DUETS II - Red giant asteroseismic binaries. Binary confirmation and prospects for double-seismic model inference

Introduction

Asteroseismology of solar-like oscillators, including red giants (RGs), allow for highly precise inference of fundamental stellar parameters (e.g. [23]). With photometric monitoring provided by the CoRot, Kepler, and TESS space missions ([4, 14, 97]), thousands of RGs can be studied asteroseismically, allowing us to improve our understanding of both stellar and Galactic evolution (Noels-Grotsh & Miglio 2025). Particularly for RG with long-baseline photometric monitoring as provided by the Kepler mission, model inferences using individual mode frequencies can be used for Galactic archaeology, as the stellar mass and age can be inferred with better than 2 and 10% precision, respectively (see, e.g., [81, 114]). However, such inferences inherently rely on the use of stellar evolution models. In order to improve the accuracy of these predictions, calibration laboratories are needed to constrain current uncertainties in stellar models (for example, initial helium mass fraction and convection, see e.g. [65, 59]). At the same time, validation benchmarks are needed for testing the predictions of state-of-the-art calibrated models. Binary stars containing a solar-like oscillator, particularly detached eclipsing binaries (dEBs), have been shown as very suitable for the task of independent validator for the accuracy of asteroseismic predictions (e.g. [46, 18, 17 Thembel et al.] 2018; Benbakoura et al. [12]; Thomsen et al. [113, 114]). This is because dEBs allow the fundamental measurement of stellar masses and radii at a precision down to at least 0.2% (Maxted et al. [74]), without dependence on stellar or binary evolution models (for a review, see Torres et al. [116]). However, the sample size of suitable dEBs is currently small, with less than two dozen having Kepler observations (Gaulme et al. [46]; Gaulme & Guzik [44]; Benbakoura et al. [12]; Hedlund et al. [53]). In the Kepler field, a few suitable open clusters also exist, which host multiple oscillating RGs with detectable oscillations. Such stellar clusters are each a large laboratory at fixed age and metallicity, where oscillators and models thereof can both be inter-compared, or benchmarked against independent cluster constraints from dEBs and photometry (see, e.g., Brogaard et al. [19, 15, 16]; Handberg et al. [52]; McKeever et al. [76]; Dufresne et al. [35]). However, their exploration of the mass-metallicity parameter space is limited, and open and globular cluster constraints outside of the Kepler field are hampered by lower seismic quality (e.g. Miglio et al. [77]; Lund et al. [69]; Tailo et al. [107]; Howell et al. [55, 56]; Stello et al. [104]).

We therefore need more stellar systems which can provide either strong constraints for seismic calibration of stellar models, or independent benchmarking of asteroseismic predictions. Asteroseismic binaries (ABs, Miglio et al. [78]), which are gravitationally bound stellar systems where both stars show detectable oscillations, are a unique type of system that can fill the gap for calibrators. ABs do not necessarily offer stellar-model-independent constraints on fundamental parameters. However, when the two oscillators’ mode frequencies can be disentangled, ABs can allow us to perform analysis of two coeval oscillators, typically at different luminosities and/or different evolutionary states, similar to seismology in clusters. Expectations from population synthesis put their numbers in the Kepler field at 20-80 ABs following the age and metallicity distribution of the field stars (Mazzi et al. [75]). Most of these are expected to contain two RGs. Uniquely, Mazzi et al. [75] predicted that practically no RG ABs should have interacted during their past evolution. Given the short evolutionary timescale of the red-giant-branch (RGB) and later RG stages, their initial masses should therefore be almost equal. So far, only a few ABs have been confirmed or studied as true binary systems (Appourchaux et al. [2]; White et al. [121]; Li et al. 2018; Beck et al. [8]; Marcadon et al. [72]; Murphy et al. [86]; Grossmann et al. [50]; Schimak et al. [101]), but many more ABC candidates (ABCs) have been published, investigated, and/or disproven, through kinematics, photometry, and/or seismology (e.g., Themessl et al. [110]; Bell et al. [11]; Espinoza-Rojas et al. [37]; Choi et al. [25], and Mazzi et al. in prep.).

The search effort for evolved ABs is still ongoing, with new techniques under development (see, e.g. Choi et al. [26, 25]). Part of the challenge is that the current space missions such as Kepler and TESS have coarse spatial resolution. This leads to frequent false-positive ABCs due to crowding, where the flux from two neighbouring (on-sky) oscillators of similar apparent magnitude are summed to produce an apparent AB. When these stars can be optically resolved, for example with Gaia DR3 photometry (Gaia Collaboration et al. [43]), it is possible to confirm that the two oscillators have different origins on-sky (see e.g. Colman et al. [28]; Choi et al. [25]). Techniques involving the detection of a photometric excess can also be used, where astrometric and photometric data of high on-sky resolution is used to measure the absolute flux, which is then compared with an estimate of the intrinsic flux from asteroseismology (Mazzi et al. [75], and Mazzi et al., in prep.). For ABs, the detection probability of the dimmer star’s oscillations in the power spectrum decreases as the binary luminosity ratio decreases from unity towards zero. Binaries with a detectable second oscillator therefore tend to have higher levels of photometric excess (Mazzi et al. [75]), making the combined photometric/asteroseismic method ideal for searching for new ABCs. However, separating optically unresolved chance alignments from true binaries remains a challenge. In those cases, the detection of Keplerian orbital motion, for example through spectroscopy or astrometry, is the only certain way of confirming that an ABC is in fact a gravitationally bound AB.

Spectroscopic observations

Spectroscopic binaries are typically identified through temporal radial velocity (RV) variability (single-lined spectroscopic binary, SB1), and/or through the detection of two RV components (double-lined spectroscopic binary, SB2). The RV semi-amplitude is proportional to $P^{-1/3}$ (Torres et al. [116]), where $P$ is the orbital period. The detected change in RV over a finite baseline therefore decreases with increasing period. For typical oscillating Kepler RGs, activity and/or pulsations can complicate the RV measurement up to the 0.1 km/s level (Hekker et al. [54]), but binary RV signals larger than this can still be detected with standard methods. An example of this in the literature is Price-Whelan et al. [93].

In this work, our aims are two-fold: To obtain a new sample of confirmed binaries with solar-like oscillating RGs, as well as demonstrate the modeling possibilities offered by ABs. For our first aim, we apply standard RV diagnostics to a sample of ABCs, as well as candidate binaries having only a single detectable oscillator. In Sect. 2, we outline the details of our spectroscopic observing programme of 60 candidates for binary systems, selected based on their seismology (ABCs) and/or based on observed excess photometry compared with expectations from seismology (Mazzi et al., in prep.). In Sect. 2.1, we quantify the RV sensitivity of our observations as a function of orbital period. In Sect. 3, we present the analysis of spectral line broadening functions, which we used to quantify spectroscopic variability in our sample. We summarise the most interesting targets from the spectroscopic study in Sect. 3.4.

Our second aim is to demonstrate the additional modeling possibilities offered by ABs compared to single stars. To this end, in Sect. 4, we perform a detailed asteroseismic inference for a subsample of binaries/binary candidates, including the peak-bagging and modeling of both stars’ oscillation mode frequencies in the case of ABCs, in order to demonstrate the benefits of a two-star seismic modeling approach. Finally, we summarise and conclude in Sect. 5.

We performed spectroscopic follow-up observations of 60 binary candidates with the high-resolution ($R \sim67{,}000$, with full width at half maximum (FWHM) of $\sim4.5$ km/s) spectrograph FIES at the Nordic Optical Telescope (Telting et al. [109]), in order to confirm them as spectroscopic binaries. With our observational strategy, we aimed to obtain at least two spectra with a long baseline, for as many stars as possible, and to follow up with more epochs on the most promising candidate binary systems. For 37/60 of our targets, we obtained at least two spectra, allowing us to investigate potential spectroscopic variability. This observing proposal was run with filler time status, which meant that observations were only fit into the observing queue on nights with scheduling gaps. For this reason, we kept the exposure times short, aiming for Signal/Noise (S/N) values of 15–25 per spectrum. Due to the low predicted S/N of our observations, we did not attempt a detailed spectroscopic analysis of the individual photospheric lines, instead prioritising the average RV measurement and line shape, where we could effectively stack absorption lines to increase the measurement S/N. Each spectrum had a Thorium-Argon wavelength calibration spectrum taken immediately before observation. This is typically sufficient for achieving RV precision of 20–40 m/s (see e.g. Thomsen et al. [113]; Thomsen [112]; Thomsen et al. [115]). The échelle spectra were reduced by the observatory pipeline, which employs FIEStool (Stempels & Telting [106]).

The target selection was an ad-hoc mix between several sources of candidates:

• 33 targets from an early version of a photometric-asteroseismic catalogue of candidate binaries, based on data from Willett et al. [122]. This catalogue will be presented in Mazzi et al. (in prep.).

• A sample of 22 asteroseismic oscillators with poorly fitting single star background fits, which we confirmed through visual inspection as having an additional signal in the power spectrum or peculiar oscillations, making them ABCs (priv. comm., Josefina Montalbán).

• 12 ABCs that we found by manually investigating the KEPSEISMIC power spectra (e.g. Pires et al. [91], and references therein).

• 13 targets from the samples of ABCs and peculiar oscillators presented in Colman et al. [28]; ); Bell et al. [11]; ); Gaulme et al. [45]; ); Schonhut-Stasik et al. [102].

There is overlap between these sources. The Tables A.1 and A.2 in the appendix highlight the source(s) for each target, as well as the number of observations for each. For the 37 of 60 stars for which we obtained more than one spectrum, the typical number of observations was 2. Our targets were selected from a larger preliminary collection, after cross-matching with the Gaia DR3 catalogue to remove targets with a potential contaminating star, since those could be due to a chance alignment (see, e.g., Miglio et al. [78]; Colman et al. [28]). Due to this, our target sample is unlikely to be complete. However, this significantly helped reduce observing time requirements. Of the 60 targets in our sample, only KIC 4346953, 5015647, 6501237, 12117790, 9392647 and 9392650 had a nearby ($< 10^{\prime\prime}$) contaminant less than 3 magnitudes dimmer. These targets’ contaminants are investigated in detail in Sect. 3, when relevant.

