimum or being highly irregular. For the rest of the analysis, we separately analyze the ellipsoidal (being restricted to P_VR/P_ph ≥ 1.5) and rotational (P_VR/P_ph < 1.5) binary candidates.

Fig. 2. G-band and RV curves for one ellipsoidal binary candidate (the two top panels) and one rotational candidate (the two bottom panels). The G-band light curve was phase-folded using the period from the RV curve in the case of the ellipsoidal variable, recovering the two minima per orbital cycle.

In the following sections, four samples are analyzed based on independent input catalogs. (i) The input sample, which has atmospheric parameters (effective temperature and surface gravity) for 372 ellipsoidal and 43 rotational candidates from either the GSP-Spec module (Recio-Blanco et al. 2023) or XGBoost (Andrae et al. 2023), nine and 32 of them, respectively, also have an estimate for the Gaia stellar activity index parameters (only considering those with positive values for the activityindex_espcs parameter; see Lanzafame et al. 2023). From the spectroscopic atmospheric parameters, the physical parameters such as the luminosity, radius, and mass were derived. (ii) Orbital properties, including orbital periods and semi-amplitudes (for the full input sample) and eccentricities (available only for 154 stars) are from the NSS gaiadr3.nss_two_body_orbit table. (iii) The kinematic properties, including position, distances, RV, and proper motions, available for all the sources in the input sample, are from Gaia gaiadr3.gaia_source. (iv) The chemical properties, including [M/H], [α/Fe], and [Ce/Fe] are based on GaiaGSP-Spec data, only for ellipsoidal variables, available for 125, 43, and eight binaries, after applying quality cuts, respectively (see Sect. 5).

2.2. Atmospheric parameters: T_eff, logg, [M/H]

The input sample of binaries has been observed with either the Gaia Radial Velocity Spectrometer (RVS; ℛ ∼ 11 500, Sartoretti et al. 2023) and/or with the BP/RP low-resolution specto-photometers (XP spectra; ℛ ∼ 25–100, De Angeli et al. 2023). Atmospheric parameters from RVS spectra were derived and validated by the GaiaGSP-Spec module, available in the gaiadr3.astrophysical_parameters table; see Recio-Blanco et al. (2023, hereinafter the “GSP-Spec sample/parameters”). Atmospheric parameters derived from low-resolution Gaia XP spectra using a data-driven approach from the XGBoost algorithm (see Andrae et al. 2023) are also available for most of the sources (hereinafter, the “XGBoost sample/parameters”).

In the case of ellipsoidal variable candidates, for those with the GSP-Spec flag KMgiantPar = 0 (i.e., KM-giants without issues in their parametrization; see Table C.8 from Recio-Blanco et al. 2023), the GSP-Spec surface gravity and metallicity were calibrated based on their effective temperature through the relations presented in Table A.1 in Recio-Blanco et al. (2024). The [α/Fe] abundances were calibrated using the coefficients in Table 4 of Recio-Blanco et al. (2023). In the rest of this analysis, only the calibrated atmospheric parameters are used. More than half of our sample has quality flag KMgiantPar = 1, 2, corresponding to cool giant stars (T_eff < 4000 K, log g < 3.5), for which the raw logg estimation had a significant bias and was replaced by a constant value (see the full definition of this flag in Table C.8 of Recio-Blanco et al. 2023). For those stars, when available, we adopted the atmospheric parameters from XGBoost. In this case, we set the [α/Fe] abundance (which is necessary to derive the bolometric correction; see Sect. 3.1) according to the standard relation for the Galactic disk:

$$\begin{array}{cc}\hfill [\alpha /\text{Fe}]& =+0.0\text{dex, for}\text{[M/H]}\ge \text{0.0 dex;}\hfill \\ \hfill [\alpha /\text{Fe}]& =-0.4\text{dex}\times \text{[M/H]}\text{, for}-1.0\text{dex}\le \text{[M/H]}<0.0\text{dex;}\hfill \\ \hfill [\alpha /\text{Fe}]& =+0.4\text{dex, for}\text{[M/H]}<-1.0\text{dex.}\hfill \end{array}$$(2)

In tidally locked rotational binaries, the induced rotation is generally associated with an enhanced chromospheric activity, which can bias the atmospheric parameter measurements (Morel et al. 2004; Cao et al. 2023). To test the potential effect of stellar activity in the GSP-Spec atmospheric parameters, we compared the log g values with the activity index $logR{\prime }_{\mathrm{IRT}}$ (following Eqs. (6), (7), and Table 1 in Lanzafame et al. 2023) derived using T_eff and [M/H] from GSP-Spec, and the activity index from Gaia DR3 activityindex_espcs which is available for sources with photometric log g ≥ 3.0 dex. Figure 3 shows the log g and $logR{\prime }_{\mathrm{IRT}}$, which is a measure of the flux difference between the observed flux with respect to the radiative equilibrium approximation in the core of the Ca II IRT lines, derived as a synthetic spectrum having the same atmospheric parameters as those derived by the Gaia GSP-Phot module (Lanzafame et al. 2023). The color code corresponds to the log χ² of GSP-Spec, which represents the goodness-of-fit of the atmospheric parameters. There is a trend, although with significant scatter, between both quantities, which could be explained considering that active stars have an excess in the Ca II equivalent width, with respect to an inactive star, which could impact the fit in the GSP-Spec module leading to potentially overestimated log g values and worse (higher) values of log χ². Stars having $logR{\prime }_{\mathrm{IRT}}\ge$ – 5.3 are considered as highly active in Lanzafame et al. (2023), and are exactly those with the largest surface gravities and worse goodness-of-fit, indicating that the surface gravity estimates for these stars are strongly affected by the level of activity. As the surface gravity and also the metallicity can be biased due to activity, the atmospheric parameters for those stars with GSP-Spec log g_calibrated ≥ 2.2 dex were not considered and instead, the atmospheric parameters from XGBoost were adopted (see Appendix B for a discussion about the selection of this threshold).

Fig. 3. Surface gravity and the activity index $logR{\prime }_{\mathrm{IRT}}$ for stars with available activityindex_espcs measurements in Gaia DR3. The stars are color coded according to log χ2, the goodness-of-fit of the RVS spectra from the GaiaGSP-Spec module.

Figure 4 shows the Kiel diagram for the sample. Stars for which the parameters adopted are from XGBoost due to an overestimated surface gravity measurement in GSP-Spec are shown with black edges, being mostly those rotational binaries with log g > 2.0 dex. The binary stars of our sample are color coded according to the ratio between the RV and photometric period, to separate the sample into those that are most likely of ellipsoidal type (P_VR/P_ph ≃ 2.0) to the ones that are most likely tidally locked rotational variables. A sample of high-precision, accurate GaiaGSP-Spec data set (having median uncertainties of 10 K, 0.03, and 0.01 dex in T_eff, log g, and [M/H], respectively; following the selection cuts as in Recio-Blanco et al. 2024) is included as grey dots. The Kiel diagram is consistent with cool red giants, being the ellipsoidal binary candidates more evolved than the rotational variables, although they have log g values above the position of the red clump (see Recio-Blanco et al. 2024). The different atmospheric parameters for the two groups are consistent with the presence of two sequences in Fig. 1, where the rotational candidates are hotter and less evolved, with shorter orbital periods, compared to the bulk of ellipsoidal candidates.

Fig. 4. Kiel diagram for the complete sample of red giant binaries with a spectroscopic effective temperature and surface gravity (either from GSP-Spec or XGBoost). The sample is color coded based on the ratio between the orbital and photometric period. The sources for which the parameters from XGBoost were preferred against the parameters from GSP-Spec are shown as circles with black edges. The background distribution in gray corresponds to a precise GaiaGSP-Spec sample that was selected as in Recio-Blanco et al. (2024).

In summary, from the input sample of 434 red giant binaries, atmospheric parameters from GaiaGSP-Spec, having KMgiantPar = 0 and calibrated log g < 2.2 dex, were adopted for 86 ellipsoidal candidates and two rotational candidates, while XGBoost atmospheric parameters were adopted, if available, for the rest of the cases, accounting for 292 ellipsoidal and 41 rotational candidates. From the sample, one possible contaminant is Gaia DR3 517611939345861120, which is the brightest star among the non-ellipsoidal sample, even brighter than the sequence of ellipsoidal variables in the period-luminosity diagram for its period, P_ph = 45.7 d (see Fig. 1). Its atmospheric parameters both from GSP-Spec and XGBoost place it far from the red giant sample, being much hotter than the rest of the sample. We detail the peculiarities of this system in Appendix C and we discard it from the rest of the analysis. In total, there are reliable atmospheric parameters for 424 red giant binaries.

3. Physical stellar parameters

3.1. Luminosities, radii, and spectroscopic masses

The stellar parameters of the primary star in each system (i.e., luminosity, mass, and radius) were derived using both Gaia photometry and spectroscopy following de Laverny et al. (in prep.). In this section, we briefly enumerate the steps used to derive those quantities.

The color excess E(BP−RP) was first estimated considering the effective temperature, surface gravity and metallicity and the observed Gaia (BP-RP) color. The true color was obtained using the color-T_eff relations for Gaia DR3 bandpasses² (Casagrande et al. 2021). To derive the stellar luminosity, the absolute magnitude was obtained considering the photogeometric heliocentric distance derived by Bailer-Jones et al. (2021) and the A_G extinction, obtained from the E(BP-RP) color excess. The bolometric correction BC_G was obtained using the bcutil package³, for Gaia DR3 magnitudes (Casagrande & VandenBerg 2018), considering the atmospheric parameters (T_eff, log g, [M/H], [α/Fe]) either from GSP-Spec or XGBoost. The adopted bolometric magnitude of the Sun was M_bol, ⊙ = 4.74 mag. From the luminosity estimates and the spectroscopic effective temperature, the stellar radius was also derived.

The log g measurements and the derived radii were then used to estimate the mass of the primary star as

$$\begin{array}{c}\hfill log\left(\frac{\mathcal{M}}{M_{\odot }}\right)=logg+2log\left(\frac{\mathcal{R}}{{\mathrm{R}}_{\odot }}\right)-log{g}_{\odot }\text{,}\end{array}$$(3)

adopting log g_⊙= 4.44.

The associated errors on the distance, apparent G magnitude and atmospheric parameters (T_eff, log g, [M/H], [α/Fe]) were propagated through 1000 Monte Carlo realizations. In the case of atmospheric parameters from XGBoost, the errors adopted for the atmospheric parameters were fixed to 50 K in T_eff, 0.08 dex in log g, and 0.1 in [M/H], following Andrae et al. (2023). We arbitrarily adopted an error of 0.1 dex in [α/Fe]. It is worth mentioning that this analysis does not take into account the error associated with the light contribution of the secondary both in the photometric and spectroscopic measurements. Depending on the brightness ratio among the two components, the associated uncertainties can be non-negligible and hard to estimate. We therefore do not take this error into account explicitly in the error determination. For the following analysis, stars for which unreliable extinction and/or bolometric correction estimates, due to unphysical results or values outside the color range covered by the color-T_eff relations from Casagrande et al. (2021) were discarded. These are mostly stars with T_eff ≤ 3700 K.

