11institutetext: IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette
Cedex, France
11email<EMAIL_ADDRESS>22institutetext: Université Paris Diderot, AIM,
Sorbonne Paris Cité, CEA, CNRS, F-91191 Gif-sur-Yvette Cedex, France
33institutetext: Max-Planck-Institut für Sonnensystemforschung, Justus-von-
Liebig-Weg 3, 37077 Göttingen, Germany
33email<EMAIL_ADDRESS>44institutetext: Department of Astronomy, New
Mexico State University, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003-8001,
USA 55institutetext: Deparment of Astronomy, Yale University, 52 Hillhouse
Avenue, New Haven, CT 06511, USA 66institutetext: Institute of Astronomy, KU
Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium 77institutetext:
Institute of Physics, Karl-Franzens University of Graz, NAWI Graz,
Universitätsplatz 5/II, 8010 Graz, Austria. 88institutetext: Instituto de
Astrofísica de Canarias, 38200 La Laguna, Tenerife, Spain 99institutetext:
Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna,
Tenerife, Spain 1010institutetext: Space Science Institute, 4750 Walnut Street
Suite 205, Boulder, CO 80301, USA

# Spectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by Kepler

M. Benbakoura Spectroscopic and seismic analysis of red giants in eclipsing
binaries discovered by KeplerSpectroscopic and seismic analysis of red giants
in eclipsing binaries discovered by KeplerSpectroscopic and seismic analysis
of red giants in eclipsing binaries discovered by KeplerSpectroscopic and
seismic analysis of red giants in eclipsing binaries discovered by Kepler P.
Gaulme Spectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by KeplerSpectroscopic and seismic analysis of
red giants in eclipsing binaries discovered by KeplerSpectroscopic and seismic
analysis of red giants in eclipsing binaries discovered by Kepler J. McKeever
Spectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by KeplerSpectroscopic and seismic analysis of
red giants in eclipsing binaries discovered by KeplerSpectroscopic and seismic
analysis of red giants in eclipsing binaries discovered by Kepler S. Sekaran
Spectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by Kepler P. G. Beck Spectroscopic and seismic
analysis of red giants in eclipsing binaries discovered by KeplerSpectroscopic
and seismic analysis of red giants in eclipsing binaries discovered by
KeplerSpectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by KeplerSpectroscopic and seismic analysis of
red giants in eclipsing binaries discovered by KeplerSpectroscopic and seismic
analysis of red giants in eclipsing binaries discovered by Kepler F. Spada
Spectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by Kepler J. Jackiewicz Spectroscopic and
seismic analysis of red giants in eclipsing binaries discovered by
KeplerSpectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by Kepler S. Mathis Spectroscopic and seismic analysis of red
giants in eclipsing binaries discovered by KeplerSpectroscopic and seismic
analysis of red giants in eclipsing binaries discovered by KeplerSpectroscopic
and seismic analysis of red giants in eclipsing binaries discovered by
KeplerSpectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by Kepler S. Mathur Spectroscopic and seismic analysis of red
giants in eclipsing binaries discovered by KeplerSpectroscopic and seismic
analysis of red giants in eclipsing binaries discovered by KeplerSpectroscopic
and seismic analysis of red giants in eclipsing binaries discovered by
KeplerSpectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by KeplerSpectroscopic and seismic analysis of
red giants in eclipsing binaries discovered by Kepler A. Tkachenko
Spectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by Kepler R. A. García Spectroscopic and seismic
analysis of red giants in eclipsing binaries discovered by KeplerSpectroscopic
and seismic analysis of red giants in eclipsing binaries discovered by
KeplerSpectroscopic and seismic analysis of red giants in eclipsing binaries
discovered by KeplerSpectroscopic and seismic analysis of red giants in
eclipsing binaries discovered by Kepler

(Received Feb 20, 2020; accepted Jan 13, 2021)

Eclipsing binaries (EBs) are unique targets for measuring accurate stellar
properties and constraining stellar evolution models. In particular, it is
possible to measure masses and radii at the few percent level for both
components of a double-lined spectroscopic EB (SB2-EB). On the one hand,
detached EBs hosting at least one star with detectable solar-like oscillations
constitute ideal test objects to verify the ability of ensemble
asteroseismology to derive stellar properties. On the other hand, the
oscillations and surface activity of stars that belong to EBs offer unique
information about the evolution of binary systems. This paper builds upon
previous works dedicated to red giant stars (RG) in EBs; so far 20 known
systems have been discovered by the NASA Kepler mission. We report the
discovery of 16 RGs in EBs, which are also from the Kepler data, leading to a
total of 36 confirmed RG stars in EBs from the original Kepler mission. This
new sample includes three SB2-EBs with oscillations, resulting in a total of
14 known SB2-EBs with an oscillating RG component. This sample also includes
six close systems in which the RG display a clear surface activity and
complete oscillation suppression. Based on dedicated high-resolution
spectroscopic observations (Apache Point Observatory, Observatoire de Haute
Provence), we focus on three main aspects. Firstly, from the extended sample
of 14 SB2-EBs, we confirm that the simple application of the asteroseismic
scaling relations to RGs overestimates masses and radii of RGs by about 15 %
and 5 %. This bias can be reduced by employing either new asteroseismic
reference values for RGs or model-based corrections of the asteroseismic
parameters. Secondly, we confirm that close binarity leads to a high level of
photometric modulation (up to 10 %) and a suppression of solar-like
oscillations. In particular, we show that it reduces the lifetime of radial
modes by a factor of up to 10. Thirdly, we use our 16 new systems to
complement previous observational studies that aimed to constrain tidal
dissipation in interacting binaries. We confirm the important role of the
equilibrium tide in binary evolution, but we also identify systems with
circular orbits despite relatively young ages, which suggests the need to
explore complementary tidal dissipation mechanisms in the future. Finally, as
a by-product, we report the measurements of mass, radius, and age of three
M-dwarf companion stars.