Sensitivity to binarity

True binarity requires that the stars are gravitationally bound and orbit each other. From the population synthesis simulation of Mazzi et al. [75] using the Moe & Di Stefano (2017) binary parameter distributions, $\sim20\%$ of RG asteroseismic binaries are expected to have orbital periods below $10^{3}$ days, $\sim40\%$ below $10^{4}$ days, and $\sim60\%$ below $10^{5}$ days. For the 37 stars where we have at least two spectra, our observational baseline spans between 42 and 413 days. We here present a simplified calculation of the expected RV signals of gravitationally bound binaries, to simulate the detection sensitivity of our observational strategy as a function of orbital period. We remark that the goal of our campaign was to confirm as many true binaries as possible, for the purpose of future study of those systems, and not to obtain a complete account of all ABs in our sample, nor in the full Kepler RG sample.

For each orbital period evaluated, we simulated 10.000 gravitationally bound orbits, assuming that both stellar components have $M = 1\mathrm{M}_{\odot}$ ($M_{2}/M_{1} = 1$). We assumed an isotropic distribution of orbital inclinations ($i$ uniform distribution in $\cos i$ between $[0, 1[$), and a uniform distribution in periastron longitude between $[0^{\circ}, 360^{\circ}[$. For the eccentricity $e$, we assumed the solar-type distribution from Moe & Di Stefano (2017), with $p_{e} \propto e^{0.4}$ and $e < 1 - (P/2\ \mathrm{days})^{-2/3}$, where $P$ is the orbital period in days. We verified that the results do not change noticeably if we adopted a uniform eccentricity distribution between $]0, 1[$. Finally, we assumed a uniform distribution for the time of first observation, between $[t_{0,\mathrm{peri}}, t_{0,\mathrm{peri}} + P[$, where $t_{0,\mathrm{peri}}$ is the time of periastron passage. For each simulated orbit, we then evaluated the component RVs assuming that the target was observed only two times, with a separation between consecutive observations (baseline) of either 50 or 400 days. These baselines are approximately representative of the upper and lower limit for our campaign.

For targets where one star produces most of the flux, the variation in RV of the brightest component can approximately describe the binary detection probability. For the other extreme, where the binary luminosity ratio is close to unity, the spectroscopic profile will be clearly resolvable as bimodal only if the difference in RV ($rv_{1} - rv_{2}$) is larger than the FWHM of the two stellar component’s absorption profiles. With low RV difference, the composite profile will be indistinguishable from a typical single-lined absorption profile, only with a slightly larger width. In that case, a change in $rv_{1} - rv_{2}$ will modify the apparent width of this composite profile, which we approximate using

where $\sigma_{\mathrm{init}}$ is the original width of a single component.

In Fig. 1, we present these variation measures for the simulated binaries; either the RV variation $\Delta rv$ of a spectroscopic profile dominated by a single star, or the change in apparent width $\Delta\sigma$ of an unresolved combination of two stellar components’ absorption lines with equal luminosity ratio. For calculating $\Delta\sigma$, we assumed that the width of the spectroscopic profiles are dominated by the instrumental broadening of FIES (FWHM $\sim4.5$ km/s) rather than stellar surface rotation. For most RGs, this is a reasonable assumption (e.g. Ceillier et al. [22]).

To estimate a detection probability, we assumed a limiting RV precision of 0.1 km/s per spectrum, which is a reasonable limit when considering the typical astrophysical variability of RGs with $\log g > 2$ (Hekker et al. [54]). If we obtained just two spectra, the 99.7% confidence detection limit for $\Delta rv$ is therefore 0.42 km/s. For the $\Delta\sigma$ estimate, the role of astrophysical variability is less obvious to estimate. We therefore conservatively assumed the same limit for simulating the detection probability. We find that both measures remain sensitive to the signal induced by a binary orbit, even for periods above $10^{4}$ days for a 400 day baseline. For binaries with period 10–100 days, we predict an integrated average detection probability of 95% (98%) for the 400 (50) day baseline. For 100–1000 days this is 96% (93%), and for 1000–10.000 days we predict an average detection probability of 80% (24%).

If all observations were taken with a baseline of 400 days, we estimate an approximate completion factor of $\sim40\%$ for the confirmation of ABs of unknown orbital periods, based on our simulated detection probabilities and the period distribution of simulated ABs in Mazzi et al. [75].

Broadening function analysis

We aimed to derive spectroscopic measures of binarity. In order to conclusively confirm binarity spectroscopically in this work, we require that they have significant temporal variability of the average spectroscopic line profile (see Sect. 2.1). The measures required to confirm binarity are outlined in Sect. 3.1. For all stars, we furthermore estimated the width and skew of the average line profile (see Sect. 3.2), as these can be an indicator of binarity.

Before detailing the binary indicators based on the line profile, we first outline the calculation of the average line profile, and considerations for RV fitting and uncertainty estimation. We performed dimensionality reduction on the wavelength spectra by calculating the average line broadening function (BF) [98] of each spectrum. The BF is obtained by least-squares deconvolution of the observed spectrum using a sharp-line template spectrum. It is therefore a best-fit representation of the average shape and Doppler-shift of the spectral lines. Large asymmetries, bimodality, as well as changes in BF shape and RV over time can be indicators of binarity, which can be explored with model profile fitting. A double-lined binary (SB2) will have a bimodal line profile that varies following a Keplerian orbit of the two stellar components, while a single-lined binary (SB1) will have a unimodal line profile following only the orbit of the brighter star. A static but bimodal BF can indicate a chance alignment of two stars that are not optically resolved, but this can require a long time baseline to verify unless the stars are well-separated in RV. The detection of binarity through spectroscopic variability measurements such as ours was illustrated in Sect. 2.1.

We used a fixed sharp-line synthetic template spectrum for all stars from Coelho et al. [27], with $T_{\mathrm{eff}} = 4750$K, $\log g = 2.5$, [Fe/H] = 0.0, and [$\alpha$/Fe] = 0.0, and limited the calculation to the optical region 4500 − 5825Å to avoid telluric lines and interstellar Na in the observations, as well as low-Signal/Noise (S/N) in the blue. We further smoothed the BFs with a Gaussian kernel having $\sigma= 1$km/s to reduce regression-induced noise from the wavelength-to-velocity transformation.

To quantify spectroscopic binarity of the targets, we performed model fits to the BF of each spectrum. We used a Gaussian model unless otherwise stated. With this fit we assumed that the target is single-lined and not significantly broadened by rotation. The latter is a reasonable assumption for most RGs, because the line profile is often dominated by instrumental broadening due to slow surface rotation (see, e.g., Ceillier et al. [22]). The Gaussian model is:

with $a$ and $\sigma$ being the amplitude and standard deviation of the Gaussian function, while $v$ is the velocity bin and $rv$ is the RV center of the Gaussian.

For parameter fitting and uncertainty estimation, we used non-linear least squares optimisation. The fitted-parameter uncertainties are formal least-squares estimates, whose reliability depends on the uncertainties assigned to the input BF values. We estimated the uncertainty of the BF data from the variance outside of the line profile. Later in this section, we evaluate whether this estimate is sufficient.

In cases where the line profile was clearly bimodal, we fitted a combined two-Gaussian model. Here, we fitted all the BFs simultaneously, to enforce the same line widths and amplitude ratios. We performed a linear least squares fit within the non-linear optimisation, in order to marginalise out the continuum and absolute amplitude of each BF. This way, the non-linear optimisation had $3 + 2n$ free parameters ($a_2/a_1$, $\sigma_1$, $\sigma_2$, $n \times rv_1$, and $n \times rv_2$), where $n$ is the number of spectra. In Table A.1, we call this bimodal model "SB2", and the corresponding unimodal model "SB1". The use of this model does not inherently mean that the stars are true binaries, just that we fitted them with a double- or single-lined profile.

The data in the BFs includes a significant level of correlation (sinusoid-like features in Fig. 2). Some of this correlation is systematic and due to a mismatch between some of the features of the template and the observed spectrum. However, the majority comes from the transformation of a noisy spectrum from wavelength to velocity space (see Rucinski [98]). This can also be considered overfitting noise, since it is amplified by the size of the BF design matrix. We have attempted to dampen this noise through smoothing with a Gaussian filter having $\sigma= 1$km/s. This reduces the amplitude, but also imprints an additional correlation between the velocity bins. For KIC 2971380, which is the only binary where we had sufficient spectra to model the full orbital motion, we explored the impact of the total correlation on the output uncertainties. We assumed that the residuals follow a multivariate normal distribution with a stationary covariance, that is, one which is dependent only on the velocity difference between two bins, and not the absolute velocity. We estimated this covariance matrix by calculating the autocorrelation function of the residuals, after a best-fitting BF model was subtracted. We found that the resulting orbital parameters and uncertainties of KIC 2971380 are not significantly different from that obtained when neglecting this correlation. The output parameters for KIC 2971380 presented in this work were calculated including this contribution. However, based on these findings we have neglected the correlation for the targets in the sample that have less spectra, in order to preserve computational efficiency.

Binary signature - multiple nights

Below, we detail the variability flags used to quantify binarity. We observed 37 stars with observations over at least two nights. For these stars, we explored if temporal variations were detectable in the BF. These are summarised in Table A.1 in the appendix. The measures quoted in the table are outlined below.

Slope $\frac{dv}{dt}$: The RV slope of a linear fit of the RVs as a function of time, thereby assuming that the candidate binary has a period significantly longer than the baseline.

Slope fit $\Delta$BIC: The fit quality of the above line fit against a constant fit, by comparing the Bayesian information criterion (BIC) of both. Negative $\Delta$BIC means that the line fit was preferred over the constant.

RV scatter $\Delta v$: The RV variation, estimated as the combination of the two RV measurements with highest significant difference relative to their quadrature-combined uncertainty.

Change in width $\Delta\sigma$: The most significant variation in Gaussian width $\sigma$, by fitting a single Gaussian profile to the BF.

We added 100 m/s in quadrature to all RV and $\sigma$ uncertainties, estimated to account for potential astrophysical variability in the line profile (see Sect. 2.1).

For ten of the 37 systems, the BF profile was visually bimodal, indicating the presence of two resolved stellar absorption components. We therefore fitted a combination of two Gaussians, with the same method as described for KIC 2971380 in Sect. 3. We verified that these two-profile models had a better BIC than a one-profile fit. For these ten systems, the velocity values reported in Table A.1 refer to the separation $RV_2 - RV_1$, rather than the absolute velocities. For example, the parameter $v$ is the most significant difference of all the measurements of $\lvert RV_2 - RV_1\rvert$. These double-lined measurements are independent of any potential drift in the instrumental zero-point, but they can still contain astrophysical variability of the line profile.