As the estimate of the spectroscopic masses depends strongly on the accuracy and precision of the surface gravity measurements (see Eq. (3) and the comparison with masses based on asteroseismology in Recio-Blanco et al. 2024), in a few cases, the primary masses recovered had large errors (> 50%) or a significantly large value. Based on the temperature and luminosity of our sample, it is not expected to have sources with primary masses larger than ∼6.0 M_⊙ (depending on the metallicity). We revised those cases individually (see Appendix D), which led to the rejection of three stars, the validation of their masses (two stars), or the adoption of a different mass value using the set of atmospheric parameters from XGBoost instead of GSP-Spec (six stars). The median values for the extinction, luminosity, mass, and radii, as well as the 84th and 16th percentile values (see de Laverny et al., in prep.) for this revised sample are included in Table E.1. We have included as well a quality flag for the variability classification based on the visual inspection of the light curve. Those having a well-defined phase-folded G-band light curve, presenting two clear minima (for the case of ellipsoidal candidates) or one sinusoidal shape (rotational candidates) have a flag “Good” (G), while those presenting more scatter in the light curve or gaps in the phase coverage have been marked as “Regular” (R), and for the most irregular cases, we chose to mark them as “Uncertain” (U). As visual inspection may be prone to be subjective, the flags should be considered only as an indication of the quality of the light curve. Our results and conclusions do not change if, for instance, the sources flagged as “U” are removed from the sample.

In total, we recovered reliable masses for 243 ellipsoidal variable candidates and 39 rotational candidates. The all-sky Aitoff projection of the ellipsoidal variables is shown in Fig. 5, where each source is color coded according to the spectroscopic mass of the primary star. Rotational candidates are not included in this figure for clarity, since they are less than 40 systems, with similar mass values (their masses can be seen in Fig. 6).

Fig. 5. All-sky Aitoff projection of the ellipsoidal variable candidates with reliable physical parameters (luminosity, radius, and mass) from the primary star. The color bar corresponds to the mass of the primary ℳ1. The background image was generated as part of the Gaia eDR3, based on more than 1.8 billion sources (Image credits: ESA/Gaia/DPAC).

Fig. 6. Hertzsprung-Russell diagram for the sample of rotational and ellipsoidal binaries. From left to right, the points are color coded according to the logarithm of its orbital period, PVR, the mass of the primary star, and the adopted spectroscopic metallicity [M/H]. Black points correspond to stars with unreliable extinction determination (mostly stars with Teff ≤ 3700 K; see Sect. 3.1) and therefore potentially unreliable stellar parameters, while those with a thick black edge are the rotational candidates. The grey lines correspond to constant radii of 10, 30, 60, 90, 120, 150, and 180 R⊙. In the right panel, the evolutionary tracks for a 1 M⊙ (green curve) and a 6 M⊙ (green dashed curve) star, having Z = 0.004 ([M/H]∼ − 0.6), from the grid computed by Lagarde et al. (2012), based on the STAREVOL (Siess et al. 2000) code, are included.

The Hertszprung-Russell (HR) diagram for the luminosities, radii, and masses derived is shown in Fig. 6. The left panel has a color bar for the orbital period, in logarithmic scale, also including lines for the stellar radius. For the ellipsoidal candidates, the spectroscopic radii range from ∼10 to > 180 R_⊙, with a median value of ∼60 R_⊙. The rotational candidates have smaller radii, not larger than ∼30 R_⊙. This is an expected result, since binary systems with longer orbital periods have larger separations, and therefore a larger radius is needed to reach the Roche-lobe and to be detectable as an ellipsoidal variable. The stellar masses for the primary star ℳ₁ (middle panel) show low to intermediate masses for both rotational and ellipsoidal candidates, with a handful of cases for which ℳ₁≥ 6.0 M_⊙ (the more massive stars are compared against evolutionary tracks in Appendix D).

The right panel of Fig. 6 shows the spectroscopic metallicity [M/H] associated with the adopted atmospheric parameters. The metallicities of rotational candidates are mostly supersolar. Having an enhanced chromospheric activity (see Sect. 2.2), their metallicity values could be as well overestimated. In fact, previous studies have found subsolar metallicities for active single-line spectroscopic binaries and RS CVn systems, although the sample sizes were rather small (see, e.g., Morel et al. 2004, 2006). The corresponding adopted metallicities from XGBoost are quite different from those in GSP-Spec, probably due to the effect of enhanced activity. For the rest of the analysis, we therefore decided to exclude rotational variables when interpreting chemical content.

Ellipsoidal variables have mainly subsolar metallicities. For reference, we include the evolutionary tracks of a Z = 0.004 ([M/H]∼ − 0.6), 1.0 M_⊙, and 6.0 M_⊙ star as continuous and dashed green lines, respectively. These were computed with the STAREVOL code (Siess et al. 2000) by Lagarde et al. (2012). The position in the HR diagram for most of the ellipsoidal variables is compatible with those tracks, although their metallicities may be different from the adopted ones in the evolutionary tracks. Their metallicity distribution function is further explored in Sect. 5.1.

3.2. Validation of the spectroscopic masses

The spectroscopic masses obtained are highly sensitive to the accuracy of the surface gravity, which may be strongly affected by, for example, enhanced chromospheric activity (see Sect. 2.2). To test the accuracy of the Gaia log g estimates, the catalog of oscillating red giant binaries from Beck et al. (2024) is used as a reference sample. It is based on Gaia DR3 orbital solutions and solar-like oscillators having asteroseismology measurements from Kepler (Borucki et al. 2010; Howell et al. 2014) and TESS (Ricker et al. 2014) missions. We crossmatch the subsample of giant star binaries in this catalog (having the same range of orbital periods as our sample) with the atmospheric parameter information from Gaia DR3 and XGBoost, to compare surface gravities and activity levels. The top panel in Fig. 7 shows the log g derived from asteroseismic measurements and the spectroscopic values in Gaia DR3, either from the GSP-Spec module (crosses) or the XGBoost catalog (circles). For those sources having an entry for the activity index, the $logR{\prime }_{\mathrm{IRT}}$ activity index was estimated (see Sect. 2.2 and Fig. 3) and it is shown in the color bar, while the two spectroscopic measurements are connected with a vertical dashed line. There is a good agreement between both spectroscopic and asteroseismic measurements for log g values lower than 2.0 dex, that is, more evolved stars, which corresponds to our sample of ellipsoidal variables. For larger surface gravities, there are more discrepancies, particularly for the stars having a measured higher activity index. The values of log g larger than ∼2.0 dex from GSP-Spec tend to be overestimated in most of the cases which is generally not the case for XGBoost (see also the discussion in Appendix B and Fig. B.1) since BP/RP spectra have lower sensitivity to chromospheric effects. This comparison supports the selection of XGBoost atmospheric parameters for the less evolved sample, which is mostly composed of rotational variables.

Fig. 7. Spectroscopic GSP-Spec (crosses) and XGBoost (circles) parameters and asteroseismic measurements of the surface gravity (top panel) and masses (bottom panel) of red giant binaries (Beck et al. 2024) and rotational binaries (Gaulme et al. 2020) with solar-like oscillations. The two spectroscopic values are connected with a vertical dashed line. The color bar shows the activity index and the difference in Δlog g in the top and bottom panels, respectively. The median difference and dispersion between spectroscopic and asteroseismic masses are quoted in the bottom panel.

Based on the spectroscopic Gaia atmospheric parameters, the luminosity, radius, and masses of the oscillating red giant binaries are derived, following the same procedure as for our sample, and the spectroscopic mass estimates compare to the asteroseismic mass, obtained from the scaling relations for ν_max, Δν, and effective temperature as in Beck et al. (2024). The bottom panel in Fig. 7 shows the obtained mass when using the GSP-Spec (plus signs) and XGBoost (circles) atmospheric parameters, colored based on the difference in the spectroscopic and asteroseismic log g values. There is an overall good agreement, with a mean bias in the spectroscopic mass of −0.1 M_⊙ for the two sets of atmospheric parameters. The unfilled symbols correspond to rotational binaries from Gaulme et al. (2020) which have also indications of enhanced activity. The mean bias in the spectroscopic mass is of −0.14 M_⊙ when using the XGBoost parameters, while in the case of the GSP-Spec parameters, some measurements are outside the range of masses shown in the plot, having a bias of more than 1.0 M_⊙.

Although this literature sample of red giant binaries is not composed of ellipsoidal variables, the atmospheric parameters and orbital period ranges are close to our input sample. This comparison therefore serves as a probe of the method and the effect of accurate surface gravities into reliable physical parameters, particularly the mass. Moreover, the effect of activity into the surface gravity measurements based on GSP-Spec and XGBoost samples is evident and supports our decision to adopt XGBoost parameters for stars with enhanced activity (rotational variables, having log g from GSP-Spec exceedingly large).

4. Binary population properties

4.1. Period-radius, e-period, f(ℳ)- period relations

The orbital period, P_nss; semi-amplitude of the primary star, K₁; and eccentricity, e, for 154 binaries in our sample are available in the Gaia NSS nss_two_body_orbit catalog. All of them have the orbital solution as being “SB1.” The orbital period and RV semi-amplitude values from the NSS catalog were consistent with the RV period P_VR and RV amplitude amplitude_rv reported in the FPR table (see Gaia Collaboration 2023c), while the eccentricity is only available in the former. Having the orbital parameters, the mass function of the binary system, f(ℳ), can then be estimated as

$$\begin{array}{c}\hfill f(\mathcal{M})=\frac{P{K_1}^3{(1-e^2)}^{3/2}}{2\pi G}\end{array}$$(4)

for the 154 stars with published eccentricities. For the rest of the sample (i.e., those not included in the NSS catalog), the FPR values for the period and RV amplitude are used to get an upper limit for the mass function by adopting an eccentricity of e = 0.

Figure 8 shows the period-radius (left panels), eccentricity-period (middle panels), and mass function f(ℳ)- period (right panels) distributions for rotational variable candidates (top row) and ellipsoidal variables (bottom row). A threshold or transition period at which the orbit is circular has been found in different binary populations (Jorissen et al. 2019; Escorza et al. 2020), being this period longer as the radius and luminosity of the star are larger along the red giant branch. An analytical expression for this threshold period can be obtained assuming the radius of the primary star reaches the Roche-lobe in the Kepler’s third law, being P_threshold a function of the primary radius R₁, ℳ₁ and ℳ₂ the masses of the primary and secondary component, respectively. Binary systems having lower periods than this threshold are unlikely to be found as in this case, the primary would have filled up its Roche lobe radius, leading to the subsequent mass-transfer and common-envelope phase, which are short-lived stages. This expression was derived in Gaia Collaboration (2023a) and corresponds to

$$\begin{array}{cc}\hfill log(P_{\mathrm{thr}}/365.25)& =(3/2)log(R_1/216R_{\odot })\hfill \\ \hfill & -(1/2)log({\mathcal{M}}_1+{\mathcal{M}}_2)\hfill \\ \hfill & +(3/2)(log0.38+0.2log{\mathcal{M}}_1/{\mathcal{M}}_2).\hfill \end{array}$$(5)

Fig. 8. Period versus radius (left), eccentricity (middle), and mass-function (left) for rotational variables (top panels), and ellipsoidal variable candidates (bottom panels). Left panels: Stellar radius of the primary star versus the orbital period. The color coding is based on the mass of the primary star. The dashed line corresponds to the threshold period while the black dots are ellipsoidal binaries in the LMC (Nie et al. 2017). Middle panels: Orbital period versus the eccentricity for sources with an NSS orbital solution of “SB1.” The color coding is according to the primary radius. For ellipsoidal variables, the circularization threshold for two values of radius is shown as dotted grey lines and black dots are ellipsoidal binaries in the LMC. Right panels: Orbital period versus mass function f(ℳ). The color coding is according to the primary radius. Sources with eccentricity estimates are shown as squares, while those without eccentricity measurements are shown as circles.