###### Key Words.:

asteroseismology – binaries: eclipsing – binaries: spectroscopic – stars:
fundamental parameters – stars: oscillations – stars: evolution

##  1 Introduction

Stellar astrophysics relies on precise and accurate measurements of stellar
parameters. Over the past decade, high-precision photometric space missions
such as CoRoT111CoRoT: Convection, Rotation et Transits planétaires, Kepler,
and TESS222TESS: Transiting Exoplanet Survey Satellite (Baglin et al., 2006;
Borucki et al., 2010; Ricker et al., 2014) have led to significant progress in
this direction. As a result of the unprecedented performance of these
missions, tens of thousands of stars have been characterized through
asteroseismology. Among the different types of pulsating stars (e.g., Aerts et
al., 2010), solar-like oscillators are the most observed. The vast majority of
solar-like oscillators observed by Kepler are red giants (RGs) because most
targets were observed at a 29.4244 min cadence, which does not allow us to
detect oscillations of main-sequence (MS) and subgiant stars. In total, solar-
like pulsations were detected for more than 20 000 RG and 500 MS stars
(Chaplin & Miglio, 2013; Hon et al., 2019; García & Ballot, 2019).

The oscillation properties of a solar-like oscillator are unambiguously
connected to its mass and radius. The simplest and most popular application of
asteroseismology consists of comparing the global oscillation properties333The
oscillation frequency at their maximum amplitude $\nu_{\mathrm{max}}$ and the
mean frequency spacing $\Delta\nu$ between consecutive overtones. of a given
star to those of the Sun and retrieving its mass and radius from asteroseismic
scaling relations (Brown et al., 1991; Kjeldsen & Bedding, 1995). For RGs, the
evolutionary state (hydrogen shell or helium core burning) and core rotation
can also be determined from the analysis of the mixed modes, which result from
the interaction of gravity ($g$) modes in the radiative core and acoustic
pressure ($p$) modes in the convective envelope (Beck et al., 2011, 2012;
Bedding et al., 2011; Mosser et al., 2011a, 2012; Deheuvels et al., 2012,
2014, 2016; Gehan et al., 2018).

Given the central role of solar-like oscillators as tests for stellar models,
it is of critical importance to identify a set of benchmark stars. Such
references are stars whose main physical properties are known with high
precision, especially mass, radius, metallicity, and temperature. Eclipsing
binaries (EBs) hosting at least one star with detectable solar-like
oscillations constitute ideal test benches as they can be accurately
characterized from the combination of both spectroscopic and photometric
observations. It is possible to determine the mass and radius of each
component of a double-line spectroscopic binary (SB2) from measurements of
eclipse photometry and radial velocities. Hitherto, all solar-like oscillators
belonging to EBs are RGs detected by the Kepler mission (Hekker et al., 2010;
Gaulme et al., 2013, 2014; Beck et al., 2014, 2015; Kuszlewicz et al., 2019;
Gaulme & Guzik, 2019). So far, 11 wide SB2 EBs, including an oscillating RG,
have been fully characterized with the help of ground-based radial velocity
support (Frandsen et al., 2013; Rawls et al., 2016; Gaulme et al., 2016a;
Brogaard et al., 2018; Themeßl et al., 2018). We note that an equivalent
number of RGs displaying oscillations have been detected in highly eccentric
non-eclipsing binaries (heartbeat systems, see Beck et al., 2014, 2015; Gaulme
et al., 2013, 2014; Kuszlewicz et al., 2019), but most do not show eclipses
and are single-line spectroscopic binaries (SB1s).

In that context, oscillating RGs in SB2 EBs are perfect targets to verify the
accuracy of masses and radii obtained with asteroseismology. Gaulme et al.
(2016a) find that the strict application of the scaling laws as defined by
Kjeldsen & Bedding (1995) leads to overestimating masses and radii by about
25% and 10%, respectively. Corrections of the asteroseismic scaling relations
that were proposed at the time (Kallinger et al., 2010; Chaplin et al., 2011;
Mosser et al., 2013; White et al., 2011; Epstein et al., 2014; Sharma et al.,
2016; Guggenberger et al., 2016) reduced these discrepancies to 15% and 5%.
Since then, new corrections to the seismic scaling relations have been
proposed (e.g., Rodrigues et al., 2017; Kallinger et al., 2018; Sahlholdt &
Silva Aguirre, 2018). Huber et al. (2017) find excellent agreement between
radii obtained through the asteroseismic scaling relations and those computed
from TGAS parallaxes (Gaia Collaboration et al., 2016). Brogaard et al. (2018)
obtain additional radial velocities for three sources that were previously
observed by Gaulme et al. (2016a) and show that the correction published by
Rodrigues et al. (2017) improved the accuracy of the seismic estimates of mass
and radius. Themeßl et al. (2018) report the detection of an 11th pulsating
red giant in an eclipsing binary and propose new “solar” reference values by
showing that it leads to a better agreement. Theoretical studies based on RG
in EBs have already been undertaken to constrain stellar models. For example
Li et al. (2018) obtain a better agreement between the dynamical and
asteroseismic masses by increasing the convective overshoot by about 14 %.
Besides, Ball et al. (2018) suggest that differences between the composition
profile of the stellar models and the actual profile could explain part of the
current mismatch between the dynamical and seismic masses and radii. More such
benchmark systems are needed to go further.

In parallel to this, significant advances were made possible by Kepler
concerning observational studies of the tidal evolution of binary systems.
First, the long-term photometric stability of Kepler made the measurement of
stellar rotation rates up to periods as long as half a year possible (Ceillier
et al., 2017; Gaulme et al., 2020). This opened the door to observational
studies of tidal synchronization (Lurie et al., 2017). In particular, Gaulme
et al. (2014) observe that RGs in the most close-in eclipsing binary systems
of their sample did not oscillate as expected. Among the 19 Kepler RGs in EBs
they studied, six displayed partially suppressed oscillations and the giants
in the four closest systems showed no detectable oscillations.

Gaulme et al. (2014) suggest that the mode suppression in binary systems
originates from tidal interaction. Red giant stars that normally rotate in
several tens of days, sometimes in a few hundreds, are spun up during
synchronization, which leads them to develop a stronger dynamo mechanism
inside the convective envelope (see also Carlberg et al., 2011; Aurière et
al., 2015). The magnetic field generated by this dynamo reduces the excitation
of pressure waves by partially suppressing convective motions. Additionally,
spots absorb part of the energy of the pressure modes, altogether leading to
oscillation suppression.