In order to report a star as significantly variable in Table A.1, we required that either $\Delta$BIC $< -10$ (SB1), $\Delta$BIC $< -2$ (SB2), time variation in the width ($\Delta\sigma> 3 \cdot\operatorname{Err}(\Delta\sigma)$), or in the velocity ($\Delta v > 3 \cdot\operatorname{Err}(\Delta v)$). A few stars show tentative indications of binarity, either $\Delta\sigma/\operatorname{Err}(\Delta\sigma) \sim2$–3, or both the slope and $\Delta v$ approximately similar to the uncertainty. In particular, KIC 11299484 shows a clearly bimodal line profile, but the RV variation is only at the $1\sigma$ significance level over a baseline of 255 days. In total, we detect highly significant variability ($> 99.7\%$ confidence) for 12 systems, 8 of which we further confirm as SB2. 8/12 systems are ABCs. We detect variability at marginal significance for another 7 systems (all ABCs).

Single spectrum indicators

For 23 out of 60 targets, we only have FIES observations from a single night. For those, it is not possible to conclusively confirm binarity through RV variability. SB2 systems, however, might still show significant deviations in the line profile relative to what is expected for a RG. We quantify this through two measures; the width $\sigma$ of a Gaussian fitted to the observed broadening function, and the asymmetry factor $\alpha$ of an asymmetric Gaussian model (Azalini 1985):

The asymmetry factor is not expected to be centered on zero for real stars, since the FIES instrumental profile is asymmetric (priv. comm., John Telting) and the stellar lines are affected by convective blueshift Gray [49]. The two measures are shown in Figure 3 and Table A.2 for the whole sample. This way, we can compare the single-epoch stars to the SB1 variable stars, the stars with a clear bimodal profile and multiple spectra ("Double-lined"), and the single-lined stars that have multiple observations. The latter category can in principle serve as a control sample for the expected profile shape for single stars. See Sect. 3.1 for the determination of RV variability.

From our measures, it appears that 5–6 single-observation stars are outliers compared to the typically expected skewness ($\sim1$) and width (3–3.8 km/s). These are KIC 3860550, 3955502, 4058578, 5700488, 6706199, and potentially 4282111. Qualitatively, we further remark that the broadening function profile of KIC 3860550 has clear visual indications of being bimodal.

Binary indicators - APOGEE and Gaia

We cross-matched our sample with Gaia DR3 [43] and APOGEE DR17 [1], to compare with variability measures from the two catalogues. In Table A.2, we have summarised the Gaia DR3 astrometric excess measure RUWE (renormalised unit weight error), the Gaia RV variability flag (called Var/DR3) following Katz et al. [61], obtained by requiring rv_chisq_pvalue < 0.01 and rv_renormalised_gof > 4. We also include the non-single-star (NSS) flag (Gaia Collaboration et al. [41]), the maximum Gaia RV amplitude after outlier removal (Katz et al. [61]), and the APOGEE DR17 RV scatter (Abdurro’uf et al. [1]). There is overlap between ours and the catalogue determinations, particularly for the single-lined RV variable stars. The survey indicators are less clear for the SB2 systems, likely due to the lower spectral resolution employed.

Based on this cross-comparison (see Tables A.1,A.2) for the targets that are unconfirmed and have one or more spectra, we add the following sources as likely binaries: KIC 4282111, 4637699 (ABC), 8181509, 8295007 (ABC), 10841730 (ABC), 11299484 (ABC), 11352644 (ABC), 11465942, and 12117790 (ABC). These have either one clear signature in Gaia/APOGEE, or tentative indication of binarity from two or more sources. Note in particular that KIC 10841730 is a confirmed AB (Schimak et al. [101]), and KIC 6206407 was already identified in Espinoza-Rojas et al. [37] as an ABC with a high RUWE value.

Binary systems

In this section we present specific details and analysis for some of the systems where we managed to use the spectroscopic indicators (Sect. 3.2, 3.1, 3.3) to either confirm, or indicate stars as binaries. We furthermore include a few cases where we disprove binarity, based on the arguments presented in the corresponding sections (KIC 6369592 & KIC 9392647/50).

KIC 2971380. A low-luminosity RGB star with an observed asteroseismic period spacing of $\Delta P = 70.84 \pm0.03$ (Mosser et al. [84]), and a photometric excess (Mazzi et al., in prep). It has been studied in detail with asteroseismology, as its chemical composition and Galactic kinematics support an ex-situ origin, likely from Gaia Enceladus ([81, 13]). We confirm it as an SB2 system with a luminosity ratio around 25%, based on the BF amplitudes. We performed a Keplerian two-body orbit fit to the RVs and confirm that the mass ratio is consistent with unity at 1% precision, suggesting that the companion is likely evolved past the main sequence as well. The Kepler power spectrum does not show indications of oscillations from the dimmer companion. The orbit fit is shown in Figure 4 and Table 1, and the RVs are reported in Table A.3.

	Value
$M_{\mathrm{ass}}$	1.005 (10)
$M_{\mathrm{bright}}$
$M_{\mathrm{bright}} \sin^3 i$ ($M_\odot$)	0.170 (11)
$M_{\mathrm{dim}} \sin^3 i$ ($M_\odot$)	0.171 (11)
$a \sin i$ ($R_\odot$)	75.1 (17)
RV semi-amplitude $K_{\mathrm{bright}}$ (km/s)	15.28 (30)
RV semi-amplitude $K_{\mathrm{dim}}$ (km/s)	15.20 (34)
Eccentricity $e$	0.2643 (47)
Periastron longitude $\omega$ (°)	222.4 (42)
Orbital period (days)	129.26 (33)
$t_{0,\mathrm{peri}}$ (days)	1030.2 (26)
RV zero-point $\gamma_{\mathrm{bright}}$ (km/s)	-193.82 (22)
RV zero-point $\gamma_{\mathrm{dim}}$ (km/s)	-194.22 (24)

KIC 4260884, 7697607, 8479383, 10592924. These are ABs with separated oscillation envelopes. We confirm them as double-lined binaries with RV variation. KIC 8479383 contains at least one core-helium burning (CHeB) star, as evidenced by the star’s mixed modes (see, e.g., Bedding et al. [9]). KIC 7697607 has two oscillators with a small separation in $\nu_{\max}$, which means the oscillation envelopes partially overlap for at least one radial order.

The power spectrum of KIC 4260884 appears noisy, particularly for the brightest star. All its oscillation modes appear complex and broadened, which is unlike a typical CHeB mixed mode pattern (see, e.g., Bedding et al. [9]).

KIC 6501237. There are two stars within 3″ on-sky, with $\Delta G = 2.3$, with a parallax-derived line-of-sight separation of $0.03 \pm0.6$ pc, and Galactocentric velocity difference of only $\sim2$ km/s. These stars were flagged by (Espinoza-Rojas et al. [37]) as having a bound-binary configuration probability of 50%. We have two spectra of the brightest star, taken $\sim150$ days apart, showing a small change in its RV and width. Unfortunately, one of the spectra was taken with observational seeing of 2″, and likely contains a contribution from both stars, which can explain the RV variation. Given their close proximity and low RV difference, it is plausible that they are either in a bound orbit or in a close association. In Sect. 4, we treat them as a coeval pair, in order to explore if we can obtain a good asteroseismic double-star model fit under this assumption. A seismic confirmation would be interesting as Miglio et al. [78] predicted that all resolved AB candidate systems in Kepler should be chance alignments.

KIC 5300269, 8479182, 8649099, and 3860550. These stars have a photometric excess when a seismic estimate of the intrinsic luminosity is compared with the apparent magnitude and Gaia DR3 derived parallax-distance (Mazzi et al., in prep.). They furthermore show complicated oscillation envelopes that could indicate the presence of two oscillation signals overlapping in frequency. We followed Choi et al. [26], and measured the Shannon entropy of the oscillation envelope, together with the maximum signal-to-noise ratio (S/N). This gives a measure of the complexity of the oscillation envelope (Choi et al. [26]). The top panel of Figure 5 demonstrates that all four systems have comparably high entropy and low S/N relative to the typical Kepler field RGs. By comparing them with artificial ABs from Choi et al. [26], which were constructed by combining the light curves of two RGs with a flux ratio $\ge0.9$ and $\nu_{\max}$ difference $< 10\%$ (see Figure 5, bottom panel), the four stars are compatible with having two overlapping RG oscillators.

KIC 5300269 shows a change in BF shape over $\sim120$ days, indicating the presence of two absorption features. KIC 8479182 and KIC 8649099 have photometric luminosities and APOGEE DR17 temperatures that put them at $\sim2 \times L_{\mathrm{RC}}$. We confirm them as double-lined and RV variable. Such systems are expected to be the most prevalent Kepler ABs (Mazzi et al. [75]).

We only obtained one spectrum for KIC 3860550. However, the absorption line width and shape indicates the presence of two partially overlapping sets of absorption features of similar strength, which further supports that two stars are present within the aperture. Without a measure of long term RV variability, we have not confirmed binarity, but it seems unlikely that a chance alignment would have so similar RVs for the two stars.

KIC 5978324. Both Gaia data (see Beck et al. [7]) and our spectra confirm KIC 5978324 as SB1. The star was studied in Crawford et al. [32, 33] as part of a sample of the 48 most massive solar-like oscillators observed by Kepler, where they found $M = 4.7 \pm0.3M_{\odot}$. To date not many oscillating RG binaries in the 4–5$M_{\odot}$ range have been studied in detail, and it is of interest as it is near the mass where stars show Cepheid pulsations during part of their evolution.

KIC 6369592. Both the power spectrum and spectroscopic follow-up show two stars, but the $\nu_{\max}$ ratio of $0.516 \pm0.006$ and BF integral ratio of $\sim0.1 - 0.2$ give discrepant indicators for the luminosity ratio. The amplitude ratio of the two asteroseismic oscillation envelopes of $0.218 \pm0.011$ support the luminosity ratio estimated from spectroscopy, suggesting that the spectroscopic lines match the two oscillators detected in the power spectrum. The RV separation of $21.2 \pm0.1$ km/s does not vary over 400 days, which confirms that the two stars cannot gravitationally bound. The large RUWE value and negative parallax from Gaia could indicate that they are partially resolved by Gaia, despite not having been identified as such.

KIC 5015647. This system shows very high RV variation (19 km/s per year) based on the two spectra taken 141 days apart, which is a clear confirmation of binarity. Its Kepler power spectrum presents a complicated solar-like oscillation pattern at $\sim30\mu$Hz, with a forest of narrow modes potentially indicative of an atypical mixed mode coupling strength (see, e.g., Takata (2016); Matteuzzi et al. [73]; van Rossem et al. [118]). In addition, the power spectrum contains a set of higher-amplitude, coherent peaks from $180\mu$Hz until the Nyquist frequency. The nearby source (8″) KIC 5015657 (Gaia DR3 205325368473842928) has a magnitude difference of only $\sim2$ in the Gaia G band. We checked pixel-per-pixel power spectra for the two sources following Colman et al. [28]; Choi et al. [25], and there is no indication that the nearby source (KIC 5015657) is the cause of any of the two oscillation signals in the power spectrum.