The left panels in Fig. 8 include this threshold period as a dashed line adopting the mean values ℳ₁ = 1.5, and 1.7 M_⊙ for rotational and ellipsoidal variables, respectively, and ℳ₂ = 0.7 M_⊙ (see Fig. 9). The black dots in the bottom left panel are ellipsoidal binaries from the LMC observed from Nie et al. (2017). Almost all the Gaia binaries are located below the threshold period, meaning that the radius of the primary, in all the systems, has not reached its Roche-lobe, that is, the systems are detached (non-contact) binaries. Nonetheless, a large fraction of the ellipsoidal candidates have stellar radii and periods almost at the boundary, consistent with their ellipsoidal nature.

Fig. 9. Masses of the primary, ℳ1, derived using spectroscopic atmospheric parameters and the minimum mass for the secondary star, ℳ2, min, derived based on the orbital period and RV amplitude. The systems are color coded according to their mass function, f(ℳ).

The distribution of orbital periods and eccentricities from the NSS catalog is shown in the middle panels of Fig. 8, color coded according to the primary radius. The black dots in the bottom middle panel correspond to measurements for ellipsoidal variables in the LMC (Nie et al. 2017). The circularization threshold, that is, the period at which the binary system should reach zero eccentricity for two values of the radius, ℛ₁ = 50, 100 R_⊙, and mean values of the masses of the components ℳ₁ = 1.7 M_⊙, ℳ₂ = 0.7 M_⊙ (see Fig. 9) is shown as dotted grey lines for the ellipsoidal binaries. The plot for rotational variables (top) and ellipsoidal (bottom) variables show the effects of tidal circularization of the orbits: systems with shorter periods (P_nss ≤ 100 days) tend to have mostly circular orbits (e ≤ 0.05), while for binaries with longer orbital periods, the eccentricities tend to be higher than circular. In fact, tidally locked variables are expected to have circular orbits, as is the case of rotational variables systems. This effect is expected as the timescale for tidal circularization strongly depends on the radius, particularly for giant stars with radiative envelopes (Mazeh 2008), as well as on the mass ratio of the system. Based on this distribution, adopting an eccentricity of e = 0, for the systems without eccentricities determined in the NSS catalog, seems reasonable.

The right panels of Fig. 8 show the orbital period from the RV curve against the mass function⁴, color coded according to the radius of the primary star. To derive the mass function the eccentricity from the NSS orbital solution was adopted, when available (square symbols), while for those systems without eccentricity estimates a circular orbit was adopted (circles). As shown in Eq. (4), the eccentricity factor in the mass function goes as (1–e²)^3/2, and for eccentricities between zero to 0.3 (middle panels in Fig. 8), the mass function is reduced by 13%. The majority of the systems have an eccentricity lower than 0.1 (see also Fig. 13), which implies a difference of only 0.01% in the mass function. Therefore, the adopted e = 0 should have a small impact on the mass function. The mass function for rotational variables is mostly independent of the radius while the ellipsoidal variables have larger radii as larger is the period, as expected. In the case of rotational variables, given their shorter orbital periods than ellipsoidal variables, to get similar values of the mass function they need to have larger RV semi-amplitudes (see Fig. 10 in Gaia Collaboration 2023c).

4.2. Minimum mass estimates for the secondary star

The mass of the secondary star in the binary can also be estimated through its mass function (see Eq. (4)), expressed as

$$\begin{array}{c}\hfill \frac{P{K}_1^3{(1-e^2)}^{3/2}}{2\pi G}=\frac{M_2^{3}sin{i}^3}{{({\mathcal{M}}_1+{\mathcal{M}}_2)}^2}\text{.}\end{array}$$(6)

Using P_VR as the orbital period and the amplitude_rv as K₁, Eq. (6) can be numerically solved to get an estimate of ℳ₂ sin i. The inclination of the binary is not known; therefore, an edge-on orientation (i = π/2) corresponding to the maximum value for sin i was adopted. In this case, the mass function of the system corresponds to the maximum value and the mass of the secondary obtained corresponds to the minimum mass ℳ_2, min. It is worth mentioning that if the inclination is edge-on, the systems would be eclipsing binaries, which is not the case according to the Gaia variability classification of all the sources in our sample as LPVs. Although, given the cadence of Gaia observations, some eclipsing binaries could have not been detected (see, e.g., Rowan et al. 2024). Therefore, the minimum mass should be considered as a strict lower limit. The errors on the secondary minimum mass were obtained through 1000 Monte Carlo simulations sampling the errors in the period and the mass of the primary. As the error for the amplitude of the RV is not reported in the Gaia FPR table, the possible contribution of this measurement error is not considered.

Figure 9 shows the mass of the primary ℳ₁ versus the minimum mass of the secondary ℳ_2, min, color coded according to their mass function f(ℳ). The top panel shows the rotational candidates while the ellipsoidal variables are shown in the bottom panel. For reference, the masses of both components for ellipsoidal variables in the LMC are shown as grey dots (Nie et al. 2017). Overall, the masses recovered for the ellipsoidal variables in Gaia are similar to those observed in the sample for LMC ellipsoidal variables, despite the fact that the latter has the mass of the companion estimated, including the inclination of the orbit, and not the minimum mass, as it is our case. For a fixed mass function value, the mass of the primary and minimum mass of the secondary have a strong correlation, which is most likely the result of adopting a fixed inclination value. A high fraction of the systems have a minimum mass for the secondary component lower than 1.0 M_⊙, indicating that possibly the companion could be a stellar remnant (either a white dwarf or a neutron star) or a low-mass main-sequence star. Binaries having a white dwarf and a red giant companion are considered as one possible channel of the single-degenerate scenario to the formation of Type Ia SNe (Branch et al. 1995; Liu et al. 2019, 2023). Theoretical predictions for the evolution of red giant plus white dwarf binaries (Liu et al. 2019; Ablimit et al. 2022) predict a possible Type Ia SN in systems that have a secondary mass greater than 0.9 M_⊙ while having orbital periods shorter than 100 days, as is the case for several ellipsoidal candidates of the present study.

The masses for the primary and secondary components of the rotational binaries are restricted to ≲3 M_⊙ and ≲1 M_⊙, respectively. This is consistent with a primary star that is a subgiant while the secondary is a main-sequence star.

4.3. Maximum mass estimates for the secondary star

In an attempt to constrain, as much as possible, the mass of the companion, an estimate of the maximum value for the inclination was derived. Following Mahy et al. (2022), we estimated the critical rotational velocity of the primary star (see their Eq. (3)) and used the spectral line broadening estimate (vbroad from Gaia DR3) as an upper limit for the v sin i. This relation is only valid if the orbital and rotational axes are aligned, which is a reasonable assumption since both synchronization and alignment of binary systems are reached in a shorter timescale than circularization (see, e.g., Hut 1981; Glebocki & Stawikowski 1997; Mazeh 2008; Daher et al. 2022). Based on this, a minimum value for sin i is derived. This implies a minimum value for the mass function and therefore an upper limit for the mass of the companion.

The left panel in Fig. 10 shows the dependence of the secondary mass on the inclination values for one ellipsoidal candidate, Gaia DR3 178734862161885440. The minimum mass corresponds to the value obtained for sin i = 1, while the maximum mass corresponds to the minimum inclination, based on the measured broadening velocity. Both values are reported in the top right corner of the panel. The uncertainty in the minimum inclination (horizontal dashed orange lines), which is obtained through the error propagation of the primary mass and radius, is significant and allows for the mass of the secondary to range from ∼1.5 M_⊙ up to ∼4.3 M_⊙. The inclinations recovered are a lower limit and certainly represent much lower values than inclination values derived for ellipsoidal variables in the literature (Nie et al. 2017; Wrona et al. 2022). Therefore, the obtained maximum mass for the companion could be largely overestimated when the minimum inclination is too low (i_min ≤ 30 deg).

Fig. 10. Dependence of the mass of the secondary component as a function of the inclination of the binary. Left panel: Secondary mass versus inclination for Gaia DR3 178734862161885440 ellipsoidal candidate. The black vertical line marks the minimum mass computed, for sin i = 1, while the dashed vertical line is its associated error. The horizontal orange line is the minimum inclination of the system, while the dashed orange lines are the inclination error. In the top right corner, the minimum mass and the mass obtained from the minimum inclination are reported. The area under the curve corresponds to the range of masses possible for this system. Right panel: Minimum secondary mass versus the maximum secondary mass. The color coding is based on the minimum inclination of the system.

The subsample of stars for which a maximum for the secondary mass can be estimated is shown in the right panel of Fig. 10. The minimum and maximum mass for the companion are shown, color coded based on the minimum value for the inclination. Depending on the minimum inclination, the range of values for the mass of the companion is wide and it is not possible to constrain it. There is a small subsample of systems that have a minimum and maximum mass for the secondary component relatively constrained (i.e., ℳ₂(i_min) − ℳ_2,min < 1.0 M_⊙), most of them having a minimum value for the inclination of i ≳ 30 deg.

For ellipsoidal binaries in which the maximum mass of the secondary star is ≤ 1.2 M_⊙, some models for the evolution of binaries place them as potential Type Ia SNe progenitors. Figure 11 shows the orbital period against the mass of the primary, while the minimum mass for the secondary is shown in the color bar. The parameter space inside which a binary system having a red giant as primary star and white dwarf as a secondary, for different initial masses of the white dwarf, is shown as brown solid line (from Liu et al. 2019) and black and grey dashed lines (from Ablimit et al. 2022). There are 13 ellipsoidal binaries inside the boundaries from the literature and having ℳ_2, max up to 1.2 M_⊙. Despite the range of primary masses and periods changes depending on the model, the ellipsoidal binary sample studied in this work may contain promising binary systems to follow-up as potential Type Ia SNe progenitors, particularly those with orbital periods of less than 400 days and ℳ₁≤ 2.0 M_⊙.

Fig. 11. Orbital period versus the spectroscopic mass of the primary, ℳ1. The colors are based on the minimum mass of the secondary star, ℳ2, min. The boundaries for potential Type Ia SNe progenitors in red giant stars and white dwarf binaries from Liu et al. (2019) and Ablimit et al. (2022) are shown as solid and dashed lines. The ellipsoidal binaries with a ℳ2, max ≤ 1.2 M⊙ are marked with black pentagons.