Gaulme et al. (2016a) show that the absence of mode detection was not an
observational bias but a true mode damping. The shorter the orbital period and
the closer the stars are, the weaker the oscillation modes become until
complete mode depletion is reached. These authors observe the damping of modes
in systems with an orbital period shorter than approximately 40 days, for
which most orbits are circularized and rotation periods are synchronized. This
suppression of mode power confirms the inverse relation between mode amplitude
and magnetic activity observed for the Sun and other solar-like stars (for
more details, see, e.g., García et al., 2010; Mathur et al., 2019). This is
further confirmed by Beck et al. (2018b), who show that systems with short
circularization timescales have suppressed oscillations.

The Kepler light curves also enabled the study of the tidal circularization of
binary systems by, for example, Van Eylen et al. (2016) and Beck et al.
(2018b). While the former studied mainly MS stars, the latter focused on RGs.
Beck et al. test the theoretical predictions of Zahn (1966a, b, c, 1977,
1989), Mathis (2015), and Gallet et al. (2017) for tidal evolution timescales
by comparing them to observational constraints obtained on well-characterized
Kepler RGs belonging to binary systems. Doing so, Beck et al. continued the
study led by Verbunt & Phinney (1995) by extending the sample to a total of 50
stars and pushing further the calculations. Beck et al. find that the most up-
to-date theory of tidal dissipation mechanisms was able to predict the orbital
configuration of the systems they considered. Consequently, extending their
sample to find challenging cases or confirm their conclusion is necessary to
reinforce the connection between observational and theoretical studies of
tidal interactions.

In this paper, we report the identification of 16 new RGs in EB systems from
the Kepler data, for which we lead a detailed photometric analysis, including
oscillations properties, mixed dipolar modes, and surface rotation and
activity. We then present the results of three years of high-resolution
spectroscopic observations, primarily obtained at the Apache Point
Observatory, with complementary support from the Haute-Provence Observatory.
The objectives of the present paper are: 1) to test and improve the
calibration of the asteroseismic scaling relations of RGs; 2) to study the
properties of oscillations and surface activity444 In this paper, ”surface
activity” refers to any signal in the light curve of a star that is not linked
to stellar oscillations or eclipses.  of stars under the influence of a close
stellar companion; and 3) to provide new benchmark stars for tidal evolution
theories. We first present our sample and describe the photometric and
spectroscopic data sets we use (Sect. 2). We then detail the methods employed
to perform the seismic, dynamical, and orbital analyses of each binary we
considered (Sect. 3). Results and discussions about each objective of the
paper are covered in Sect. 4. Finally, our conclusions are presented in Sect.
5.

##  2 Observations and data reduction

In total, we observed and analyzed the data of 17 stars: 16 were new
dectections and one, KIC 4663623, had already been published by Gaulme et al.
(2016a). We found these systems by crossing catalogs of variable stars (e.g.,
the General Catalog of Variable Stars; Samus’ et al., 2017), EBs (e.g., the
Kepler Eclipsing Binary Catalog; Prša et al., 2011; Abdul-Masih et al., 2016),
and RGs (e.g., the APOKASC catalog; Pinsonneault et al., 2014).We used two
different types of data: photometric light curves obtained by the Kepler
satellite and stellar spectra obtained at ground-based telescopes. We
processed the Kepler data in three different ways to optimize the light curves
to study the eclipses, stellar oscillations, and surface dynamics. From the
spectroscopic observations, we derived the atmospheric parameters, chemical
composition, and radial velocities of the stars in our sample.

###  2.1 Kepler photometry

We worked with the Kepler target pixel files (TPF) to create our own aperture
photometry and to produce the Kepler light curves, following the same approach
as Bloemen (2014). For each quarter, we defined a mask, that is, a set of
pixels around the star, which maximizes the stellar signal while minimizing
the noise and other sources of pollution. The resultant light curves of each
quarter were then assembled following three different methods to obtain the
seismic, eclipse, and rotation light curves. Light curves are used for three
purposes: eclipse modeling, asteroseismic modeling, and surface rotation
analysis. This entails modeling eclipse shapes by removing surface activity
and measuring solar-like oscillations by removing eclipse features (Gaulme et
al., 2013, 2014, 2016a).

For the seismic light curve, we first removed the eclipses using the
timestamps from the Kepler Eclipsing Binary Catalog (KEBC; Abdul-Masih et al.,
2016). The light curves of each quarter were then corrected and stitched
together following García et al. (2011). The first step of their method
consists of correcting the light curves of each quarter for outliers in the
point-to-point deviation function, sudden jumps of the mean value, and drifts.
Then, to connect two light curves together at a quarter edge without
discontinuity, two methods are considered: first, computing the mean value of
the flux, at the end of Q(n) and at the beginning of Q(n+1), and adding or
subtracting the difference to the Q(n+1) light curve; and second, fitting the
end of Q(n) and beginning of Q(n+1) with first-order polynomials and linking
the fits together at the midpoint of the gap between them. Both options are
applied and that with the lowest $\chi^{2}$ is chosen. The light curves we
obtained through this process still had long-period trends and periodic gaps
owing to instrumental reasons and the eclipse removal. To reduce their impact
in the time series, we applied a high-pass filter with a cutoff period of 20
days and filled the gaps using a multiscale discrete cosine transform of an
in-painting algorithm (García et al., 2014b; Pires et al., 2015).

The preparation of light curves optimized to analyze the surface rotation
follows the same steps as for asteroseismic analysis. However, a cutoff period
of 20 days would not be suited to study the rotation of RGs because it would
filter out most of the signal (García et al., 2014a). Since the Kepler
quarters are approximately 90 days long, signals with a period longer than
this duration are not reliable, thus we set the cutoff period to 80 days for
the surface-rotation light curves.

For the study of the eclipses, we assembled the light curves in a different
way. We computed the average of the flux at the end of Q(n) and at the
beginning of Q(n+1) and we equalized them to ensure the best continuity in the
time series. We then followed Gaulme et al. (2013, see their Sect. 3.2), who
defined five categories of EBs, depending on their orbital period and surface
activity, and described the methods they used to smooth them.