KIC 4637699, 8295007, 9412408, 10841730, 11299484. These show two separated oscillators in their power spectra. From our RVs, some show marginal detections of variability. When combined with Gaia DR3 and APOGEE DR17 indicators of binarity, these all have at least mild indications of spectroscopic and/or astrometric variability from two different sources. Particularly, KIC 11299484 clearly presents two absorption features with FIES, and indications of binarity from APOGEE DR17 and Gaia DR3, making it a high-likelihood binary. KIC 4637699 has an abnormal line shape, Gaia DR3 RUWE=1.1, and mild RV variation with FIES.

KIC 4282111, 8181509, 11352644, 11465942, 12117790. These are not obviously ABCs, but when cross-matched with Gaia astrometry/spectroscopy and APOGEE spectroscopy, they have indications of binarity. KIC 8181509, 11352644, and 12117790 have a photometric excess similar to the stars marked in Figure 5 (Mazzi et al., in prep.). KIC 12117790 appears to have a second set of oscillations close to the Nyquist frequency, making it an ABC. Additionally, the Kepler aperture contains two stars with Gaia G magnitude difference of only 0.6 and 0.6″ optical separation on-sky. KIC 11465942 appears visually to have a wide oscillation envelope, and potentially show signs of dipole mode depression (see, e.g., Moser et al. 2012; Stello et al. 2016). KIC 11352644 shows a complex power spectrum, and might be containing two overlapping oscillators.

KIC 9392647 and 9392650. These appear to be a chance alignment of two oscillators on the sky, as also found by Espinoza-Rojas et al. [37]. The amplitude ratio of the two oscillation envelopes are different for the two stars’ KEPSEISMIC power spectra, which indicates that the ratio depends on which pixels are included in the aperture photometry. Therefore, the oscillations belong to the two different resolved stars on the sky.

Although KIC 9392647 and 9392650 have similar distance and sky position, their kinematics rule out a bound configuration. Their RVs differ by $\sim40$ km/s, and their proper-motion difference of $\sim6.6$ mas/yr corresponds to $\sim62$ km/s. Their angular separation of $6.2 \pm0.012$" implies a projected separation of at least $\sim11400$ AU, for which the escape velocity is only $\sim500$ m/s. This makes the relative velocity far too large for the two resolved stars to be gravitationally bound.

An unresolved companion to one of the stars could in principle shift one measured RV away from the systemic velocity. However, a companion capable of producing an offset of tens of km/s would leave a clear signature, either through an inflated Gaia RUWE or through a larger RV change between our two spectra. We therefore interpret KIC 9392647 and KIC 9392650 as a chance alignment rather than a bound pair. However, we still detect low significance RV variability for the lines of both stars. We have not identified the cause of this, but it could be either due to instrumental drift or intrinsic variability [54].

Asteroseismic inference of binaries

In this section, we present detailed peakbagging and asteroseismic inference of one ex-situ (accreted) Galactic binary for which we measured the binary mass ratio with RVs in Sect. 3 (KIC 2971380), and a proof-of-concept seismic investigation for one confirmed AB (KIC 10592924) and two ABCs (KIC 6501237 and 11299484), with the aim of using the oscillations of both stars. We selected the AB and ABCs based on a preliminary visual inspection of their power spectra, where we confirmed based on their mixed modes [9] that they were likely to contain two RGB stars with oscillations well-separated in frequency. The two ABCs were also selected to investigate with asteroseismology if their two oscillators were compatible with having formed as a binary or part of a common stellar population.

Oscillation frequency measurement

To measure the observed oscillation frequencies in the KEPSEISMIC power spectra [e.g. 91 and references therein], we performed peakbagging by fitting a Lorentzian profile to each observed radial ($l = 0$), dipole ($l = 1$), and quadrupole ($l = 2$) mode. The aim was to accurately measure the radial mode frequencies for asteroseismic inference, and in cases where dipole modes were challenging to model with a single Lorentzian profile, we excluded them from the fit.

First, we fitted an asteroseismic background and power excess with DIAMONDS [29] to capture granulation, oscillation power excess, and white noise $W$. For the granulation signal of KIC 2971380, we used three super-Lorentzian profiles [60]. For ABs, we implemented a model with two super-Lorentzian profiles and two Gaussian power excesses:

$\eta$ is the attenuation function accounting for the finite integration time of Kepler. We attempted with more granulation terms to match both stars in the ABs, but these could not be constrained independently. When we attempted to fit the low-frequency power with a third granulation component, we had issues with getting DIAMONDS to complete the sampling. For the ABs, we excluded the data from 0-4 $\mu$Hz, while for KIC 2971380 we only excluded data with the downward frequency of the KEPSEISMIC light curve filter (20 days, $\sim0.6\mu$Hz).

After background fitting, we performed peakbagging of KIC 2971380 with DIAMONDS. The $\ell= 1$ modes had a well-resolved mixed mode characteristic, and therefore were fitted the individual mixed modes with narrow Lorentzians as well, since they were not fully unresolved as sinc profiles.

For the ABs, we peakbagged the oscillation modes with a custom-made script using the affine-invariant Markov-Chain Monte Carlo (MCMC) sampler EMCEE [39]. This was necessary as current automatic peakbagging codes (e.g. PBJam, DIAMONDS, FAMED Nielsen et al. 2021; Corsaro & De Ridder 2014; Corsaro et al. 2020) are not designed to handle two oscillation envelopes. For the peakbagging we also accounted for the impact of the integration time on the oscillation amplitude. When evaluating the likelihood, we assumed that the noise characteristics of the power spectrum follows a $\chi^2$ distribution with two degrees of freedom.

The individual oscillation frequencies are reported in Table. A.4. The observed $\ell= 1$ modes of KIC 2971380 are reported in Table A.5. In addition to this, we measured the large frequency separation between radial orders $\Delta\nu_0$ (Table 2), by performing a linear fit of the radial mode frequencies, weighing the modes by the inverse of the observed variance. The reported uncertainties for $\Delta\nu_0$ are only the formal uncertainties. We also used the observed asymptotic relation of Mosser et al. [82, 85] to measure $\Delta\nu_{\mathrm{obs}}$, small frequency separation $\delta\nu_{\mathrm{obs},02}$, offset $\epsilon_{\mathrm{obs}}$, and curvature $\alpha_{\mathrm{obs}}$. Specifically, we used the relation

KIC	6501237	10592924	11299484	2971380
Asym. fit (Bright)
$\nu_{\mathrm{max}}^{\mathrm{a}}$ $\mu$Hz	62.86 (19)	52.52 (24)	48.27 (23)	77.63 (26)
$\Delta\nu_0$ $\mu$Hz	6.1538 (42)	5.3827 (42)	4.9899 (48)	7.8457 (45)
$\Delta\nu_{\mathrm{obs}}$ $\mu$Hz	6.1822 (81)	5.402 (11)	5.056 (12)	7.920 (14)
$\delta\nu_{\mathrm{obs},02}$ $\mu$Hz	0.831 (29)	0.743 (39)	0.673 (39)	1.115 (49)
$\epsilon_{\mathrm{obs}}$	0.075 (14)	0.084 (20)	0.062 (22)	0.131 (19)
$\alpha_{\mathrm{obs}}$	0.0145 (16)	0.0168 (24)	0.0168 (33)	0.0154 (27)
$\sigma_{\mathrm{jitter}}$ $\mu$Hz	0.046 (13)	0.065 (18)	0.059 (19)	0.068 (22)
Asym. fit (Dim)
$\nu_{\mathrm{max}}^{\mathrm{a}}$ $\mu$Hz	123.18 (41)	130.56 (82)	89.82 (41)
$\Delta\nu_0$ $\mu$Hz	10.4818 (77)	11.0416 (76)	8.1095 (86)
$\Delta\nu_{\mathrm{obs}}$ $\mu$Hz	10.538 (20)	11.059 (15)	8.154 (25)
$\delta\nu_{\mathrm{obs},02}$ $\mu$Hz	1.339 (52)	1.436 (38)	1.084 (44)
$\epsilon_{\mathrm{obs}}$	0.180 (22)	0.246 (16)	0.159 (34)
$\alpha_{\mathrm{obs}}$	0.0092 (33)	0.0000 (22)	0.0183 (63)
$\sigma_{\mathrm{jitter}}$ $\mu$Hz	0.065 (24)	0.049 (18)	0.056 (28)

Here, we sampled the probability distribution with MCMC, including the observed $\nu_{\mathrm{max}}$ (with uncertainty). We furthermore included a nuisance parameter $\sigma_{\mathrm{jitter}}$ to account for intrinsic scatter, inflating the uncertainties by $\sigma= \sqrt{\sigma_{\mathrm{obs}}^2 + \sigma_{\mathrm{jitter}}^2}$, since the detailed structure of the mode frequencies is not modeled with the asymptotic relation. This resulted in significantly higher parameter uncertainty estimates. The quoted uncertainties for $\Delta\nu_{\mathrm{obs}}$ in Table 2 are therefore more realistic than those reported for $\Delta\nu_0$.

Asteroseismic modeling inference

We performed an asteroseismic inference using a grid of stellar models with calculated theoretical oscillation frequencies. We used the alpha-version of AIMS², which is a partial re-implementation of the Bayesian inference code AIMS (Asteroseismic Inference on a Massive Scale, Rendle et al. 2019). AIMS3 allowed us to define a likelihood function including two stars, whereas we could only study one star at a time in the previous version. For mode identification, we used the older version of AIMS, since this was not reimplemented in AIMS3.

We used a grid of stellar evolutionary tracks and theoretical frequencies calculated with MESA version 11701 [90 and references therein] and GYRE [117]. This grid will be presented in full detail in Tailo et al. (in prep.), but it has already been tested on the dEB KIC 10001167 [114]. Each model was evolved from the pre-main-sequence until the first thermal pulse. However, we restricted the grid to the sub-giant and RGB phases when fitting. The full grid spans [Fe/H] from -2.0 to +0.55 with typical step of 0.25 dex, with solar mixture from Asplund et al. [3]; [$\alpha$/Fe] from -0.2 to 0.4 in steps of 0.2 dex; initial helium abundance $Y_{\mathrm{i}}$ from 0.22 to 0.34 in steps of 0.03; and masses from 0.6 to 1.8 in steps of 0.05 M$_{\odot}$, with additional models at mass 2.0, 2.15, 2.3, 2.45, 2.75, 3.0 M$_{\odot}$. The atmosphere description by Krishna Swamy [63] was used, and we included microscopic diffusion. Further choices regarding equation of state, opacities, and mixing were the same as in Miglio et al. [79]. The mixing-length-theory (MLT) was chosen to describe convection with the formula from Cox & Giuli [31], and $\alpha_{\mathrm{MLT}} = 2.2902$ was obtained by solar calibration.