4.4. Mass ratio and filling factors

The “minimum” mass ratio q ≡ ℳ_2, min/ℳ₁ as a function of the filling factor, f_filling (the ratio between the radius of the primary star and its Roche-lobe radius) is shown in Fig. 12, for rotational (blue squares), and ellipsoidal candidates (pink circles). Ellipsoidal binaries having a difference in the maximum and minimum secondary mass being ≤1 M_⊙ are shown colored based on the average secondary mass, and their mass fraction is estimated based on this ℳ_2, average. Uncertainties are estimated based on error propagation, including the error on the radius, mass of the primary, minimum mass of the secondary, and orbital period.

Fig. 12. Filling factor versus mass-ratio for rotational candidates (blue squares) and ellipsoidal variable candidates (pale pink circles). For the systems in which the difference between the maximum and minimum mass for the secondary is lower than 1.0 M⊙, the data points are color coded by the average between the maximum and minimum secondary mass, and their mass ratio corresponds to that average mass for the secondary.

The Roche-lobe radius R_1,RL was derived based on Eq. (2) from Eggleton (1983) as

$$\begin{array}{c}\hfill \frac{R_{1,\mathrm{RL}}}{a}=\frac{0.49q^{-2/3}}{0.6q^{-2/3}+ln(1+q^{-1/3})}\text{,}\end{array}$$(7)

where a is the semi-major axis of the system. This approximation is valid for circular orbits. In eccentric binaries, the Roche-lobe radius depends on the instantaneous separation between the two stars, being minimum at periastron and maximum at apastron. For the present analysis, we considered a circular orbit for all the stars, which implies that for eccentric orbits, the Roche-lobe radius and filling factor estimates will be an average value.

The projected semi-major axis, a sin i, can be obtained from the projected semi-major axis of the primary star a₁ sin i as

$$\begin{array}{cc}\hfill a_{1}sini& =\frac{K_{1}P\sqrt{1-e^2}}{2\pi }\hfill \\ \hfill asini& =\left(\frac{{\mathcal{M}}_1+{\mathcal{M}}_2}{{\mathcal{M}}_2}\right)a_{1}sini.\hfill \end{array}$$(8)

Adopting the maximum value for the sin i ≡ 1, an estimate of the maximum semi-major axis, under the assumption of circular orbit, can be obtained as well as the corresponding maximum Roche-lobe radius R_1, RL and a minimum value for the filling factor f_filling≡ R₁/R_1, RL. In eccentric orbits, the minimum orbital separation would be r_peri = a(1 − e) when the Roche-lobe radius shrinks, and mass transfer is more likely to occur. In this case, the maximum value for the filling factor would be larger than the value we obtained assuming circular orbits and sin i ≡ 1. Adopting a zero eccentricity for eccentric orbits is similar to adopting a median orbital separation r = (r_peri + r_apo)/2 ∼ a to estimate the filling factor.

Figure 12 shows that rotational binaries show a cut-off in the mass ratios and filling factors of around ∼0.75, while ellipsoidal variables reach higher values, as expected since the former does not show signs of ellipsoidal modulation due to the deformation of the primary star. They all have filling factors smaller than unity, meaning the systems are not in contact. On the contrary, the ellipsoidal candidates span a much larger range of mass ratios and filling factors, even reaching the region in which the secondary star has a larger mass than the primary (q > 1, three binaries) or those where the primary star has reached the Roche-lobe radius, and therefore the systems could be in contact (f_filling > 1). Ellipsoidal binaries having ℳ_2, min≥ ℳ₁ could be due to secondary stars being either massive main-sequence stars or compact objects (Price-Whelan et al. 2020), which can be massive but not contributing to the flux in the spectrum (single-line spectroscopic binaries). Another possible scenario would be that these systems are in the process of mass transfer, as is the case of semi-detached binaries. Two of these three systems have filling factors of the order of 0.6, meaning that they are most likely not in contact, while there is one ellipsoidal binary with larger than unity filling factor and mass ratio (Gaia DR3 1107618979843202944). 20 ellipsoidal candidates have f_filling ≥ 1; that is, the radius of the primary is larger than the Roche-lobe radius, and therefore they could be non-detached binaries. A small subsample of potential contact binaries was recovered as well in the analysis of single-line spectroscopic binaries in the APOGEE survey (Price-Whelan et al. 2020). Unfortunately, without the orbital inclination, these values are only upper limits; therefore, it could be the case that these systems are detached ellipsoidal variables, as the rest of the sample.

The filling factor should be correlated with the tidal circularization time of the orbit, which goes as (R₁/a)⁻⁸. The orbital separation a sin i can be expressed as a function of the Roche-lobe radius R_1, RL (see Eq. (7)). This implies that systems having larger filling factors are closer to reach the eccentricity zero, while non-circular binaries will tend to have smaller filling factors. In the case of eccentric orbits, the instantaneous filling factor will be larger at apoastron and smaller at periastron (see unfilled circles in Fig. 13), and therefore, adopting an eccentricity of zero in those binaries to derive the filling factor gives a more representative estimate of the average value along the orbit. The orbital period of the system (proportional to the radius of the primary stars) also plays a role in the circularization time. We combined this information in Fig. 13 where the eccentricity is shown as a function of the filling factor, and orbital period. The distributions of filling factors (for the full sample for which we have radii and masses) and only those that have eccentricity estimates available are shown as white and grey histograms, respectively, in the top panel. The eccentricity distribution is shown in the right horizontal panel. The dependence on the filling factor to have circular orbits is clearly seen, as the distribution of eccentricities tends to decrease as the filling factor increases. The period dependence is seen as those systems having shorter periods (smaller orbital separations) are those with larger filling factors.

Fig. 13. Filling factor ffilling versus eccentricity for a subsample of ellipsoidal variables. The data points are color coded based on the orbital period. For the most eccentric binaries, the filling factor at apo- and periastron is included as unfilled circles, connected to the average value obtained considered a zero eccentricity. The top and right panel shows the distribution (gray histogram) of filling factors and eccentricities, respectively. The top panel includes the distribution of filling factors for all the ellipsoidals having reliable measurements for their radii (black-edge histogram).

Table E.2 lists the minimum mass for the secondary component, obtained by solving numerically the mass function (Eq. (4), adopting sin i = 1) and its standard deviation obtained through Monte Carlo simulations, the maximum value for the mass of the secondary companion, obtained using the broadening velocity (see Sect. 4.3), and its propagated uncertainty, the minimum mass ratio q, and the filling factor (adopting a zero eccentricity) and their associated uncertainties. Binary systems for which there is no broadening velocity published in Gaia DR3 or for which the estimate is a non-physical result (negative masses, relative errors larger than one) do not have a maximum mass estimate in the Table.

5. Chemo-dynamical population properties

5.1. Metallicity distribution function

The distribution of spectroscopic [M/H] from GaiaGSP-Spec is shown in Fig. 14 for ellipsoidal candidates (aquamarine filled histogram). Only observations having the flag vbroadM < 2 and vradM < 2 have been included, meaning that the potential biases due to uncertainties in the rotational and RV shifts account for Δ[M/H] < 0.5 dex (see Tables C.1 and C.2 in Recio-Blanco et al. 2023). The error in metallicity, derived as half the difference between the upper and lower values reported by the GSP-Spec module, was also restricted to be less than 0.1 dex. The distribution is mostly metal-poor, having a peak at ∼−0.35 dex, and a dispersion of 0.4 dex. GaiaGSP-Spec metallicities, without a restriction in KMgiantPar, were preferred against XGBoost metallicities as the latter is less accurate at [M/H]<  − 1 and cool giants, due to the limitations of the training sample (Andrae et al. 2023). For a comparison between the metallicities from XGBoost and GSP-Spec, see Appendix F.

Figure 14 includes the metallicity distribution of the giant-dwarf and giant-giant SB1 binaries (dashed orange line) from the Galactic Archaeology with HERMES (GALAH) survey (Traven et al. 2020) and the close giant binaries from APOGEE (purple dotted line, from Price-Whelan et al. 2020). Only binaries having the same range of effective temperature and surface gravities as our sample of ellipsoidal variables were selected. The metallicity distribution of ellipsoidal candidates based on Gaia measurements is similar to the one derived based on GALAH and APOGEE observations, with a broad, metal-poor distribution, closely resembling the MDF measured by APOGEE although without ellipsoidal binaries as metal-poor as [M/H] ≤ −1.5 dex. It is worth mentioning that different surveys have different limiting magnitudes and, therefore, probe up to different Galactocentric radii, implying possible metallicity biases. Moreover, some metal-poor stars may not be recovered as such by GaiaGSP-Spec (see Gaia Collaboration 2023b; Matsuno et al. 2024). Thus, the discrepancies found might not be due to an intrinsic difference among the binary populations, and, overall, the GaiaGSP-Spec metallicities for the ellipsoidal samples seem to be in fair agreement with independent MDF for single-line spectroscopic binaries with a giant as a primary star.

Fig. 14. Metallicity distribution function of ellipsoidal candidates having vbroadM < 2, vradM < 2, and Δ[M/H] ≤ 0.1 dex from Gaia RVS spectra (aquamarine filled histogram), SB1 stars from the GALAH survey (dashed orange line), and APOGEE close giant binaries (purple dotted line).

5.2. [α/Fe] – [M/H], Galactic velocities

With the astrophysical parameters derived as part of the GaiaGSP-Spec module, the properties of ellipsoidal and rotational binaries can be analyzed in the context of Galactic stellar populations. Figure 15 shows the [α/Fe] versus [M/H] plane for ellipsoidal variables, color coded according to the orbital period P_VR (top panel) and mass of the primary (bottom panel). The same restrictions in metallicity error and vbroadM and vradM quality flags as in the previous section were applied. The sample is further reduced compared to previous plots as only stars with KMgiantPar = 0 are included, since for stars with KMgiantPar = 1 or 2, no [α/Fe] estimate is available in Gaia DR3.

Fig. 15. [α/Fe] versus [M/H] (from GSP-Spec) for ellipsoidal candidates. In the top panel, the points are color coded according to their orbital period. Solar values are marked with dotted gray lines. In the bottom panel is the same sample, but the color bar corresponds to the spectroscopic mass of the primary. The YAR stars from Jofré et al. (2023) based on APOGEE observations are included as squares; those with a red cross mark are spectroscopic binaries.

The distribution of periods and metallicities in the top panel of Fig. 15 shows that most of the shortest-period ellipsoidal binaries are metal-rich and non-α enhanced, while those with the largest periods are mostly metal-poor ([M/H] ∼ –0.5 dex) and α-enhanced with respect to the solar value. Such an α-enrichment level, at a given metallicity, is consistent with the disk population, although at the low metallicity tail, some stars could be part of the halo population. To the best of our knowledge, this is the first time that the [α/Fe]–[M/H] diagram has been presented for ellipsoidal binary stars.