Figure 1: Three light curves of KIC 10015516 computed from the Kepler
observations. Top panel: Light curve optimized to analyze the surface
rotation. Middle panel: The same data optimized for the asteroseismic
analysis. Bottom panel: The same for eclipse analysis.

Figure 1 shows the three light curves we produced for KIC 10015516. It should
be noted that, in the middle panel, the modulations caused by the surface
rotation are not totally erased in the seismic light curve. Suppressing these
would imply to choose a shorter cutoff period for the high-pass filter.
However, as explained in Sect. 3.1, it is important to keep the signature of
the granulation in the power spectrum to perform the seismic analysis, which
is why we kept the value of 20 days for the cutoff period.

###  2.2 Spectroscopic observations

The majority of the spectra we used were obtained during a four-year campaign
with the ARCES spectrograph (Wang et al., 2003, $R\sim 31\,000$) mounted on
the 3.5 m telescope at Apache Point Observatory (APO). We also used one other
instrument, SOPHIE (Bouchy & the SOPHIE Team, 2006, $R\sim 40\,000$ in High-
Efficiency mode) at the 1.93 m telescope at the Haute-Provence Observatory
(OHP). We used spectra from both instruments to compute the radial velocities,
but only kept those obtained with ARCES to derive the atmospheric parameters.

Table 1: Atmospheric parameters of the giant stars in our sample.

Label | KIC | $\textsl{T}_{\mathrm{eff}}$ | $\log g$ | [Fe/H] | $v_{\mathrm{micro}}$ | $v_{\mathrm{broad}}$
---|---|---|---|---|---|---
|  | (K) | (dex) | (dex) | (km s-1) | (km s-1)
A | 4054905aa$a$For these SB2 systems, we fixed the value of $\log g$ during the spectroscopic analysis to that provided by the dynamical analysis (see Table 3). | 4790 $\pm$ 190 | … | -0.72 $\pm$ 0.31 | 0.74 $\pm$ 0.75 | 57.6 $\pm$ 5.5
B | 4360072 | 5020 $\pm$ 210 | 2.79 $\pm$ 0.45 | -0.14 $\pm$ 0.23 | 0.57 $\pm$ 0.58 | 38.0 $\pm$ 3.3
C | 4473933 | 4530 $\pm$ 220 | 2.89 $\pm$ 0.59 | -0.41 $\pm$ 0.28 | 1.25 $\pm$ 0.80 | 49.8 $\pm$ 4.5
D | 4663623bb$b$KIC 4663623: atmospheric parameters from Gaulme et al. (2016a). | 4812 $\pm$ 92 | 2.7 $\pm$ 0.2 | -0.13 $\pm$ 0.06 | … | …
E | 5193386cc$c$KIC 5193386: atmospheric parameters from APOGEE DR14 (Abolfathi et al., 2018). | 4780 $\pm$ 100 | 3.284$\pm$ 0.014 | -0.36 $\pm$ 0.06 | … | …
F | 5866138 | 4960 $\pm$ 120 | 3.04 $\pm$ 0.24 | 0.05 $\pm$ 0.13 | 1.40 $\pm$ 0.33 | 5.4 $\pm$ 1.6
G | 6307537aa$a$For these SB2 systems, we fixed the value of $\log g$ during the spectroscopic analysis to that provided by the dynamical analysis (see Table 3). | 4960 $\pm$ 240 | … | -0.03 $\pm$ 0.43 | 2.0 $\pm$ 1.4 | 95.4 $\pm$ 8.1
H | 6757558 | 4590 $\pm$ 110 | 2.30 $\pm$ 0.31 | -0.04 $\pm$ 0.13 | 1.24 $\pm$ 0.40 | 4.9 $\pm$ 1.9
I | 7133286aa$a$For these SB2 systems, we fixed the value of $\log g$ during the spectroscopic analysis to that provided by the dynamical analysis (see Table 3). | 4500 $\pm$ 110 | … | -0.60 $\pm$ 0.18 | 1.40 $\pm$ 0.58 | 31.1 $\pm$ 2.4
J | 7293054aa$a$For these SB2 systems, we fixed the value of $\log g$ during the spectroscopic analysis to that provided by the dynamical analysis (see Table 3). | 4790 $\pm$ 160 | … | 0.11 $\pm$ 0.26 | 1.99 $\pm$ 0.86 | 26.1 $\pm$ 2.2
K | 7768447 | 4760 $\pm$ 160 | 2.96 $\pm$ 0.24 | 0.17 $\pm$ 0.25 | 3.0 $\pm$ 1.4 | 16.2 $\pm$ 2.8
L | 8435232aa$a$For these SB2 systems, we fixed the value of $\log g$ during the spectroscopic analysis to that provided by the dynamical analysis (see Table 3). | 4460 $\pm$ 130 | … | -0.15 $\pm$ 0.24 | 2.00 $\pm$ 0.85 | 30.9 $\pm$ 3.0
M | 9153621 | 4760 $\pm$ 190 | 2.34 $\pm$ 0.39 | -0.35 $\pm$ 0.21 | 1.38 $\pm$ 0.55 | 16.6 $\pm$ 2.3
N | 9904059 | 4830 $\pm$ 160 | 2.83 $\pm$ 0.24 | 0.01 $\pm$ 0.26 | 1.05 $\pm$ 0.69 | 24.5 $\pm$ 2.3
O | 10015516 | 4830 $\pm$ 130 | 1.83 $\pm$ 0.22 | -0.43 $\pm$ 0.15 | 1.27 $\pm$ 0.35 | 23.6 $\pm$ 1.4
P | 10074700dd$d$KIC 10074700: The spectroscopic analysis with GSSP did not converge; we used the values from the Kepler Input Catalog, where no uncertainty is given. We thus adopt the typical error bar found for this sample.  | 5070 $\pm$ 100 | 4.53 $\pm$ 0.20 | -0.40 $\pm$ 0.10 | … | …
Q | 11235323aa$a$For these SB2 systems, we fixed the value of $\log g$ during the spectroscopic analysis to that provided by the dynamical analysis (see Table 3). | 4840 $\pm$ 200 | … | -0.36 $\pm$ 0.25 | 2.6 $\pm$ 1.4 | 26.3 $\pm$ 3.0
555For some systems, we added an extra step in the GSSP analysis or used
different values.