As observational constraints in AIMS3, we used the radial mode oscillation frequencies and the frequency of maximum oscillation power, and the observed surface metal fraction $(Z/X)_{\mathrm{surf}}$, obtained from the iron abundance [Fe/H] combined with [$\alpha$/Fe], both from APOGEE DR17 [1]. We convert to $Z/X$ with:

The [M/H] calculation is based on the Salaris et al. [100] correction, using the Asplund et al. [3] solar mixture. Since all the stars we analysed are in binary systems, we only apply the metallicity constraint on the brightest star. The metallicity could be biased by dilution from the companion and blending of the lines. In Appendix B, we confirm that the expected bias on the spectroscopy from the presence of two overlapping sources is at maximum 0.1 dex for our targets, and we therefore adopted this limit for the metallicity uncertainty.

We corrected the theoretical frequencies for the surface effect (stemming from model inaccuracies near the surface) using the cubic (one-term) prescription of Ball & Gizon [6] unless otherwise stated, with a correction for each star. These are included as additional sampling parameters. For KIC 6501237, the fit quality was much better when using the two-term prescription of Ball & Gizon [6], including an inverse term [see also 58]. The two-term prescription is

while the cubic (one-term) prescription excludes the $a_{-1}$ term. Here, $\nu$ is a theoretical mode frequency, $\nu_{\mathrm{ac}}$ is the acoustic cutoff frequency, and $I$ is the normalised mode inertia. As proxy of $\nu_{\mathrm{ac}}$, we used the model $\nu_{\mathrm{max}}$. Since $\nu_{\mathrm{ac}}$ and $\nu_{\mathrm{max}}$ are approximately proportional [20, 10], this replacement simply results in a rescaling of $a_3$ and $a_{-1}$.

We defined a logarithmic likelihood function comprised of the following $\chi^2$ terms for the brighter (bri) and dimmer (dim) stellar components in the ABs:

With this likelihood, we do not include any relative weighing of the "classical" and "seismic" constraints, since our only non-seismic constraint is the metallicity, which is only conservatively constrained with an uncertainty of 0.1 dex on [Fe/H].

For sampling the likelihood, we used MCMC with emcee [39]. We used an RGB subgrid of the MESA grid, with fixed [$\alpha$/Fe] = 0.0 for the ABs, and [$\alpha$/Fe] = 0.15 for KIC 2971380. We sampled the following stellar parameters: Mass of the brightest star, mass ratio of the binary, shared metallicity [Fe/H], shared initial helium fraction $Y_{\mathrm{i}}$, and a-dimensional age $\tau$ (one for each star). We define $\tau$ as the mass of the helium core, which is a feature that increases monotonically with real age $\mathcal{A}$ during the full RGB. We used $\tau$ in place of the real age, both for sampling and interpolation, in order to reduce the occurrence rate of interpolation failure during sampling [see 96]. We verified that this parameter transformation did not bias the likelihood sampling, since the logarithm of the Jacobian (the logarithm of the partial derivative $\ln(\partial\tau/\partial\mathcal{A})$) is well-approximated as locally constant relative to the overall gradient of the likelihood.

We sample an adimensional age $\tau$ for each star, but enforce coevality by including a Gaussian prior on the age difference of the stars, requiring that their real ages agree within 5% of the mean age of the two stars (e.g. 250 Myr for 5 Gyr). This is roughly 50 – 90% of the typical statistical uncertainty on age that we expect for a single RGB star with Kepler data on individual mode frequencies (see, e.g., Montalbán et al. 2021; Thomsen et al. 2025a), and it is therefore not a particularly restrictive constraint. The agreement (or disagreement) between the posterior ages of the two stars, together with the seismic fit quality, can therefore further inform us of whether coevality is a good assumption.

Inference results

The asteroseismic inference based on radial mode frequencies converged to a single solution for all four binaries. The results of our seismic inferences are summarised in Table 3.

KIC	6501237	10592924	11299484	2971380
Input: $(Z/X)_{\mathrm{surf,bright}}$		0.0152 (35)	0.0096 (22)	0.0191 (44)	0.0039 (13)
Input: $\nu_{\max,\mathrm{bright}}$	$\mu\mathrm{Hz}$	62.86 (19)	52.52 (24)	48.27 (0.23)
Input: $\nu_{\max,\mathrm{dim}}$	$\mu\mathrm{Hz}$	123.18 (41)	130.56 (82)	89.82 (0.41)
Input: $[\alpha/\mathrm{Fe}]$	dex	0.0	0.0	0.0	0.15
Input: $M_{\mathrm{dim}}/M_{\mathrm{bright}}$					1.005 (10)
Input: $L_{\mathrm{dim}}/L_{\mathrm{bright}}$					0.25 (5)
$M_{\mathrm{bright}}$	$M_\odot$	1.167 (21)	1.223 (18)	1.200 (18)	0.871 (17)
$M_{\mathrm{dim}}$	$M_\odot$	1.165 (20)	1.215 (19)	1.203 (19)	0.865 (17)
$M_{\mathrm{dim}}/M_{\mathrm{bright}}$		0.9980 (91)	0.993 (10)	1.001 (10)	0.9940 (29)
$[\mathrm{Fe}/\mathrm{H}]$	dex	−0.10 (10)	−0.322 (78)	−0.038 (83)	−0.752 (86)
$Y_i$		0.296 (11)	0.2667 (84)	0.2720 (86)	0.25154 (89)$^{b}$
$\mathrm{Age}_{\mathrm{bright}}$	Gyr	4.65 (49)	4.00 (32)	5.47 (61)	11.70 (99)
$\mathrm{Age}_{\mathrm{dim}}$	Gyr	4.63 (52)	4.03 (34)	5.41 (62)
$R_{\mathrm{bright}}$	$R_\odot$	7.975 (56)	8.930 (42)	9.228 (48)	6.167 (40)
$R_{\mathrm{dim}}$	$R_\odot$	5.645 (35)	5.562 (31)	6.751 (38)	2.80 (32)
$\log g_{\mathrm{bright}}$	dex	2.7020 (21)	2.6238 (21)	2.5871 (22)	2.7981 (27)
$\log g_{\mathrm{dim}}$	dex	3.0012 (22)	3.0320 (21)	2.8595 (21)	3.48 (10)
$\rho_{\mathrm{bright}}$	$10^{-3}\rho_\odot$	2.301 (10)	1.7173 (14)	1.5265 (25)	3.7151 (70)
$\rho_{\mathrm{dim}}$	$10^{-3}\rho_\odot$	6.473 (25)	7.0596 (78)	3.9118 (44)	39 (15)
$L_{\mathrm{bright}}$	$L_\odot$	31.6 (14)	40.7 (14)	38.5 (16)	21.06 (72)
$L_{\mathrm{dim}}$	$L_\odot$	17.46 (78)	17.99 (62)	22.63 (95)	5.1 (10)
$(Z/X)_{\mathrm{surf,bright}}$		0.0152 (31)	0.0091 (15)	0.0173 (32)	0.00411 (90)
$(Z/X)_{\mathrm{surf,dim}}$		0.0151 (31)	0.0091 (15)	0.0173 (32)	0.00390 (70)
$T_{\mathrm{eff,bright}}$	K	4848 (42)	4880 (32)	4733 (38)	4982 (35)
$T_{\mathrm{eff,dim}}$	K	4967 (43)	5041 (33)	4846 (40)	5178 (58)
$\nu_{\max,\mathrm{bright}}$	$\mu\mathrm{Hz}$	62.77 (15)	52.29 (16)	48.38 (14)	76.79 (41)
$\nu_{\max,\mathrm{dim}}$	$\mu\mathrm{Hz}$	123.22 (32)	131.31 (46)	89.63 (27)	361 (86)
Surf. cor. $a_{3,\mathrm{bright}}$	$10^{-6}$	−0.688 (73)	−0.496 (44)	−0.395 (42)	−0.638 (56)
Surf. cor. $a_{-1,\mathrm{bright}}$	$10^{-6}$	−1.30 (20)
Surf. cor. $a_{3,\mathrm{dim}}$	$10^{-6}$	−0.418 (41)	−0.371 (24)	−0.399 (36)
Surf. cor. $a_{-1,\mathrm{dim}}$	$10^{-6}$	−0.51 (16)
Orbit $i^{c}$	°				35.43 (94)
Orbit $a^{c}$	$R_\odot$				129.6 (42)

The ex-situ binary, KIC 2971380

The oscillations of KIC 2971380 are shown in Figure 6, together with the fit result of our seismic modeling inference. The power spectrum of KIC 2971380 only has detectable oscillations for the bright component. From seismic inference, we are able to constrain the mass of the brightest star. When combined with the RV orbital motion fit, we have inferred a stellar-model-dependent orbital inclination and semi-major axis of $35.43 \pm0.94^{\circ}$ and $129.6 \pm4.2R_{\odot}$, respectively. The radius of the brightest star relative to the orbit is therefore $4.76 \pm0.16\%$. With the eccentricity of 0.264 ± 0.005, we should not expect binary interaction to have impacted the evolution of this star yet. As demonstrated in Montalbán et al. [81], this system was most likely not formed in the Milky Way, but accreted later on. This is exemplified by its high Galactic eccentricity, but also by its APOGEE DR17 abundances; it has a relatively low $\alpha$ enhancement ($[\alpha/\mathrm{Fe}] = 0.15$) for its metallicity ($[\mathrm{Fe}/\mathrm{H}] = -0.77$), as well as a low $[\mathrm{Al}/\mathrm{Fe}] = -0.04$ and high $[\mathrm{Mg}/\mathrm{Mn}] = 0.50$ (see, e.g., Das et al. [34]). Based on the binary orbital parameters, the system is similar to the thick disk benchmark dEB KIC 10001167 studied in Thomsen et al. [114], with a similar orbital period, eccentricity, and semi-major axis. It is worth mentioning that the seismically inferred age of KIC 2971380 places it at 11.7 ± 1.0 Gyr, which is 1.4 ± 1.1 Gyr (∼1.2σ) older than KIC 10001167. This is roughly similar to the age difference found between the two systems in Montalbán et al. [81], who used the CLES stellar evolution code (Scuflaire et al. 2008), which indicates that the result is robust against model systematics.