It is also worth noting that some of the α-enhanced stars have masses greater than one solar mass, resembling the population of young α-rich (YAR) stars in the thick disk. These stars were originally considered young systems due to their intermediate mass and enhanced [α/Fe], consistent with relatively old ages. Most of these systems have been found to belong to binary systems (Jofré et al. 2023) and their chemical enrichment is likely due to mass transfer. The bottom panel in Fig. 15 shows the spectroscopic mass estimate for the primary, along with the sample of YAR stars from Jofré et al. (2023), based on APOGEE measurements for the abundances, including those spectroscopically confirmed to be binaries. Our population of ellipsoidal binaries, particularly those with the shortest periods, has [α/Fe] abundances consistent with YAR stars, which may imply that some of these systems have already experienced mass transfer events that enriched the chemistry of the current primary star.

Combining the chemical information with the kinematics, Fig. 16 shows the Galactic spherical velocities, metallicities and α-element abundances for ellipsoidal variable candidates. The Galactic velocities and Zmax of the orbit, as well as their low and upper limits, were retrieved from the gaiadr3.chemical_cartography table, part of Gaia DR3 (see the description of the catalog in Gaia Collaboration 2023b)⁵. The top panel shows the azimuthal velocity V_ϕ versus the tangential velocity component $V_{\perp }=\sqrt{V_R^2+V_Z^2}$, color coded by the maximum Z above the plane, for ellipsoidal (circles) and rotational binaries (squares), without applying any cut in the quality of the atmospheric parameters. The middle and bottom panels present only ellipsoidal candidates having a metallicity error < 0.15 dex from the GSP-Spec module, color coded based on their [M/H] (middle panel) and [α/Fe] (bottom panel) calibrated abundances. The dashed circular line corresponds to the boundary inside which resides the disk population, that is, $\sqrt{V_R^2+V_Z^2+{(V_{\varphi }-V_0)}^2}<210$ km s⁻¹, where V₀ = 238.5 km s⁻¹, as in Gaia Collaboration (2023b). From the kinematics, it is clear that all the rotational binaries are part of the disk population, having all prograde circular V_ϕ velocities, centered around ∼220 km s⁻¹. In the literature, a sample of eight rotational RS CVn systems having chemo-dynamical information has also been found to be all disk population by Morel et al. (2004) while there is only one known RS CVn system in the halo (Bubar et al. 2011). The effect of the induced activity can severely affect the metallicities and [α/Fe] abundances of rotational, close-binaries, and therefore we do not aim to see any trends in chemo-dynamical space for these stars.

Fig. 16. Toomre diagram. Top panel: Ellipsoidal and rotational binary candidates. The color coding is according to the maximum height from the Galactic plane Zmax. Middle panel: Ellipsoidal candidates only. The candidates are color coded based on their spectroscopic metallicity [M/H] (middle panel). Bottom panel: Abundance of [α/Fe]. The dashed circle marks the kinematics of the Galactic disk at $\sqrt{V_R^2+V_Z^2+{(V_{\varphi }-V_0)}^2}<210$ km s−1.

The chemo-dynamical properties of ellipsoidal variables are much more varied: the kinematics are consistent with thin/thick disk as well as halo populations. As expected, the stars having halo-like kinematics are the most metal-poor of the sample, having also relatively high [α/Fe] values. Nonetheless, some systems with kinematics of the disk have the highest α-enhancement. These are the stars with the shortest periods (see Fig. 15) which may indicate that the interaction with the companion star is affecting the measurements of chemical abundances in the primary, as it happens in the case of rotational binaries.

Given that the primary star in the case of rotational variables is less evolved than the one in the ellipsoidal systems (see their location in the Kiel and HR diagram in Figs. 4 and 6, respectively) which, combined with their kinematics and metallicities (mostly consistent with a disk population; see Fig. 16) may indicate a different stellar population also in terms of age. To test this, the velocity dispersion of the sample could be used as an indirect proxy for their relative ages. Figure 17 shows the velocity dispersion, based on the quadratic sum of the velocity dispersion in R, Z, and ϕ directions in bins of primary radius, ℛ₁, which is the physical parameter with the lowest associated error, compared to, for example, the mass of the primary. There is a significant difference in the velocity dispersion of rotational candidates (having P_VR/P_phot∼ 1.0 and radii smaller than 30 R_⊙), being no larger than 30 km s⁻¹. Ellipsoidal variables tend to have an almost flat, much larger velocity dispersion, of the order of 50 km s⁻¹, for radii between 40 to 80 R_⊙. This marked difference in velocity dispersion may indicate that ellipsoidal variables, at least in the current sample, represent an older population than rotational candidates.

Fig. 17. Velocity dispersion as a function of the primary radius in equal bins of width ∼9.0 R⊙. The color bar corresponds to the ratio between the RV and photometric period.

Summarizing, both samples appear to be intrinsically different in terms of radii, Galactic velocities, metallicities, and not only in orbital separations/orbital periods. Even though some outliers could be present in both samples, mostly in the case of poorly sampled light curves, their main stellar properties are markedly different. Nonetheless, we cannot exclude that they are two evolutionary stages of the same phenomenon: a binary in a close orbit in which, depending on the mass and evolution of the primary, can get tidally circularized rapidly, getting a synchronized rotation (induced by the tides) and orbital motion, leading to an enhanced chromospheric activity; or if massive enough and having a larger orbital separation, the system can evolve up to point in which the primary star increases its radius, being able to substantially fill its Roche lobe and get tidally deformed.

5.3. Chemical enrichment: Cerium abundance

From Gaia RVS spectra, chemical abundances for up to 12 elements were derived⁶ in Gaia DR3, including, for example, α-elements ([Mg/Fe], [Si/Fe], [S/Fe], [Ca/Fe], [Ti/Fe]), iron-peak elements ([Cr/Fe], [Ni/Fe]), and heavy-elements ([Zr/Fe], [Ce/Fe], [Nd/Fe]; see Gaia Collaboration 2023b, for a detailed analysis of the abundance distribution of these elements in the Milky Way). Among them, the abundance of Cerium and Neodymium, s-process elements of the second peak, are of great importance during the stellar evolution of single AGB stars as their abundances change depending on the stellar mass, metallicity, mass-loss, and the number of thermal pulses and thermal dredge-up episodes (Contursi et al. 2023, 2024). In the context of binaries, red giant branch or early AGB stars in binary systems having experienced mass-transfer, can also present an overabundance of s-process elements, as is the case of S-stars (Shetye et al. 2018) and Ba-stars (Merle et al. 2016; Escorza et al. 2017; Jorissen et al. 2019). Therefore, the analysis of the Ce abundances, as representative of s-process elements, can shed light on the secondary component; in the case of binaries that went through mass transfer, the former primary (currently the secondary, probably a stellar remnant) was the donor which transferred the mass to the secondary (currently the primary, more luminous component); or could indicate that the current primary star has evolved without any influence from the companion, following the expected evolution of a single AGB star.

Figure 18 shows [Ce/Fe] abundances for the ellipsoidal candidates as a function of different parameters associated to the orbit of the binary (orbital period), chemical abundances of the primary star (metallicity [M/H] and α-element abundances [α/Fe]), and the masses of the system (mass of the primary ℳ₁, minimum mass of the secondary ℳ_2, min, and the mass ratio q ≡ ℳ_2, min/ℳ₁). Stars having a GSP-Spec measurement of [Ce/Fe] abundances without any extra quality cuts are shown as mint circles, in all panels, while those that additionally have good quality flags associated with the determination of the [Ce/Fe] abundances (CeUpLim < 3, flagCeUncer < 2; see Table 2 in Recio-Blanco et al. 2023), vbroad ≤ 13 km s⁻¹, extrapol ≤ 1, and [Ce/Fe] abundance uncertainty ≤ 0.2 dex (see Contursi et al. 2023, 2024) as well as those sources with good metallicity flags (vbroadM, vradM < 2; see Appendix F) are included as purple circles. Ba stars from Jorissen et al. (2019) are also included as empty magenta diamonds and arrows, for those having [Ce/Fe] > 1.2 dex. Overall, the sample of ellipsoidal variables having Ce abundances covered similar ranges of period, primary mass and secondary mass as the sample of Jorissen et al. (2019), although having lower [Ce/Fe] values. This could indicate that our sample is not representative of binaries having experienced s-process enhancement due to mass-transfer.

Fig. 18. [Ce/Fe] abundances as a function of different orbital and stellar properties for ellipsoidal candidates with available measurements. The top row shows [Ce/Fe] against the orbital period (PVR from Gaia FPR, left panel), GSP-Spec calibrated [M/H], and [α/Fe] (middle and right panel, respectively). The bottom row shows the abundance of Cerium as a function of the mass of the primary star ℳ1 (left panel), the minimum mass of the secondary ℳ2, min (middle panel), and the mass ratio q (right panel). In all the panels, only ellipsoidal binaries with good quality flags for the extinction are included (mint circles). Stars following a cut in the [Ce/Fe] and [M/H] quality flags (see the main text) are shown as purple circles. For comparison, Ba stars from Jorissen et al. (2019) having orbital periods of ≤1000 days are included as magenta diamonds and arrows (when their [Ce/Fe] abundance is larger than 1.2 dex).

In terms of the metallicity content, our sample tends to be slightly more metal-poor compared to the measurements in Jorissen et al. (2019). An anti-correlation in the Ce abundance as a function of the metallicity can be seen, being those more metal-rich the ones with the lower values of [Ce/Fe]. This is expected from the AGB evolution, as the production of s-process elements is less efficient in more metal-rich stars (Jorissen et al. 2019; Cristallo et al. 2015; Contursi et al. 2024). However, single AGB chemical evolution models predict different abundances of Ce based on the metallicity, and mass of the AGB star. In particular, the less massive (ℳ₁ ∼ 0.7 M_⊙) star in our sample has an elevated Ce abundance [Ce/Fe] ∼ 0.8, while models predict a much lower Ce overabundance, of the order of ∼0.2 dex, for any metallicity (see Fig. 9 in Contursi et al. 2024). This overabundance of Ce could be the result of a previous episode of mass-transfer, in which the secondary star was in the AGB phase and was the donor of material. Only a handful of sources with [Ce/Fe] measurements have also [α/Fe] abundances determined from GSP-Spec. Despite being limited in number, a tentative positive correlation seems to be present, as the more metal-poor stars are also the ones with higher α-overabundance.

For single AGB star evolution, Contursi et al. (2024) found discrepant results using two different AGB yield models. For solar-mass stars, having [Fe/H] ∼− 0.7, the maximum Ce abundance based on the two models predicted are [Ce/Fe] ≃ 0.2 and ≃0.7 dex. Overall, the abundance of [Ce/Fe] in the sample of ellipsoidal candidates is lower than the predictions for metal-poor, intermediate-mass AGB in the Monash models (Karakas et al. 2018, and references therein) but higher than the predictions of the FRUITY (Cristallo et al. 2015, and references therein) models (see Fig. 9 of Contursi et al. 2024). For stars having primary masses of 2.0 to 4.0 M_⊙, the [Ce/Fe] abundances observed are within the values predicted by the models (see Figs. 9 and 10 in Contursi et al. 2024).