####  2.2.1 Radial velocities

From the reduced 1D spectra obtained at APO, we computed the radial velocities
with the broadening-function technique (BF; Rucinski, 1999, 2002). The
fundamental hypothesis of this method is that the program spectra can be
reconstructed as the convolution of a template spectrum and a broadening
function. The latter can then be fitted by a Gaussian function whose central
value is equal to the radial velocity of the star. For SB2 systems, the BF
shows two peaks that correspond to the radial velocities of both components of
the binary star.

For the BF template spectra, we used stellar atmosphere models generated by
the PHOENIX BT-Settl code (Allard et al., 2003). These spectra were computed
using solar abundances published by Asplund et al. (2009). We used templates
of MS stars with $\textsl{T}_{\mathrm{eff}}$ = 5500 K or 5800 K to maximize
the probability of detecting the radial velocity of the companion. Moreover,
the RG atmosphere models contain numerous lines that generate noise in the BF.
As a consequence, even the radial velocity of the giant component is easier to
determine using an atmosphere model of a MS star.

For each star in our sample, we defined a wavelength range on which we
computed the BF. The portion of spectra we used are typically between 4 500 Å
and 5 800 Å. The lower limit of the wavelength range cannot be less than 4 300
Å because the APO spectra are too noisy below this value. We did not consider
wavelengths above 6 300 Å for two main reasons. First, we wanted to maximize
the contribution of the companion in the spectrum used for the BF. Since our
systems are composed of a RG and a hotter star, this implied we would only
keep the bluest wavelengths possible. Second, telluric lines arising from the
absorption of light by $\mathrm{O}_{2}$ and $\mathrm{H}_{2}\mathrm{O}$
molecules in the terrestrial atmosphere pollute the stellar spectra. If we
neglect the impact of the $\mathrm{O}_{2}$ $\delta$ band, the first absorption
lines of this molecule are located around 6 288 Å, which corresponds to the
$\mathrm{O}_{2}$ $\gamma$ band (Newnham & Ballard, 1998).

Prior to the BF computation, the spectra had to be evenly spaced in velocity.
For each star in the sample, we used a specific step size in velocity,
typically around 1 km s-1. The wavelength range and the velocity step size
could vary from one star to another. For example, when the companion was not
luminous enough, we considered bluer wavelength ranges to maximize our chances
to detect its radial velocity.

For the SOPHIE data, an existing pipeline allows us to determine the radial
velocities from the spectra. More details on the data reduction and radial
velocity measurement from the SOPHIE spectra are given in, for example,
Santerne et al. (2011b, a), and references therein. The radial velocities we
used in this work are compiled in Table LABEL:tab:radial_velocities.

####  2.2.2 Atmospheric parameters

From our high-resolution spectra, we determined the stellar atmospheric
parameters: the effective temperature $\textsl{T}_{\mathrm{eff}}$, logarithmic
surface gravity $\log g$, metallicity $[\mathrm{Fe/H}]$, microturbulent
velocity $v_{\mathrm{micro}}$, and the total non-microturbulent velocity
broadening666We quote the value for the total non-microturbulent velocity
broadening $v_{\mathrm{broad}}$ instead of the more conventional projected
rotational velocity along the line-of-sight $v\sin i$, since most of the
velocity broadening of the spectral lines of RGs is a result of
macroturbulence, which is degenerate with the rotational broadening.,
$v_{\mathrm{broad}}$. Given that the targets are all EBs, we cannot directly
derive the parameters from the optical spectra. We wanted to make use of all
the spectra we had (about 15 spectra per star). However, we first needed to
deal with the fact that each observed spectrum is a combination of the spectra
of two stars that are in motion.

For our SB2 systems, we disentangled our observed spectra with the FDBinary
software described by Ilijic et al. (2004). Then, we analyzed the resulting
spectra of the giant component with the Grid Search in Stellar Parameters
(GSSP) code (Tkachenko, 2015). The GSSP code works by fitting synthetic
spectra, generated using the SynthV radiative transfer code (Tsymbal, 1996)
combined with a grid of atmospheric models from the LLmodels code (Shulyak et
al., 2004), to our disentangled spectra. For our SB1 systems, the spectra of
both components could not be disentangled owing to the small light
contribution of the secondary component, so we analyzed the spectra assuming
that the contribution of the companion was independent of the wavelength. To
estimate this contribution, we used the light ratios determined by the
orbital-parameter analysis (see section 3.3). This method differs from that of
Gaulme et al. (2016a), who had determined the atmospheric parameters of their
giants from averaged spectra without taking into account the presence of the
companion.

The atmospheric parameters derived from the spectra are given in Table 1. The
effective temperatures of the secondary components are given later in the
paper (see Table 4). These temperatures were obtained through our JKTEBOP
dynamical analysis (see Sect. 3.3).