For our analysis of KIC 2971380, we only included the metallicity and radial mode frequencies as observational constraints, excluding a constraint on $\nu_{\max}$. This way, we can make a model prediction of it using the mode frequencies, independently of the observed value. $\nu_{\max}$ is frequently coupled to the surface gravity $g$ through a solar scaling relation, which is derived under assumption that $\nu_{\max}$ is proportional to the acoustic cutoff frequency $\nu_{\mathrm{cutoff}}$ (Brown et al. [20]; Kjeldsen & Bedding [62]; Belkacem et al. [10]):

We use the solar values $\nu_{\max,\odot}=3090\,\mathrm{\mu Hz}$, $T_{\mathrm{eff}}=5772\,\mathrm{K}$, and $g_\odot=27420.01\,\mathrm{cm}/\mathrm{s}^2$ (Handberg et al. [52]; Prša et al. (2016)). The $\nu_{\max}$ scaling relation in this form is expected to have systematic uncertainties reflected in the unknown correction factor $f_{\nu_{\max}}$ (e.g., Belkacem et al. [10]; Viani et al. [120]), and recent model-dependent asteroseismic inferences of metal-poor stars appear to support this as well (Li et al. (2024); Huber et al. [57]; Larsen et al. [64]; Lundkvist et al. [70]; Lindsay et al. [68]). Since we did not include $\nu_{\max}$ as an observational constraint for KIC 2971380, we can predict $f_{\nu_{\max}}$ using the model-inferred $g$, $T_{\mathrm{eff}}$, and observed $\nu_{\max}$. This will be a model-dependent estimate, performed under the assumption that the individual-mode frequency inference represents the ground truth. We used the model $T_{\mathrm{eff}}$ for this, because we do not have temperature observations that were derived while accounting for the companion star. As found by Li et al. (2024), model-predicted $f_{\nu_{\max}}$ in principle depend on the model temperature scale, and thereby the mixing length. Our stellar model grid uses a fixed solar-calibrated mixing-length value, and a systematic difference between observed and model temperatures could be expected on the RGB. When using this same grid of models, the observed $T_{\mathrm{eff}}$ of the RG in the dEB KIC 10001167 was $\sim40$ K lower than the model-inferred $T_{\mathrm{eff}}$ (Thomsen et al. [114]). When estimating $f_{\nu_{\max}}$ this way, we replaced the statistical uncertainty on $T_{\mathrm{eff}}$ with 80 K in order to simulate the typical accuracy of spectroscopy (Bruntt et al. [21]).

With this we derived $f_{\nu_{\max}} = 1.019 \pm0.011$, which is of low significance but indicative of the need for a correction larger than one for metal-poor stars. Particularly if $f_{\nu_{\max}}$ is increasing with decreasing metallicity, this would be consistent with the larger corrections inferred from individual mode frequencies for the most metal-poor oscillators (KIC 8144907 Huber et al. [57], KIC 4671239 & 7693833 Larsen et al. [64], HD140283 Lundkvist et al. [70], HD175305 & 128279 Lindsay et al. [68], $\nu$ Indi Chaplin et al. [24]). We can further compare with the most well-studied low-metallicity dEBs in Kepler that also contain a solar-like oscillator, KIC 10001167, 4054905, 8430105, and 9970396 ([114, 17, 113, 18]). For these dEBs, the surface gravity measurement is dependent only on the orbital and eclipse modeling, and therefore fully independent of stellar evolutionary models. We show the comparison in Figure 7. The dEBs further support the need for a correction larger than unity for low-metallicity stars.

From the spectroscopy (see Figure 2), the ratio of the line profile integrals of the binary is roughly 25%. While the exact value is dependent on the assumed spectroscopic template, the true luminosity ratio of the binary is likely within the same order of magnitude. Together with the radial velocity mass ratio, we have used this to estimate the properties of the dimmer companion, assuming $L_{\mathrm{dim}}/L_{\mathrm{bright}} \sim0.25 \pm0.05$ and that the two stellar ages agree to at least 1%. From stellar inference, we estimate that the companion is compatible with a star at the base of the RGB, having $R \sim2.8R_{\odot}$ and $\nu_{\max} \sim361 \pm86\,\mu\mathrm{Hz}$. This puts it at or above the Nyquist frequency of Kepler long-cadence data. Unfortunately, with an apparent magnitude of $G = 12.6$, the system is far too dim for the TESS photometry to have photometric precision sufficient to measure oscillations from either star. With a future pointing of the PLATO space mission (Rauer et al. [95]), or with the Earth 2.0 telescope (Ge et al. 2022), this system should be considered a strong target of interest for detection of the companion. With the upcoming Gaia Data Release 4, a potential astrometric orbit fit would allow for a fundamental measurement of the mass of the brightest star, providing the first accreted star with solar-like oscillations and an absolute mass measurement. This would make KIC 2971380 an excellent benchmark system for Galactic archaeology and for studying the early merger history, together with the old thick disk dEB KIC 10001167 [114].

The AB/ABCs KIC 6501237, 10592924, and 11299484

For KIC 6501237 and 10592924, Fig. A.1 and A.2 in the appendix show the posterior distributions of the dim and bright star. The posterior distribution of KIC 11299484 behaves similarly. In the appendix, Fig. A.3, A.4, A.5, A.6, A.7 and A.8 show the power spectra, observed frequencies, and theoretical frequencies for the three systems. Note that we excluded one radial mode from the brighter star of KIC 6501237, due to its high uncertainty and very low peakbagged amplitude. Given the large uncertainty, it would not have affected the inference results.

When we include only a cubic term to the surface correction, the best fit theoretical frequencies of KIC 6501237 deviate significantly from the observed. For the brighter star, most modes were $1-5\sigma$ different, while for the dimmer component, all modes deviated by $1-1.5\sigma$. We verified that this discrepancy remains when fitting the two stars separately. When we included an additional inverse term to the Ball & Gizon [6] surface correction, we recover a good fit of the modes. However, the inverse term of the brighter star is an order of magnitude larger than the cubic one, which is not expected to be correct [6]. This suggests that the discrepancy stems from a systematic difference between the stellar models and the two stars. Despite this, the seismic inference of KIC 6501237 can clearly be reproduced with a coeval model. The stellar ages agree far better (0.4%) than expected from the Gaussian prior (5%). If the dimmer set of oscillations come from the dimmer optically resolved star located at $\sim3$” on-sky separation, the two stars must either be in a very long period orbit, or part of the same stellar association. Based on the predictions of Miglio et al. [78], all optically resolved ABCs in Kepler should in principle be false positives (chance alignments), and the confirmation of such a system is therefore notable.

For KIC 10592924 and KIC 11299484, we find a reasonable agreement between theoretical and observed oscillation mode frequencies when using just the cubic correction. The fit quality of the brighter star in KIC 10592924 was marginally better when including an inverse term. As with KIC 6501237, the high fit quality supports that the stars are well-described as coeval.

For all three, it appears to be possible to infer the initial helium content, at 3% precision for KIC 10592924 and 11299484, and at 4% precision for KIC 6501237. We have illustrated this in the corner plots in the appendix (Fig. A.1 and A.2). In comparison, we could infer helium to 5% precision when studying only the brightest oscillator of an AB. McKeever et al. [76] similarly performed seismic modeling of RGB stars in NGC 6791, and showed that inferring a precise helium mass fraction from a single RGB star can be challenging. Since the stars are on the RGB, the treatment of diffusion and gravitational settling is not expected to have a significant impact on the inferred initial helium values, which is generally a major challenge for main sequence seismology [e.g. 119, 89]. This makes RGB+RGB ABs potential helium calibration systems. In Figure 8, we compare the inferred helium values to the proto-Sun [3], NGC 6791 [19], and Big-Bang Nucleosynthesis [38]. We remark that including an inverse surface term for the brighter star in KIC 10592924 (one-term or two-term) increased the inferred helium value at $\sim0.9\sigma$ significance. In addition, the derived helium value of KIC 6501237 is $\sim2\sigma$ larger than what is expected for the system’s metallicity (for illustration, see Figure 8). Given the need for a large inverse term to the surface effect for KIC 6501237, we tentatively conclude that we have over-fitted its observed frequencies with the additional surface term.

The inference of a precise helium value relied on a $\nu_{\max}$ constraint, using the asteroseismic scaling relation (eq. (11)). This might be avoided if we had observational constraints on the stellar luminosities, however, this is beyond the current scope of this work. Therefore, we note that these first helium measurements, precise but systematically uncertain, should serve as an encouraging motivation to study ABs. In a future study, we will return to these systems with a detailed modeling effort.

The dimmer companions in KIC 6501237 and 10592924 seem to show peculiar dipole modes (Fig. A.4, A.6). Particularly for KIC 10592924, the dipole modes appear depressed compared to the other mode amplitudes. This can be an indication of magnetic activity (e.g., Fuller et al. 2015; Stello et al. 2016).

Conclusion

Binary stars containing two oscillating RGs offer particularly powerful constraints on models of stellar evolution, if the oscillations of the two stars can be disentangled. With high-resolution spectroscopy, we have detected RV variability in 12 candidate binary systems, consistent with them being single-lined or double-lined binaries. Eight of them are also detected as ABs, with three having indications of two overlapping sets of oscillations, four having separate oscillation envelopes, and one (KIC 5015647) showing a very complex power spectrum indicative of a non-solar-like oscillating companion. 5-6 additional systems have spectroscopic line shapes that are atypical of RGs, but with only a single observation with FIES, we have not been able to explore variability in their spectra. By cross-matching our observations with Gaia DR3 and APOGEE DR17, we find an additional 9 likely binaries (6 ABCs), most of which have tentative but supporting indications of binarity across several sources of measurement. Additionally, we confirmed the high-mass evolved oscillator KIC 5978324 (Crawford et al. [32, 33]) as RV variable based on three spectra obtained over 406 days, with $dv/dt = -2.85 \pm0.05$ km/s/year.