Contursi et al. (2023) found a potential offset of up to 0.2 dex between the mean Ce abundance derived by GaiaGSP-Spec and other spectroscopic surveys (see their Fig. 7), although such an offset is not seen compared to some surveys. Therefore, other chemical abundances, such as Y, Ba and Pb would be useful to determine if the systems have s-process abundances consistent with the evolution of an AGB star, irrespectively of its companion or if the systems have gone through mass-transfer events.

6. Period-luminosity relations

Ellipsoidal variables are known to define a linear sequence in the period-luminosity (absolute magnitude) diagram, first detected in the LMC as the sequence E (Soszyński et al. 2004, 2007). In the Milky Way, this relation has not been explored beyond the Galactic bulge region (see, e.g., Wrona et al. 2022), as this requires the knowledge of a large sample of ellipsoidal variables with known distances. Gaia DR3 provides photo-geometric distances for hundreds of ellipsoidal variables, allowing us to study this relation for the Galactic population. In this section we aim to probe the effects of different parameters that are available thanks to the Gaia observations into the period-luminosity relation of ellipsoidal variables and its intrinsic dispersion.

Figure 19 shows the orbital period against the luminosity for ellipsoidal binaries. The top panel shows the ellipsoidal stars in this plane, colored according to the mass of the primary star. It reveals that the faintest systems have mostly lower masses, while the brighter systems, for a given period, are those with the largest masses. A few outliers at L/L_⊙ ≤ 10² could have an erroneous period determination. Excluding those, the trend in mass is striking. This is an expected behavior as more massive systems have larger orbital separations a for a given period, making only the larger, more luminous primary stars detectable as ellipsoidal variables due to their ellipsoidal distortion. The same trend, although restricted to ∼80 stars, was observed in the sample of ellipsoidal variables in the LMC in Nie et al. (2017). For reference, we fitted a straight line to the low-mass (≤1.85 M_⊙) ellipsoidal binaries in Nie et al. (2017), similar to their Fig. 7 but the fit was done directly into luminosity instead of I magnitude. Our sample covers a larger range in period than the sample in the LMC but overall, for the low-mass systems, the slope of the period-luminosity sequence agrees, having a non-negligible population of low-mass binaries having lower luminosities than the fit, as in Nie et al. (2017).

Fig. 19. Period-luminosity diagram for the ellipsoidal candidates. The colors are based on the primary mass (top panel) and filling factor (bottom panel). We note that both color bars are shown in logarithmic scale. Systems having a filling factor larger than one are shown as unfilled circles. In both panels, the black dashed line corresponds to the fit to the sample of low-mass ellipsoidal variables in Nie et al. (2017).

Another parameter that could impact the period-luminosity sequence of ellipsoidal variables is the filling factor. For a given period and mass, there is a range of possible values for the filling factor under which the systems will undergo ellipsoidal variations. The bottom panel of Fig. 19 shows the Galactic ellipsoidal binaries color coded according to the filling factor (see Sect. 4.4). The same trend as in Nie et al. (2017) is recovered: the brighter systems tend to have larger filling factors, at a given period. This effect introduces a mass dispersion that produces an intrinsic scatter in the period-luminosity sequence of ellipsoidal stars. Systems with larger filling factors will also have circular binary orbits, while the fainter binaries with lower filling factors should have non-circular orbits.

In the study of Nie et al. (2017), some low-mass systems (ℳ₁ ≤ 1.85 M_⊙) were found at the higher luminosity side of the period-luminosity sequence, possibly a consequence of being more metal-poor. More metal-poor stars, at a given period, will be smaller in radius, and therefore, only the bigger, more luminous low-mass stars will be detected as ellipsoidal variables. Figure 20 shows the systems in the period-luminosity diagram colored according to their GaiaGSP-Spec metallicity, while the size of the symbol is proportional to the mass of the primary star. Unfilled circles are for those systems that do not pass the metallicity quality cuts (the same as the ones applied in the Fig. 14). There are some indications of the predictions in Nie et al. (2017), as for a fixed period and low mass, the brightest systems are more metal-poor. Nonetheless, the number of metal-poor, low-mass ellipsoidal variables among the high luminosity end of the period-luminosity sequence is quite limited and the strongest dependence for the luminosity is on the mass of the primary star.

Fig. 20. Period-luminosity diagram for ellipsoidal candidates with a reliable metallicity estimate based on Gaia RVS spectra (derived by the GaiaGSP-Spec module). The size of the symbol corresponds to the mass of the primary star. Ellipsoidal variables without a reliable metallicity estimate (see Sect. 5.2) are shown as gray dots of equal size.

In the case of rotational candidates, we do not find a relation between the mass and the dispersion of the linear period-luminosity sequence, as it is visible in Fig. 1. This means that the larger in radius and therefore more luminous a rotational binary is, the more slowly it rotates. Hints of this relation are possibly found in Muraveva et al. (2014), without presenting a discussion about the origin of this sequence, as well as in Martínez et al. (2022), where a sample of RS CVn systems were analyzed in terms of their activity cycles and rotational periods.

7. Summary

In this work, we derived the physical parameters (luminosities, radii, and masses) as well as orbital and chemo-dynamical properties of long-period red giant binary stars. Our input sample consisted of more than 400 red giant binaries for which both photometric and RV time series were available as part of Gaia FPR (Gaia Collaboration 2023c).

The input sample comprised two types of binaries: ellipsoidal red giants and rotational binaries. The separation boundary of the subtypes was constrained by considering the ratio between the orbital and photometric periods; both values were derived in the Gaia FPR (Gaia Collaboration 2023c) as well as through a visual inspection of the phase-folded G-band light curves. Even though we have shown that most of the periods are in good agreement with the literature, we cannot rule out having ellipsoidal binaries with erroneous photometric or orbital periods among the rotational sample. Considering the similar distribution in the period-radius-eccentricity plane (see Fig. 8), the two samples appear to be the manifestation of the same physical configuration under two different regimes: a subgiant and a giant primary star, respectively, for rotational and ellipsoidal binaries with different orbital separations. Therefore, the variability of the rotational sample may not be due to an enhanced rotation but instead produced by the geometrical effect of a less pronounced ellipsoidal deformation (see Fig. 12). Nonetheless, the enhanced activity index in some of the rotational candidates (see Fig. 3) supports the scenario in which these binaries are chromospherically active due to enhanced rotation in a close binary, which is a variability phenomenon different from the case of ellipsoidal variables. Moreover, we confirmed that the location of the rotational candidates on the 2MASS near-IR CMD coincides with the group of RS CVn stars identified in Phillips et al. (2024) based on a sample of 50 000 rotational variables. The position in the CMD as well as their period range are consistent with the compilation of RS CVn variables in Leiner et al. (2022). Our main findings for rotational and ellipsoidal binary candidates are summarized below.

Rotational variables: Although the sample contains less than 50 stars, they appear to differ from ellipsoidal variables when considering the period range, independent period-luminosity sequence, and (most importantly) enhanced stellar activity. We find that the enhanced activity prevents the use of atmospheric parameters from the GSP-Spec module, and instead, the parameters from the XGBoost catalog based on spectro-photometric XP spectra are favored. We find that the sample of rotational variables has stellar radii between 5 to ≲30 R_⊙ and primary masses from less than one solar mass up to no more than 3 M_⊙. The minimum masses for the secondary components are below 1.0 M_⊙. In terms of the orbital properties, almost all of these variables have circularized orbits. Their kinematics reveal that they are concentrated in the Galactic disk, having preferentially a low velocity dispersion. This can be associated with a relatively younger population, at least when compared to the ellipsoidal binaries.

Ellipsoidal binaries: Physical parameters were derived for 243 ellipsoidal binaries, the largest collection with spectroscopically derived luminosities and masses. The previous largest collection with photometric and spectroscopic data comprised 81 ellipsoidal binaries in the LMC (Nie et al. 2017). The properties of our sample confirm their nature as ellipsoidal binaries since the period-radius distribution is at the edge of reaching the Roche lobe radius, with filling factors as large as unity. As expected, the larger the orbital period, the larger the radius. The eccentricities are close to zero, which is in contrast with the measurements for ellipsoidal binaries in the LMC that reach much larger values. This could imply different tidal circularization rate efficiencies (see Sect. 5 in Nie et al. 2017). The primary stars are mostly low- and intermediate-mass giants, covering a wide range from 0.4 up to 6.0 M_⊙. The minimum mass of the secondary component was found to be ≲1.0 M_⊙, which is consistent with a possible compact remnant star. The chemo-dynamics of the sample are consistent with both Galactic disk and halo stars. Some stars have enhanced [Ce/Fe] abundances, suggesting that they may be the result of a previous mass transfer, similar to the scenario of enrichment in Ba-stars. The dispersion in the period-luminosity relation of ellipsoidal binaries appears to depend primarily on the mass and filling-factor, rather than on metallicity variations.

Despite the separation of the input sample into rotational and ellipsoidal binaries, the mean stellar properties (masses, radii, and luminosities) and chemo-dynamical parameters of the binaries lead us to propose them as two manifestations of a close binary in which the primary star is a red giant (or subgiant star) with a low-mass companion where, depending on the mass of the primary and orbital separation, the tidal synchronization, or the ellipsoidal deformation takes place. Instead of considering both types of binaries as separate and unrelated classifications, this analysis has shown their connection as two evolutionary stages of the same phenomenon.

Together with this article, we release the sample of 243 ellipsoidal binaries and 39 rotational binary candidates, and we include the extinction A_G, luminosity, radius, and the spectroscopic mass of the primary component as well as the estimate for the minimum mass of the secondary component, mass ratio, and filling factors. This large sample can significantly contribute to the population studies of these two binary types as well as to future spectroscopic follow-up campaigns that seek to fully characterize these binaries.

Data availability

Tables E.1 and E.2 are available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/696/A82

Acknowledgments

The authors would like to thank Dr Márcio Catelan and the anonymous referee for their constructive comments that helped to improve this manuscript. 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. C.N. would like to thank Henry Lung, for the development and update of the mw-plot package https://milkyway-plot.readthedocs.io/en/stable/ used to produce the Figure 5. This work made use of the cmastro package https://github.com/adrn/cmastro. C.N acknowledges financial support from the Centre National d’Études Spatiales (CNES) fellowship. A.E. received the support of a fellowship from the La Caixa Foundation (ID 100010434) with fellowship code LCF/BQ/PI23/11970031.

References

Appendix A: Photometric periods in the literature

Figure A.1 shows the photometric periods from Gaia FPR against the literature periods from the catalog of Gavras et al. (2023) for all the binary candidate stars in common (239 out of 462), showing the good agreement of the Gaia periods, even at periods longer than 300 days. There is a fraction of stars that have twice the period reported in Gaia and only a handful of them have periods in the literature that are almost half of the Gaia period, which could place them in the sequence for ellipsoidal variables (P_VR/P_ph ≃ 2).

Fig. A.1. Gaia FPR photometric period, Pph, versus literature periods compiled in Gavras et al. (2023). The stars are color coded according to the ratio between the RV period and the photometric period. The dashed lines correspond to Plit/Pph = 2 and 0.5, while the solid line corresponds to the 1:1 relation.