To ensure the reliability of these values, we compared stars in our sample
with the results of the APOGEE (Gunn et al., 2006; Blanton et al., 2017;
Majewski et al., 2017; Wilson et al., 2019) DR14 (Abolfathi et al., 2018;
Holtzman et al., 2018) and DR16 (Ahumada et al., 2020) catalogs where data was
available. The APOGEE values were measured from infrared spectra through an
automated analysis. The discrepancies between ARCES and APOGEE temperatures
were on the order of 50 K, within the uncertainties, except for KIC 7293054,
7768447, and KIC 10015516. For KIC 7293054 and KIC 10015516, we obtained a
temperature smaller than the APOGEE value by 200 K. Since the luminosity
ratios of these binaries are among the highest in our sample, the contribution
of the secondary component to the total light of the system has most probably
caused the automatic APOGEE pipeline to overestimate the effective temperature
of the giant ($L_{2}/L_{1}$ = 10.8 % for KIC 10015516; see Table 3). For KIC
7293054, the luminosity ratio is unknown, but the companion is one of the most
visible in the optical spectra of the system. For KIC 7768447, we measured a
temperature higher than the APOGEE value by 160 K, which is not incompatible
with the measurement uncertainty we got from the GSSP analysis. For the
metallicity, ARCES and APOGEE values agreed within the measurement
uncertainties, with a discrepancy on the order of 0.1 to 0.2 dex, except for
KIC 6757558 and KIC 10015516. For the surface gravity, the discrepancies
between the two sets of measurements were also below the uncertainties
reported in Table 1 (typically on the order of 0.1 to 0.2 dex), except for KIC
7293054 and KIC 10015516. While the comments we made on the effective
temperature apply for the latter two binaries, the situation is different for
KIC 6757558 since the companion is a MS M dwarf (Table 4). We note that our
asteroseismic results suggest that $\log g$ for this giant is 3.01, as can be
seen in Table 4, which is closer to the APOGEE value of 2.98. We decided,
however, to report our parameters instead of those of APOGEE in Table 1,
primarily to follow the most systematic approach possible and because the
parameters from APOGEE data releases were obtained using an automatic pipeline
that does not take binarity into account.

Finally, if we did not perform any abundance analysis for individual elements,
we looked for a few special features in the optical spectra. We first checked
whether some targets show lithium absorption, given that Li enrichment in
giants could be caused by tidal interactions in binary systems (Casey et al.,
2019). It appears that none of the RGs in our study shows particular Li
absorption at 6707.7Å. Secondly, we ran a preliminary analysis of the Ca H & K
emission at 3968.5 and 3933.7 Å, respectively, which are tracers of magnetic
activity. The ARCES spectrometer is not optimized for monitoring this spectral
feature because it is at the very edge of its spectral domain. Nevertheless,
Ca H & K emission is obvious for a few systems: KICs 4473933, 5193386,
6307537, 7133286, 8435232, 10015516, and 11235323. The seven systems
correspond to those with detectable rotational modulation in the Kepler light
curves (Sect. 3.2), which is also an indicator of strong magnetic activity. At
last, the shortest-orbit system KIC 11235323 also displays variable Hα
emission at 6562.8 Å. We added comments in Table 4 to report these
peculiarities.

Table 2: Asteroseismic properties and surface magnetic activity. The
oscillation frequency at maximum amplitude $\nu_{\mathrm{max}}$ and observed
large frequency spacing $\Delta\nu_{\mathrm{obs}}$ are expressed in $\mu$Hz.
The dipole mode period spacing $\Delta\Pi_{1,\mathrm{asym}}$ is expressed in
seconds and $q$ stands for the coupling factor of the mixed modes. The
parameters $A_{\mathrm{max}}$ and $\Gamma_{\mathrm{max}}$ are the oscillation
amplitude and width of the closest $l=0$ mode to $\nu_{\mathrm{max}}$.
Rotational periods $P_{\mathrm{rot}}$ are expressed in days and photometric
activity index $S_{\mathrm{ph}}$ in percent.

KIC | $\nu_{\mathrm{max}}$ | $\Delta\nu_{\mathrm{obs}}$ | $\Delta\Pi_{1,\mathrm{asym}}$ | $q$ | $A_{\mathrm{max}}$ | $\Gamma_{\mathrm{max}}$ | $P_{\mathrm{rot}}$ | $S_{\mathrm{ph}}$
---|---|---|---|---|---|---|---|---
| ($\mu$Hz) | ($\mu$Hz) | (s) |  | (ppm) | ($\mu$Hz) | (days) | (%)
4054905 | $48.13\pm 0.21$ | $5.42\pm 0.01$ | $159.5$ | $0.10$ | 78.1 | 0.09 | … | 0.05
4360072 | $31.81\pm 0.06$ | $3.90\pm 0.01$ | $392.2$ | $0.45$ | 101.0 | 0.34 | … | 0.05
4473933 | … | … | … | … | … | … | $68.4\pm 6.1$ | 2.05
4663623 | $54.09\pm 0.24$ | $5.21\pm 0.02$ | $363.6$ | $0.10$ | 57.7 | 0.16 | … | 0.03
|  |  | $76.7^{\dagger}$ |  |  |  |  |
5193386 | … | … | … | … | … | … | $25.6\pm 2.0$ | 1.72
5866138 | $83.71\pm 0.46$ | $7.25\pm 0.01$ | $272.4$ | $0.25$ | 24.5 | 0.20 | … | 0.03
6307537 | … | … | … | … | … | … | $77.5\pm 5.9$ | 3.00
6757558 | $129.38\pm 0.28$ | $11.28\pm 0.01$ | $80.1$ | $0.15$ | 52.0 | 0.65 | … | 0.03
7133286 | … | … | … | … | … | … | $38.0\pm 2.8$ | 3.60
7293054 | $42.58\pm 0.27$ | $4.32\pm 0.01$ | … | … | 72.7 | 0.10 | … | 0.05
7768447 | $57.79\pm 0.52$ | $5.89\pm 0.02$ | … | … | 92.2 | 0.34 | … | 0.06
8435232 | … | … | … | … | … | … | $48.1\pm 3.4$ | 4.63
9153621 | $38.22\pm 0.30$ | $4.28\pm 0.01$ | … | … | 76.5 | 0.18 | … | 0.08
9904059 | $140.61\pm 0.45$ | $11.91\pm 0.01$ | $79.8$ | $0.15$ | 33.9 | 0.44 | … | 0.03
10015516 | $66.85\pm 0.67$ | $5.90\pm 0.01$ | $294.5$ | $0.25$ | 20.0 | 0.30 | $65.7\pm 6.2$ | 0.24
10074700 | $232.00\pm 2.00$ | $18.37\pm 0.02$ | … | … | 26.4 | 0.41 | … | 0.04
11235323 | … | … | … | … | … | … | $23.9\pm 1.9$ | 1.72

777For KIC 4663623, we used the values of $\Delta\nu$ and $\nu_{\mathrm{max}}$
from Gaulme et al. (2016a). †The period spacing $\Delta\Pi_{1}=76.7$ s was
estimated for the Gaulme et al. (2014) paper, but was omitted in the
manuscript.