With eight spectra of a binary system of extra-galactic origin, KIC 2971380, we were able to constrain the orbital motion, and confirm its mass ratio as consistent with unity to 1% precision. This suggests that the companion is also evolved past the main sequence. With asteroseismic inference of the brighter star, we made predictions for the properties of the companion and the orbit, estimating $\nu_{\mathrm{max,dim}} \sim361 \pm86\,\mu\mathrm{Hz}$, orbit inclination $i \sim35.4 \pm0.9^\circ$, and semi-major-axis $130 \pm4R_{\odot}$. This makes it a prospective target for detection of the companion’s oscillations with either PLATO (Rauer et al. [95]) or the Earth 2.0 Telescope (Ge et al. 2022). We derived an age of $11.7 \pm1.0$ Gyr, consistent with it being $\sim1.4 \pm1.1$ Gyr older than the thick disk dEB KIC 10001167 (Thomsen et al. [114]). Astrometry from the upcoming Gaia DR4 (Gaia Collaboration et al. [42]) might allow us to obtain a precise constraint on the stellar masses.

We performed a double-seismic inference, utilising the oscillation frequencies of both stars, for two ABCs, namely KIC 6501237 and 11299484, and the confirmed AB KIC 10592924. All three targets contain two RGB oscillators. With our inference, we confirmed that the oscillations of their two stellar components are well-modeled as coeval. We obtained precise constraints on their masses ($\sim1.5\%$), mass ratio ($\sim1\%$), and the age of the binary (8–10%), while inferring their initial helium content ($\sim3\%$). Using only the brightest oscillator, the helium could be constrained to $\sim5\%$ precision. For KIC 10592924 and 11299484, we derived helium values consistent with typically assumed linear helium-metallicity relations. Particularly KIC 11299484 agrees well with proto-Solar predictions (Asplund et al. [3]).

Helium inferred from RGs is affected by different systematic uncertainties than main sequence stars. A major challenge for the former is the treatment of diffusion and gravitational settling (e.g. Verma & Silva Aguirre [119]; Nsamba et al. [89]). The uncertainty in the stellar helium content contributes a large systematic uncertainty to stellar parameters, including the age (see, e.g., Fig. 43 of Lebreton et al. [65]). This impacts several fields relying on accurate stellar model parameters and ages, including Galactic archaeology and exoplanetary studies. With a precise helium inference, we demonstrate that ABs with RGs can serve as helium calibration laboratories.

Acknowledgements

We wish to thank the anonymous referee for their thorough review, which led to a significant improvement of the manuscript. We are grateful to Josefina Montalbán for a large number of target suggestions for AB candidates to observe, and for helpful comments on the manuscript draft. JST, AMazzi acknowledge support from Bologna University, "MUR FARE Grant Duets CUP J33C21000410001". AMiglio, Matteuzzi acknowledge support from the ERC Consolidator Grant funding scheme (project ASTEROCHRONOMETRY, https://www.asterochronometry.eu, G.A. n. 772293). JYC acknowledges support from the Klaus Tschira Foundation and funding from the ERC Consolidator Grant DipolarSound (grant agreement # 101000296). Based on observations made with the Nordic Optical Telescope, owned in collaboration by the University of Turku and Aarhus University, and operated jointly by Aarhus University, the University of Turku and the University of Oslo, representing Denmark, Finland and Norway, the University of Iceland and Stockholm University at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofísica de Canarias.

Additional tables and figures

KIC	$\Delta\sigma$<sup>a,b</sup>	$v_c$<sup>c</sup>	$\Delta v$<sup>b,c</sup>	$\frac{dv}{dt}$ (km/s/yr)<sup>c,d</sup>	$\Delta\mathrm{BIC}$<sup>e</sup>	baseline (days)	#<sup>f</sup>	model	source<sup>g</sup>
Significant variability
2971380	7.1	35.0	50.03 (29)	40.18 (68)	-3530	189	7	SB2	1
4260884	3.8	3.6	3.68 (34)	7.84 (68)	-101	180	4	SB2	4
5300269	1.7	2.9	4.1 (10)	-7.8 (18)	-18	201	3	SB2	1,2
7697607	2.1	9.8	0.35 (15)	-0.37 (12)	-8	343	3	SB2	1,2
8479182	0.8	11.8	0.38 (16)	-0.33 (15)	-3	351	5	SB2	1,3
8479383	8.7	10.8	8.19 (18)	10.99 (24)	-2081	275	4	SB2	1,4
8649099	3.3	9.8	0.73 (15)	0.92 (18)	-24	286	5	SB2	1
10592924	0.1	4.8	9.4 (10)	25.1 (27)	-87	137	2	SB2	1,2
4346953	0.03	-0.8	2.77 (14)	-7.08 (37)	-372	143	2	SB1	4
4659808	1.0	19.5	2.23 (15)	-5.59 (37)	-232	146	2	SB1	4
5015647	0.4	-32.0	7.23 (14)	-18.75 (37)	-2532	141	2	SB1	2
5978324	0.4	18.7	3.20 (14)	-2.85 (11)	-634	406	3	SB1	3
Tentative indication of variability
11299484	1.1	5.66	0.45 (25)	0.37 (21)	-2	255	3	SB2	1,2,4
4637699	0.6	-97.0	0.28 (23)	0.55 (47)	0	146	2	SB1	1,3
6501237<sup>h</sup>	2.7	-7.3	0.23 (15)	-0.49 (32)	-2	170	2	SB1	1,2
8181509	0.01	-31.2	0.27 (14)	0.24 (13)	-3	413	2	SB1	1,3
9392647<sup>i</sup>	0.3	-44.7	0.27 (18)	2.1 (14)	-1	42	2	SB1	2,3
9392650<sup>i</sup>	0.5	-83.5	0.39 (18)	3.4 (16)	-4	42	2	SB1	2,3
9412408	0.2	10.3	0.13 (14)	-0.18 (20)	-0	259	2	SB1	1,4
Insignificant variability
6369592	1.8	21.12	0.65 (23)	-0.11 (17)	2	413	4	SB2	3
2442606	0.2	16.5	0.04 (14)	0.22 (91)	1	58	2	SB1	3
4157282	1.0	-19.6	0.01 (15)	-0.03 (46)	1	119	2	SB1	1
4159205	0.3	-62.8	0.02 (14)	0.01 (17)	1	259	2	SB1	1
5024272	0.2	4.5	0.06 (14)	-0.23 (56)	1	94	2	SB1	1
5202286	0.7	16.6	0.08 (15)	-0.09 (18)	0	307	2	SB1	1
5353108	0.2	-50.5	0.05 (14)	-0.15 (41)	1	126	2	SB1	1
5630997	0.1	9.3	0.03 (18)	0.05 (29)	1	227	2	SB1	1
6206407	0.3	-47.7	0.02 (14)	0.04 (23)	1	227	2	SB1	3,4
6208846	0.2	-7.8	0.05 (14)	0.12 (36)	1	143	2	SB1	1
6221548	0.1	-41.2	0.04 (14)	0.11 (40)	1	133	2	SB1	4
6526377	0.2	-6.0	0.01 (14)	0.02 (20)	1	262	2	SB1	2,4
8708536	0.1	-18.0	0.03 (14)	-0.04 (20)	1	263	2	SB1	2
9205419	0.6	-4.7	0.07 (14)	0.04 (13)	2	276	3	SB1	1,2
9775927	0.1	-10.0	0.01 (14)	0.01 (20)	1	259	2	SB1	3,4
10464837	0.3	-22.4	0.05 (14)	0.05 (15)	1	297	2	SB1	1
11352644	0.8	-52.0	0.05 (15)	-0.03 (15)	1	300	2	SB1	1
11136690	0.8	-59.3	0.04 (14)	0.01 (16)	1	255	3	SB1	1