From the stars with P_VR/P_ph ≃ 1, there are literature periods for 22 out of 42 stars. Only four stars have periods that are either 2, 3, or 4 times the Gaia P_ph, and one has half the Gaia period⁷. A second search was made in the databases of different variability surveys, either through the Gaia source ID and/or the equatorial coordinates. Literature periods were recovered for seven stars not included in Gavras et al. (2023), all being the same or double the Gaia P_ph value, as listed in Table A.1.

There is a good agreement in the Gaia periods from FPR and those reported in the literature, although in a few cases, the phase coverage and number of epochs could prevent the recovery of the true period, obtaining instead twice or half of it. The modeling of the individual light curves and period determination is out of the scope of this paper, but we visually inspected all the sources to identify clear misclassified sources, and removeed highly uncertain cases from the analysis.

Appendix B: Surface gravities

In Sect. 2.2, stars with shorter periods and enhanced chromospheric activity are found to have overestimated spectroscopic log g from Gaia RVS spectra. Figure B.1 shows the (calibrated) log g estimates from GSP-Spec compared to the inferred values from XGBoost, for stars with good quality flags from GSP-Spec (KMgiantPar = 0), both for the sources having log g≤ 2.2 (cyan points) and those with potentially overestimated log g values (purple points). In the figure, the stars having an entry for the activity index in Gaia DR3 are colored based on log R_IRT. The good agreement between the GSP-Spec and XGBoost values at log g≤ 2.2 makes us use this boundary to select atmospheric parameters from GSP-Spec. In the rest of the cases, the atmospheric parameters from XGBoost were adopted.

Fig. B.1. Comparison between the log g values for stars with KMgiantPar = 0 as derived in GSP-Spec (calibrated based on the Teff) and in the XGBoost catalog. Cyan and purple circles correspond to stars with GSP-Spec calibrated surface gravities smaller and larger than 2.2 dex, respectively. In the later, the XGBoost parameters were adopted. The activity index (available for a subsample of sources) is shown in the color bar. Stars having overestimated GSP-Spec surface gravities are precisely those sources with enhanced activity.

Appendix C: Notes on individual systems

Gaia DR3 517611939345861120: This star has a period ratio of P_VR/P_ph ≃1.0 and therefore can be discarded as an ellipsoidal binary. However, its absolute magnitude M_G = −4.63 mag and color (BP-RP)₀ = 0.66 mag are not consistent with a red giant. Their atmospheric parameters from GSP-Spec are (T_eff, log g, [M/H]) = (6025 ± 169 K, 1.56 ± 0.9 dex, −2.28 ±0.4 dex) having KMgiantPar = 0 (i.e., good parametrization of the RVS spectrum, Recio-Blanco et al. 2023). Its low metallicity is consistent with the reported value based on BP/RP spectra from XGBoost, [M/H] = −2.12 ±0.1 dex (T_eff = 5258.7 K; log g = 1.948 dex). Based on the GSP-Spec atmospheric parameters, its spectroscopic mass should be of ∼5.8 M_⊙, overly large for its metallicity, but appropriate for its luminosity. Nonetheless, the error on the mass is quite large, having a lower value (16th-percentile) of 0.8 M_⊙ and upper value (84th percentile) of 21.2 M_⊙. If the atmospheric parameters from XGBoost are used, a larger mean mass is recovered: 16${}_{-4.1}^{+5.7}$ M_⊙. Based on its position in the period-luminosity diagram (see Fig. 1), its absolute magnitude is ∼4 mag brighter than the rest of non-ellipsoidal, rotational candidates at the same period. We believe this star is a genuine massive giant, much hotter than the rest of the sample, with an erroneous metallicity estimate. Figure C.1 shows the HR diagram position for this star compared to the rest of the sample. Evolutionary tracks from the grid computed by Lagarde et al. (2012) for stars with initial masses of 1 M_⊙ and 6 M_⊙ and different metallicities are included. The position of this star in the HR diagram is consistent with the evolutionary track of a 6 M_⊙ star with [Fe/H] ≃ −1, in the prescription that includes both thermohaline convection and rotation-induced mixing. Further spectroscopic observations of this system are required to establish its nature.

Fig. C.1. HR diagram for Gaia DR3 517611939345861120 (star symbol) along with the rest of the sample of red giant binaries, color coded by their spectroscopic mass. The grey lines correspond to radii of 1, 10, 30, 60, 90, 120, 150, 180 R⊙. Different evolutionary tracks from STAREVOL (Siess et al. 2000) have been included.

Appendix D: Overestimated spectroscopic masses

The spectroscopic masses derived in this work strongly depend on the surface gravity values’ accuracy. To confirm that the values for the masses are within the range expected given the effective temperature and luminosity measured, we compare the HR diagram of those sources having the largest masses ℳ₁≥ 5.0 M_⊙ with the expected luminosity for its given mass based on evolutionary tracks. Stars with lower masses are well within the expected position in the HR diagram (see the middle panel in Fig. 6).

Figures D.1, D.2, and D.3 show the HR diagram for those massive sources, showing both the GSP-Spec and XGBoost temperatures and luminosities (if available), STAREVOL (Siess et al. 2000) evolutionary tracks derived by Lagarde et al. (2012), for the closest metallicity and mass to our measured values and, indicating, in the title of each panel, the corresponding spectroscopic mass according to the parameters adopted, and its metallicity. In most of the cases, given the good match between the mass derived from XGBoost with respect to the evolutionary track, this spectroscopic mass was adopted even though there are atmospheric parameters measured from RVS spectra. The main culprit of the different masses is large differences in spectroscopic surface gravities.

In the case of Gaia DR3 2032380792212524800, the mass obtained based on the XGBoost parameters is in much better agreement with the evolutionary tracks than the corresponding to the GSP-Spec parameters. However, the determination of the reddening was flagged as inaccurate, and therefore, the source was removed from the final sample.

From the ellipsoidal binary sample, two sources were discarded based on the poor precision associated with their spectroscopic masses (mass uncertainty larger than the median mass value). These two sources are Gaia DR3 2216128156091604352 and 5215777399156162304. Their large errors in mass are due to the large error (≳0.4 dex) in the surface gravity measurement from GSP-Spec compared to the rest of the sample having mean log g uncertainty of 0.07 dex.

Fig. D.1. HR diagram for sources having spectroscopic masses ℳ1≥ 5.0 M⊙ and the closest STAREVOL (Siess et al. 2000) evolutionary tracks from Lagarde et al. (2012). The spectroscopic masses and metallicities from GSP-Spec and XGBoost (if available) are in the title of each panel. The parameters from XGBoost and the associated mass were adopted.

Fig. D.2. Same as Fig. D.1. The parameters from XGBoost and the associated mass were adopted.

Fig. D.3. Same as Fig. D.1. In this case, we adopted the XGBoost parameters for all the sources, but Gaia DR3 5251946383937940480, based on the good agreement with respect to the evolutionary tracks. For Gaia DR3 5329461850603601792, only atmospheric parameters from the XGBoost catalog are available and their high mass is validated based on its luminosity and temperature.

Appendix E: Supplementary material

Notes. Gaia DR3 source ID, RV (orbital) period, adopted effective temperature and surface gravity, the derived G-band extinction, A_G, luminosities, masses, and radii for rotational and ellipsoidal candidates. Only sources having conservative flags associated with the extinction estimate and validated masses are listed. The errors correspond to half the difference between the 84th- and 16th-percentile values. The Source column indicates the origin of the atmospheric parameters used to derive the extinction, luminosity, mass, and radius, being equal to 0 when the atmospheric parameters used are those from the GSP-Spec module, 1 when the atmospheric parameters are those from the XGBoost sample (KMgiantPar = 0, log g≥2.2 or in the case of an overestimated mass for its luminosity; see Appendix D), and 2 when the atmospheric parameters are only available from XGBoost (KMgiantPar = 1,2). The last column dubbed Flag indicates the quality of the light curve and therefore the certainty in the classification of the variables (G = Good, R = Regular, U = Uncertain). Only the first five rows for each binary type are shown. The full table will be available at the CDS.

Notes. Companion minimum and maximum mass, minimum mass-ratio, and filling factor (adopting a zero eccentricity) for rotational and ellipsoidal variable candidates. The errors correspond to the standard deviation for each parameter after sampling from the errors of the primary mass, orbital periods, and radii. The full table will be available at the CDS.

Appendix F: GSP-Spec [M/H] validation

Atmospheric parametrization for cool giants from Gaia RVS spectra can be challenging and in some cases, not successful (see Recio-Blanco et al. 2023). In those cases, the flag KMgiantPar was set to 1 or 2, and the reported Gaia DR3 temperature and surface gravity were fixed to 4250 K and 1.5 dex, respectively. Nonetheless, the metallicity determination, as it is based on the Ca triplet lines, can be reliably measured for those sources. To validate the metallicities obtained in this way, we crossmatched Gaia DR3 astrophysical_parameters table with the reported metallicities for ∼45 cool M-giants from Nandakumar et al. (2023). The latter were derived using near-IR high-resolution spectra. We applied the calibration to the GSP-Spec metallicities as in Recio-Blanco et al. (2024) and considering only those sources with vbroadM and vradM flags equal to zero. Figure F.1 shows the 37 stars obtained in this way, separated based on the value of the KMgiantPar flag, being 0 for the stars with successful M-giant parameterization (green circles) and ≠0 for those stars without reliable T_eff and log g (blue circles). For the latter, the metallicity was calibrated based on the fixed T_eff = 4250 K, adopted by the GaiaGSP-Spec module. At the bottom left corner, the median difference Δ in the sense Δ = [Fe/H] (Nandakumar+23) − [M/H] Gaia, as well as the dispersion between both samples, is shown. The bottom panel shows the metallicity derived by XGBoost for a subsample of the same stars.

Fig. F.1. Metallicity comparison between [Fe/H] values from Nandakumar et al. (2023), based on high-resolution spectra, and [M/H] from Gaia RVS by the GSP-Spec module (top panel), for stars having good quality flags for the metallicity estimate, and Gaia XP spectra (bottom panel, from XGBoost). Stars having KMgiantPar = 0 are shown in green circles while those having KMgiantPar≠0 are shown as blue circles. The median difference and dispersion of each group are also reported.

The median difference is of the order of 0.1 dex for XGBoost metallicities, ten times larger than the median difference between the GSP-Spec metallicities for stars with KMgiantPar = 1, 2. Figure F.1 shows that, even though the atmospheric and physical parameters such as mass and radius, cannot be derived for these sources using GSP-Spec parameters, the metallicity estimates are reliable and can be used to study the metallicity content of our sample.

All Tables

All Figures

Fig. 1. Photometric period versus the absolute Wesenheit magnitude, WBP, RP − μ, for the long-period binary candidates. The color code corresponds to the ratio between the period derived based on the RV curve and the photometric period. Stars having binary solutions in the Gaia NSS catalog are marked with empty squares. Two sequences are recovered: a sequence composed of brighter stars with PVR/Pph ≃ 2, and a tidally locked population having lower luminosities and shorter periods.