##  3 Methods

###  3.1 Asteroseismic analysis

Asteroseismology provides information on the properties of stellar interiors.
In this work, we focus on three aspects: estimating stellar masses and radii
from the asteroseismic scaling relations, measuring the amplitude and lifetime
of radial modes, and determining the stellar evolutionary states from the
frequency distribution of the mixed dipolar $p$ and $g$ modes.

####  3.1.1 Global parameters

We computed the global seismic parameters with the method employed by Gaulme
et al. (2016a). In this process, we started by fitting the power spectra with
a sum of two super-Lorentzian functions for the convection (e.g., Mathur et
al., 2011; Kallinger et al., 2014), a Gaussian envelope for the modes, and a
constant function for the white noise. The frequency of maximum power
$\nu_{\mathrm{max}}$ was determined as the central value of the Gaussian
function. Then, we computed an initial $\Delta\nu$ from the autocorrelation
function of the frequency range of the power spectrum containing oscillation
modes as described by Mosser & Appourchaux (2009). The large frequency spacing
obtained through this method may be biased because of stellar and stochastic
realization noises, as was pointed out by Hekker et al. (2009, 2011), Huber et
al. (2009), Mathur et al. (2010), and Mosser & Appourchaux (2009). Thus, we
used the universal pattern of RGs introduced by Mosser et al. (2011b) to
correct it. The principle of this method is to compare the measured
oscillation frequencies to a theoretical law, the so-called universal pattern,
predicting the variations of these frequencies as a function of $\Delta\nu$
and the radial order.

To ensure the reliability of our measurements, we performed a second
independent analysis using the A2Z pipeline developed by Mathur et al. (2010).
This method is based on three packages run consecutively: p-mode range search,
background fitting, and characterization of the p-mode envelope. First, the
large frequency separation $\Delta\nu$ is determined through the analysis of
the Fourier transform of small chunks of the power spectrum in a continuous
blind way. The resultant value is used to estimate the frequency of maximum
oscillation power $\nu_{\mathrm{max}}$ and the p-mode range, i. e., the
interval of frequency where the power excess due to stellar oscillations is
visible. Then, the background of the power spectrum is fitted by a Gaussian
function in the same manner as above. This last step provides a second
measurement of $\nu_{\mathrm{max}}$. The results of the two methods agree
within 2% for all targets with only two exceptions: the values of $\Delta\nu$
of KIC 10015516 and $\nu_{\mathrm{max}}$ of KIC 5866138 given by A2Z were 6%
and 8% greater, respectively, than those given by our reference pipeline. We
decided to use the seismic parameters provided by the same method as Gaulme et
al. (2016a) because the associated uncertainties are smaller.

The reference values are given in Table 2. It should be noted that we report
the observed value of $\Delta\nu$. Since all the oscillating stars considered
in this work are RGs, the asymptotic frequency spacing can be obtained by
multiplying this value by 1.038, as shown by Mosser et al. (2013).

Sekaran et al. (2019) simulate that if $\nu_{\mathrm{max}}$, for a binary with
one or two oscillating components differs from that of a single star. If this
were the case, oscillating RGs in binaries would not be suited for calibrating
the scaling relations. The authors show that the presence of a companion star
does not generate systematic biases. However, stellar multiplicity as well as
otherwise unrelated contaminants affect the signal-to-noise of the
oscillations with respect to the background due to photometric dilution of the
oscillation signal, as discussed by, for example, Beck et al. (2018a).

####  3.1.2 Individual oscillation frequencies

To study the suppression of oscillations in the closest systems (Sect. 4.3),
we need to determine the properties of the radial ($l=0$) modes. We note that
dipolar ($l=1$) modes are not suitable for this because they are very often
split into multiple components by interference with inner $g$ modes, which
makes the measurement of their amplitude more challenging. Moreover, it has
been shown that $l=1$ modes are often depleted in RG stars (e.g., García et
al., 2014c; Fuller et al., 2015; Stello et al., 2016; Mosser et al., 2017;
Gaulme et al., 2020), which would add another dimension to the problem.

We fit the oscillation spectra with a maximum a posteriori method, which was
originally described by Gaulme et al. (2009) and regularly updated since then.
The updates mainly consist of an improved approach for mode identification.
The routine starts by fitting the background noise of the power spectral
density (PSD) as described in Sect. 3.1.1. Then a null hypothesis statistical
significance test is performed around $\nu_{\mathrm{max}}$ to detect
significant peaks with respect to the local background model. Next, the
expected $l=0$ frequency pattern is computed according to the solar-like
oscillation universal pattern “UP”, which was originally developed to analyze
the oscillations of RGs by Mosser et al. (2011b) and extended to MS stars by
Mosser et al. (2013), as follows:

$\displaystyle\nu_{\mathrm{up,l=0}}$ $\displaystyle=$
$\displaystyle\left[n+\epsilon+\frac{\alpha}{2}\left(n-\frac{\nu_{\mathrm{max}}}{\Delta\nu}\right)^{2}\right]\Delta\nu,$
(1) $\displaystyle\nu_{\mathrm{up,l=1}}$ $\displaystyle=$
$\displaystyle\left[n+\frac{1}{2}+\epsilon-
d_{01}+\frac{\alpha}{2}\left(n-\frac{\nu_{\mathrm{max}}}{\Delta\nu}\right)^{2}\right]\Delta\nu,$
(2) $\displaystyle\nu_{\mathrm{up,l=2}}$ $\displaystyle=$
$\displaystyle\left[n+1+\epsilon-
d_{02}+\frac{\alpha}{2}\left(n-\frac{\nu_{\mathrm{max}}}{\Delta\nu}\right)^{2}\right]\Delta\nu,$
(3)

where $\alpha=2\times 0.038/n_{\mathrm{max}}$ for RGs and $\alpha=2\times
0.57/n_{\mathrm{max}}^{2}$ for MS stars (Mosser et al., 2013). The separations
relative to $\Delta\nu$ are measured to be about
$d_{01}=(-0.056-0.002\log\Delta\nu)$ and $d_{02}=(0.131-0.033\log\Delta\nu)$
(Mosser et al., 2011b).