	KIC	$\sigma$ (km/s)	$\alpha$	RUWE$^{a}$	Var/DR3 (#visit)$^{a}$	NSS$^{a}$	RV amp$^{a}$	VSCATTER (#visit)$^{b}$	source$^{c}$
Only one night	1720241	3.186 (27)	1.02 (12)	1.05	False (29)	0	14.25	0.06 (2)	3
Only one night	2304765	3.645 (16)	1.053 (61)	0.91	False (26)	0	4.41	0.02 (3)	1
Only one night	2447476	3.187 (18)	0.872 (92)	1.05	False (26)	0	5.74	0.04 (2)	1
Only one night	3660820	3.394 (18)	1.130 (70)	0.78	False (19)	0	3.38	0.03 (3)	3,4
Only one night	3855003	3.266 (25)	1.185 (99)	0.98	False (20)	0	5.85	0.13 (2)	2
Only one night	3860550	5.403 (31)	0.38 (32)	0.95	False (24)	0	5.88	0.02 (3)	1
Only one night	3955502	5.814 (44)	-0.33 (55)	0.88	False (21)	0	7.80	0.02 (2)	1
Only one night	4058578	3.323 (27)	0.2 (23)	0.98	False (22)	0	8.90		2
Only one night	4282111	3.791 (33)	0.65 (21)	1.19	False (16)	0	11.83	0.12 (3)	1
Only one night	4768054	3.402 (32)	0.89 (16)	0.97	False (18)	0	6.10		2
Only one night	5647777	3.802 (29)	1.06 (11)	1.01	False (15)	0	14.96	0.07 (2)	1
Only one night	5700488	3.550 (26)	1.551 (86)	1.07	False (16)	0	3.42		1
Only one night	5943448	3.205 (19)	1.191 (78)	0.87	False (22)	0	8.44		2
Only one night	6210603	3.501 (9)	1.064 (36)	0.84	False (8)	0	1.46		2
Only one night	6706199	3.626 (31)	1.54 (10)	1.12	False (21)	0	5.48	0.01 (2)	1
Only one night	6707691	3.296 (37)	1.01 (16)	1.93	False (19)	0	7.46		2,4
Only one night	6841636	3.739 (22)	0.922 (93)	1.08	False (17)	0			1
Only one night	7287493	3.409 (13)	1.069 (53)	1.07	False (20)	0	4.10		2
Only one night	8295007	3.263 (15)	1.046 (65)	1.12	False (19)	0	8.75	0.24 (2)	2
Only one night	10841730	3.649 (16)	0.924 (70)	47.53	True (7)	0	8.24	0.06 (2)	2
Only one night	11465942	3.375 (13)	1.194 (49)	1.69	True (19)	0	10.74		2,4
Only one night	11656670	3.481 (22)	1.242 (77)		True (20)	0	4.58		2
Only one night	12117790	3.135 (19)	0.86 (10)	4.04		0		0.06 (2)	1,4
Single-lined RV variable	4346953	3.284 (13)	1.044 (52)	1.37	True (18)	2	11.92	0.12 (5)	4
Single-lined RV variable	4659808	4.676 (20)	0.389 (40)	1.35	True (20)	2	10.11	0.10 (4)	4
Single-lined RV variable	5015647	3.484 (13)	1.033 (62)	10.31	True (22)	2	15.63	1.85 (4)	2
Single-lined RV variable	5978324	3.825 (11)	0.889 (44)	2.54	True (20)	2	9.02		3
Double-lined	2971380	3.662 (23)	0.041 (99)	1.09	True (22)	0	26.68	0.51 (2)	1
Double-lined	4260884	4.107 (13)	-0.572 (36)	13.04		0		0.02 (2)	4
Double-lined	5300269	4.267 (22)	-0.116 (45)	0.94	False (22)	0	7.92		1,2
Double-lined	6369592	3.329 (13)	0.827 (49)	4.81	False (17)	0	11.50		3
Double-lined	7697607	6.786 (23)	-5.127 (81)	0.95	False (29)	0	9.46		1,2
Double-lined	8479182	8.153 (38)	-2.62 (12)	0.90	False (18)	0	3.36	0.10 (5)	1,3
Double-lined	8479383	4.146 (11)	2.129 (37)	1.17	True (16)	0	11.13	0.17 (5)	1,4
Double-lined	8649099	6.905 (88)	-3.1 (17)	0.93	False (16)	0	3.34	0.35 (2)	1
Double-lined	10592924	4.272 (25)	0.632 (69)	1.11	True (15)	0	12.77		1,2
Double-lined	11299484	4.516 (20)	1.459 (58)	1.09	False (14)	0	11.89	0.60 (3)	1,2,4
Single-lined non-detection	2442606	3.387 (12)	1.019 (65)	0.94	False (15)	0	2.46	0.06 (5)	3
Single-lined non-detection	4157282	3.391 (22)	1.064 (95)	0.91	False (15)	0	1.91	0.07 (3)	1
Single-lined non-detection	4159205	3.430 (8)	0.984 (36)	1.07	False (21)	0	14.12	0.12 (5)	1
Single-lined non-detection	4637699	4.070 (40)	-0.23 (17)	1.09	False (22)	0			1,3
Single-lined non-detection	5024272	3.547 (13)	0.94 (10)	0.94	False (16)	0	3.92	0.13 (2)	1
Single-lined non-detection	5202286	3.352 (23)	1.090 (16)	0.98	False (23)	0	2.90	0.03 (3)	1
Single-lined non-detection	5353108	3.508 (6)	1.107 (22)	0.86	False (16)	0	0.83	0.04 (2)	1
Single-lined non-detection	5630997	3.480 (46)	1.13 (16)	1.03	False (19)	0	1.58	0.05 (4)	1
Single-lined non-detection	6206407	3.335 (13)	1.053 (57)	34.04		0			3,4
Single-lined non-detection	6208846	3.425 (9)	1.085 (34)	0.95	False (18)	0	1.15	0.05 (2)	1
Single-lined non-detection	6221548	3.801 (13)	0.931 (55)	0.94	False (18)	0	2.88	0.05 (2)	4
Single-lined non-detection	6501237	3.701 (19)	1.088 (70)	1.03	False (18)	0	6.41		1,2
Single-lined non-detection	6526377	3.414 (12)	1.154 (46)	0.89	False (6)	0	1.22	0.02 (2)	2,4
Single-lined non-detection	8181509	3.530 (7)	1.085 (27)	3.10	True (15)	2	5.35	0.22 (2)	1,3
Single-lined non-detection	8708536	3.324 (7)	1.081 (29)	0.87	False (18)	0	2.61		2
Single-lined non-detection	9205419	3.389 (10)	0.761 (40)	1.06	False (21)	0	16.74	0.07 (3)	1,2
Single-lined non-detection	9392647	3.153 (20)	0.713 (78)	1.05	False (25)	0			2,3
Single-lined non-detection	9392650	3.420 (46)	1.080 (16)	0.88	False (30)	0	3.95	0.09 (5)	2,3
Single-lined non-detection	9412408	3.397 (13)	1.026 (65)	0.94	False (15)	0	1.38		1,4
Single-lined non-detection	9775927	3.536 (8)	1.080 (31)	1.01	False (11)	0	2.81		3,4
Single-lined non-detection	10464837	3.481 (10)	1.044 (42)	1.02	False (27)	0			1
Single-lined non-detection	11136690	3.765 (14)	0.959 (57)	0.93	False (22)	0	13.00	0.52 (3)	1
Single-lined non-detection	11352644	3.519 (15)	0.951 (64)	1.09	False (15)	0		0.61 (3)	1

BJD-X	RV (bright)	RV (dim)	Cov (km$^{2}$/s$^{2}$)
744.7479	-3.778 (79)	15.38 (33)	0.00595
798.7172	16.169 (87)	-4.30 (34)	-0.00570
839.6515	13.420 (75)	-1.35 (27)	0.00674
848.5864	10.030 (66)	1.70 (28)	0.00888
862.7040	3.20 (10)	9.25 (45)	0.00709
863.4471	2.711 (64)	9.56 (27)	0.00458
888.5140	-11.547 (52)	23.37 (20)	-0.00002
933.5083	17.77 (20)	-6.03 (77)	0.00675

$\ell$	KIC 6501237	KIC 10592924	KIC 11299484	KIC 2971380$^{a}$
1	41.497 (52)	36.168 (27)
2	43.36 (18)	37.937 (26)	35.36 (13)
0	44.33 (12)	38.646 (22)	36.047 (14)	57.031 (19)
1	47.398 (27)	41.284 (29)	38.592 (18)
2	49.284 (17)	42.967 (12)	40.111 (18)	63.372 (48)
0	50.123 (13)	43.704 (10)	40.768 (17)	64.497 (16)
1	53.209 (15)	46.484 (13)	43.473 (24)
2	55.2724 (92)	48.353 (13)	45.1678 (99)	71.2577 (81)
0	56.1564 (97)	49.1114 (84)	45.8686 (68)	72.4132 (70)
3?				73.732 (19)
1	59.398 (10)	51.915 (12)	48.505 (21)
2	61.5104 (69)	53.7870 (87)	50.2217 (92)	79.143 (11)
0	62.3054 (69)	54.4933 (85)	50.901 (11)	80.2257 (90)
3?		55.5410 (74)
1	65.491 (11)	57.229 (23)	53.499 (21)
2	67.6551 (96)	59.189 (12)	55.362 (22)	87.183 (30)
0	68.432 (11)	59.935 (14)	56.011 (21)	88.227 (16)
3?				89.605 (85)
1	71.688 (19)	62.799 (33)	58.896 (33)
2	74.007 (19)	64.836 (53)	60.578 (23)	95.19 (11)
0	74.851 (16)	65.559 (37)	61.117 (86)	96.355 (30)
1	78.102 (33)	68.223 (69)
2	80.26 (19)	70.310 (64)
0	81.16 (25)	71.20 (18)
2	105.99 (22)	111.832 (42)	81.775 (16)
0	107.396 (26)	113.306 (18)	82.8346 (82)
1		118.929 (51)
2	116.552 (14)	122.984 (15)	89.940 (20)
0	117.9211 (73)	124.429 (13)	91.010 (12)
3?		126.603 (42)
1		129.980 (51)
2	126.996 (12)	133.943 (21)	98.124 (22)
0	128.297 (10)	135.3836 (98)	99.142 (18)
3?		137.630 (28)
2	137.645 (46)	145.090 (32)	106.553 (72)
0	138.945 (26)	146.506 (19)	107.610 (72)
3?		149.094 (75)
1		152.470 (33)
2		156.126 (42)
0	149.727 (79)	157.533 (92)

67.370 (19)	75.0051 (61)	81.5798 (71)	91.686 (23)
68.071 (14)	75.3706 (60)	82.034 (64)	92.191 (29)
68.3396 (68)	75.7982 (45)	82.495 (63)	92.615 (19)
68.8495 (59)	76.1408 (54)	82.959 (16)	93.0945 (73)
69.1612 (18)	76.4875 (48)	83.4818 (43)
69.4833 (56)	76.8045 (63)	83.9627 (89)
69.8227 (96)	77.1701 (28)	84.3387 (64)
	77.5727 (79)	84.6943 (53)
	77.9867 (48)	85.1309 (69)
		85.552 (21)

Spectroscopic bias from two stars

As mentioned in Sect. 2, due to our FIES observations having low S/N, we did not attempt an atmospheric analysis. However, many of our targets have also been observed at lower spectroscopic resolution ($R \sim22.500$, $\delta v \sim13$ km/s) in the near-infrared by APOGEE Majewski et al. [71], and have atmospheric parameters available in APOGEE DR17 Abdurro’uf et al. [1], derived under the assumption that the source only contained a single star. We evaluate whether this is sufficient to produce an accurate measure of atmospheric parameters for the brightest star, at least within typically adopted uncertainties for effective temperature and metallicity, in a way that is in principle similar to the investigations on unresolved main sequence binaries by El-Badry et al. [36]. Since the ABs and ABCs that we study have RV separations below the resolution of APOGEE, we can assume that both stars contribute to the lines used for atmospheric analysis. For the optically resolved system KIC 6501237, it is not certain that the companion contributed to the spectrum, and our investigation is therefore just an upper limit to the expected bias.

We used the metallicity from APOGEE DR17, together with the asteroseismically inferred luminosity ratio, effective temperatures, and log $g$’s (see Table 3). We then constructed synthetic spectra with the same atmospheric parameters, and blended them using the luminosity ratio. We computed the synthetic spectral profiles using the 2020 version of the 1D radiative transfer code Turbospectrum Plez et al. [92], accounting for Non-Local Thermodynamic Equilibrium effects. The synthesis was performed employing standard 1D plane-parallel MARCS model atmospheres Gustafsson et al. [51]. The atomic and molecular linelist for the H-band region ($1.5$–$1.7\,\mu\mathrm{m}$) was retrieved from the VALD3 database Ryabchikova et al. [99]. Finally, the synthetic profiles were convolved with a Gaussian profile to match the instrumental resolving power of $R=22,000$. For blending the two stars, we neglect the chromatic impact on the light ratio, which is sufficient since the temperature ratio is close to unity. In Fig. B.1, this is illustrated in the near-infrared for KIC 10592924. We used a Turbospectrum wrapper Gerber et al. [48] to fit the Fe I lines for each spectrum separately (i.e., component A, component B, and the combined spectrum), while keeping the atmospheric stellar parameters fixed. The derived metallicities are consistent within $\pm0.10$ dex, which is similar to typical observational uncertainties (e.g. Bruntt et al. [21]). With a similar analysis of the temperature, we determined that the brightest star is expected to be within 150K of the observed.

Since KIC 10592924 has the most equal luminosity ratio compared to the difference in effective temperature between the stars, the bias is expected to be smaller for the other stars.