In the text

	Fig. 2. G-band and RV curves for one ellipsoidal binary candidate (the two top panels) and one rotational candidate (the two bottom panels). The G-band light curve was phase-folded using the period from the RV curve in the case of the ellipsoidal variable, recovering the two minima per orbital cycle.
In the text

	Fig. 3. Surface gravity and the activity index $logR{\prime }_{\mathrm{IRT}}$ for stars with available activityindex_espcs measurements in Gaia DR3. The stars are color coded according to log χ2, the goodness-of-fit of the RVS spectra from the GaiaGSP-Spec module.
In the text

Fig. 4. Kiel diagram for the complete sample of red giant binaries with a spectroscopic effective temperature and surface gravity (either from GSP-Spec or XGBoost). The sample is color coded based on the ratio between the orbital and photometric period. The sources for which the parameters from XGBoost were preferred against the parameters from GSP-Spec are shown as circles with black edges. The background distribution in gray corresponds to a precise GaiaGSP-Spec sample that was selected as in Recio-Blanco et al. (2024).

In the text

	Fig. 5. All-sky Aitoff projection of the ellipsoidal variable candidates with reliable physical parameters (luminosity, radius, and mass) from the primary star. The color bar corresponds to the mass of the primary ℳ1. The background image was generated as part of the Gaia eDR3, based on more than 1.8 billion sources (Image credits: ESA/Gaia/DPAC).
In the text

Fig. 6. Hertzsprung-Russell diagram for the sample of rotational and ellipsoidal binaries. From left to right, the points are color coded according to the logarithm of its orbital period, PVR, the mass of the primary star, and the adopted spectroscopic metallicity [M/H]. Black points correspond to stars with unreliable extinction determination (mostly stars with Teff ≤ 3700 K; see Sect. 3.1) and therefore potentially unreliable stellar parameters, while those with a thick black edge are the rotational candidates. The grey lines correspond to constant radii of 10, 30, 60, 90, 120, 150, and 180 R⊙. In the right panel, the evolutionary tracks for a 1 M⊙ (green curve) and a 6 M⊙ (green dashed curve) star, having Z = 0.004 ([M/H]∼ − 0.6), from the grid computed by Lagarde et al. (2012), based on the STAREVOL (Siess et al. 2000) code, are included.

In the text

Fig. 7. Spectroscopic GSP-Spec (crosses) and XGBoost (circles) parameters and asteroseismic measurements of the surface gravity (top panel) and masses (bottom panel) of red giant binaries (Beck et al. 2024) and rotational binaries (Gaulme et al. 2020) with solar-like oscillations. The two spectroscopic values are connected with a vertical dashed line. The color bar shows the activity index and the difference in Δlog g in the top and bottom panels, respectively. The median difference and dispersion between spectroscopic and asteroseismic masses are quoted in the bottom panel.

In the text

Fig. 8. Period versus radius (left), eccentricity (middle), and mass-function (left) for rotational variables (top panels), and ellipsoidal variable candidates (bottom panels). Left panels: Stellar radius of the primary star versus the orbital period. The color coding is based on the mass of the primary star. The dashed line corresponds to the threshold period while the black dots are ellipsoidal binaries in the LMC (Nie et al. 2017). Middle panels: Orbital period versus the eccentricity for sources with an NSS orbital solution of “SB1.” The color coding is according to the primary radius. For ellipsoidal variables, the circularization threshold for two values of radius is shown as dotted grey lines and black dots are ellipsoidal binaries in the LMC. Right panels: Orbital period versus mass function f(ℳ). The color coding is according to the primary radius. Sources with eccentricity estimates are shown as squares, while those without eccentricity measurements are shown as circles.

In the text

	Fig. 9. Masses of the primary, ℳ1, derived using spectroscopic atmospheric parameters and the minimum mass for the secondary star, ℳ2, min, derived based on the orbital period and RV amplitude. The systems are color coded according to their mass function, f(ℳ).
In the text

Fig. 10. Dependence of the mass of the secondary component as a function of the inclination of the binary. Left panel: Secondary mass versus inclination for Gaia DR3 178734862161885440 ellipsoidal candidate. The black vertical line marks the minimum mass computed, for sin i = 1, while the dashed vertical line is its associated error. The horizontal orange line is the minimum inclination of the system, while the dashed orange lines are the inclination error. In the top right corner, the minimum mass and the mass obtained from the minimum inclination are reported. The area under the curve corresponds to the range of masses possible for this system. Right panel: Minimum secondary mass versus the maximum secondary mass. The color coding is based on the minimum inclination of the system.

In the text

Fig. 11. Orbital period versus the spectroscopic mass of the primary, ℳ1. The colors are based on the minimum mass of the secondary star, ℳ2, min. The boundaries for potential Type Ia SNe progenitors in red giant stars and white dwarf binaries from Liu et al. (2019) and Ablimit et al. (2022) are shown as solid and dashed lines. The ellipsoidal binaries with a ℳ2, max ≤ 1.2 M⊙ are marked with black pentagons.

In the text

Fig. 12. Filling factor versus mass-ratio for rotational candidates (blue squares) and ellipsoidal variable candidates (pale pink circles). For the systems in which the difference between the maximum and minimum mass for the secondary is lower than 1.0 M⊙, the data points are color coded by the average between the maximum and minimum secondary mass, and their mass ratio corresponds to that average mass for the secondary.

In the text

Fig. 13. Filling factor ffilling versus eccentricity for a subsample of ellipsoidal variables. The data points are color coded based on the orbital period. For the most eccentric binaries, the filling factor at apo- and periastron is included as unfilled circles, connected to the average value obtained considered a zero eccentricity. The top and right panel shows the distribution (gray histogram) of filling factors and eccentricities, respectively. The top panel includes the distribution of filling factors for all the ellipsoidals having reliable measurements for their radii (black-edge histogram).

In the text

	Fig. 14. Metallicity distribution function of ellipsoidal candidates having vbroadM < 2, vradM < 2, and Δ[M/H] ≤ 0.1 dex from Gaia RVS spectra (aquamarine filled histogram), SB1 stars from the GALAH survey (dashed orange line), and APOGEE close giant binaries (purple dotted line).
In the text

Fig. 15. [α/Fe] versus [M/H] (from GSP-Spec) for ellipsoidal candidates. In the top panel, the points are color coded according to their orbital period. Solar values are marked with dotted gray lines. In the bottom panel is the same sample, but the color bar corresponds to the spectroscopic mass of the primary. The YAR stars from Jofré et al. (2023) based on APOGEE observations are included as squares; those with a red cross mark are spectroscopic binaries.

In the text

Fig. 16. Toomre diagram. Top panel: Ellipsoidal and rotational binary candidates. The color coding is according to the maximum height from the Galactic plane Zmax. Middle panel: Ellipsoidal candidates only. The candidates are color coded based on their spectroscopic metallicity [M/H] (middle panel). Bottom panel: Abundance of [α/Fe]. The dashed circle marks the kinematics of the Galactic disk at $\sqrt{V_R^2+V_Z^2+{(V_{\varphi }-V_0)}^2}<210$ km s−1.

In the text

	Fig. 17. Velocity dispersion as a function of the primary radius in equal bins of width ∼9.0 R⊙. The color bar corresponds to the ratio between the RV and photometric period.
In the text

Fig. 18. [Ce/Fe] abundances as a function of different orbital and stellar properties for ellipsoidal candidates with available measurements. The top row shows [Ce/Fe] against the orbital period (PVR from Gaia FPR, left panel), GSP-Spec calibrated [M/H], and [α/Fe] (middle and right panel, respectively). The bottom row shows the abundance of Cerium as a function of the mass of the primary star ℳ1 (left panel), the minimum mass of the secondary ℳ2, min (middle panel), and the mass ratio q (right panel). In all the panels, only ellipsoidal binaries with good quality flags for the extinction are included (mint circles). Stars following a cut in the [Ce/Fe] and [M/H] quality flags (see the main text) are shown as purple circles. For comparison, Ba stars from Jorissen et al. (2019) having orbital periods of ≤1000 days are included as magenta diamonds and arrows (when their [Ce/Fe] abundance is larger than 1.2 dex).

In the text

Fig. 19. Period-luminosity diagram for the ellipsoidal candidates. The colors are based on the primary mass (top panel) and filling factor (bottom panel). We note that both color bars are shown in logarithmic scale. Systems having a filling factor larger than one are shown as unfilled circles. In both panels, the black dashed line corresponds to the fit to the sample of low-mass ellipsoidal variables in Nie et al. (2017).

In the text

	Fig. 20. Period-luminosity diagram for ellipsoidal candidates with a reliable metallicity estimate based on Gaia RVS spectra (derived by the GaiaGSP-Spec module). The size of the symbol corresponds to the mass of the primary star. Ellipsoidal variables without a reliable metallicity estimate (see Sect. 5.2) are shown as gray dots of equal size.
In the text

	Fig. A.1. Gaia FPR photometric period, Pph, versus literature periods compiled in Gavras et al. (2023). The stars are color coded according to the ratio between the RV period and the photometric period. The dashed lines correspond to Plit/Pph = 2 and 0.5, while the solid line corresponds to the 1:1 relation.
In the text

Fig. B.1. Comparison between the log g values for stars with KMgiantPar = 0 as derived in GSP-Spec (calibrated based on the Teff) and in the XGBoost catalog. Cyan and purple circles correspond to stars with GSP-Spec calibrated surface gravities smaller and larger than 2.2 dex, respectively. In the later, the XGBoost parameters were adopted. The activity index (available for a subsample of sources) is shown in the color bar. Stars having overestimated GSP-Spec surface gravities are precisely those sources with enhanced activity.

In the text

	Fig. C.1. HR diagram for Gaia DR3 517611939345861120 (star symbol) along with the rest of the sample of red giant binaries, color coded by their spectroscopic mass. The grey lines correspond to radii of 1, 10, 30, 60, 90, 120, 150, 180 R⊙. Different evolutionary tracks from STAREVOL (Siess et al. 2000) have been included.
In the text

	Fig. D.1. HR diagram for sources having spectroscopic masses ℳ1≥ 5.0 M⊙ and the closest STAREVOL (Siess et al. 2000) evolutionary tracks from Lagarde et al. (2012). The spectroscopic masses and metallicities from GSP-Spec and XGBoost (if available) are in the title of each panel. The parameters from XGBoost and the associated mass were adopted.
In the text

	Fig. D.2. Same as Fig. D.1. The parameters from XGBoost and the associated mass were adopted.
In the text

	Fig. D.3. Same as Fig. D.1. In this case, we adopted the XGBoost parameters for all the sources, but Gaia DR3 5251946383937940480, based on the good agreement with respect to the evolutionary tracks. For Gaia DR3 5329461850603601792, only atmospheric parameters from the XGBoost catalog are available and their high mass is validated based on its luminosity and temperature.
In the text

Fig. F.1. Metallicity comparison between [Fe/H] values from Nandakumar et al. (2023), based on high-resolution spectra, and [M/H] from Gaia RVS by the GSP-Spec module (top panel), for stars having good quality flags for the metallicity estimate, and Gaia XP spectra (bottom panel, from XGBoost). Stars having KMgiantPar = 0 are shown in green circles while those having KMgiantPar≠0 are shown as blue circles. The median difference and dispersion of each group are also reported.

In the text