The code then cuts the spectrum into $\pm 0.6\Delta\nu$ wide ranges around the
expected $l=0$ position and it picks the highest peak, assuming that it
corresponds with the actual position of $l=0$. It eventually searches for the
mean position of the $l=1$ ridge with the assumption of no mixed modes, which
is expected to be separated by $d_{01}$. The routine then looks for the actual
closest significant peaks to the expected ridge, which in other words allows
for only one $l=1$ mixed mode per overtone. As a final step it looks for $l=2$
modes by searching for significant peaks near the $l=0$ ridge in a separate H0
testing.

Once the modes are identified in terms of degree and order, each individual
frequency is fitted with a Lorentzian function. Since our goal is to measure
the properties of radial modes, we do not include rotational splitting or
mixed modes: one Lorentzian is used to model each $(n,l)$ mode. Optimization
is performed as described by Gaulme et al. (2009), with loose priors on the
frequency positions based on the mode identification process above. The
amplitude and mode width of the $l=0$ mode closest to $\nu_{\mathrm{max}}$ is
reported for each oscillating RG in Table 2.

####  3.1.3 Mixed modes

In stars with an inner radiative zone and an outer convective envelope,
pressure (p-) waves propagate in the whole interior and gravity (g-) waves
propagate in the radiative zone. These waves carry information on the interior
layers in which they travel. In RGs, the frequency range of the p modes
partially coincides with that of the g modes so that the two types of modes
interact. The modes resulting from this interaction are called mixed modes:
they are tracers of the physical conditions in the stellar core (e.g., Beck et
al., 2011; Bedding et al., 2011).

In particular, mixed modes are used to determine the evolutionary status of a
RG through the measurement of the period-spacing of gravity modes. As shown by
Tassoul (1980), gravity modes of equal degree can be considered evenly spaced
in period in the asymptotic regime. We denote ${\Delta\Pi}_{l}$ the period-
spacing of gravity modes of degree $l$. Since modes of degree $l=1$ travel
deeper into the stellar interior than those of higher degree, studies of mixed
modes have focused on determining the value of ${\Delta\Pi}_{1}$ (e.g.,
Buysschaert et al., 2016, and references therein). Bedding et al. (2011)
showed that this period spacing allowed one to distinguish between hydrogen-
shell-burning stars, located on the red giant branch (RGB) of the Hertzsprung-
Russell diagram and helium-core-burning stars of the horizontal branch, also
called red clump (RC).

To determine ${\Delta\Pi}_{1}$, we implemented a method similar to that
described by Buysschaert et al. (2016). They compared two approaches: one
based on a Lorentzian fitting of the observed period spacing $\Delta P$ and
the other based on an asymptotic relation derived by Mosser et al. (2012). In
the latter approach, the authors fitted three parameters, the asymptotic
period spacing ${\Delta\Pi}_{1,\mathrm{asym}}$, the coupling factor $q$, which
quantifies if the mixed modes are dominated by pressure or by gravity, and the
phase offset $\epsilon_{\mathrm{g}}$, through a $\chi^{2}$ minimization. In
this work, we used the asymptotic-relation technique with
$\epsilon_{\mathrm{g}}$ fixed to 0 to determine the value of
${\Delta\Pi}_{1,\mathrm{asym}}$ and $q$.

As shown in the last two columns of Table 2, mixed modes were not detected for
KIC 7293054, KIC 7768447, KIC 9153621, and KIC 10074700888 Given that we only
used ${\Delta\Pi}_{1}$ to determine the evolutionary state of our stars, we
did not need to compute measurement uncertainties for this quantity (for more
details, see, e.g., Bedding et al., 2011). . Two of the other stars, KIC
6757558 and KIC 9904059, are burning hydrogen in a shell. The other five
giants are burning helium in their core, as indicated by their period spacing
larger than 100 s (Bedding et al., 2011).

###  3.2 Surface activity and rotation

We analyzed the surface rotation and magnetic activity following the methods
described by García et al. (2014a) and Ceillier et al. (2016). This method
compares the periodicities obtained by three independent techniques applied to
the light curve. The first technique is the periodogram. In active stars999 In
this case, ”active” refers to stars with starspots. This phenomenon is
described in greater detail in Sect. 4.3, where we study the link between
tidal interactions, surface activity, and oscillation suppression. , the
highest peak of the power spectrum of the time series is often the signature
of the rotation due to the variability associated with starspots. These spots
induce important modulations in the light curve that often dominate the low-
frequency part of the spectrum with periods of tens of days for RGs (Ceillier
et al., 2016). However, instrumental noise and drifts can also introduce peaks
in the spectrum and a more detailed study of the nature of these low-frequency
peaks is required. This is why we also used a time-frequency analysis. The
principle of this method is to compute a two-dimensional wavelet power
spectrum (WPS) containing the evolution with time of each periodicity
(Torrence & Compo, 1998). This method allows us to distinguish sustained
periodic signals such as rotation from intermittent signals that only last for
a few days, which could be induced by instrumental perturbations. From the
WPS, we computed the global WPS (GWPS), which corresponds to the WPS
integrated along the temporal dimension. Finally, we computed the
autocorrelation of the light curve to have a third estimation of the rotation
period. We also computed a composite spectrum, which corresponds to the GWPS
multiplied by the autocorrelation function (Ceillier et al., 2016). Because
instrumental noise affects each technique differently, combining these
techniques increases the reliability of our detection (for a benchmark
comparison of various methods; see Aigrain et al., 2015).

Figure 2: Analysis of the rotation of KIC 6307037. Left: From top to bottom,
Kepler light curve, WPS, autocorrelation function, and composite spectrum.
Right: From top to bottom, power spectrum, global WPS, and results of the
analysis.

Figure 2 illustrates the different techniques applied to the light curves to
one star in our sample, KIC 6307537. In this case, all techniques agree on the
rotation period. Whereas the low-frequency periodogram peaks at a period
around 80 days, the WPS shows that this periodicity is sustained over the
whole length of the observation, which reinforces this detection. As can be
seen in the WPS, periodicities in the stellar signal do not show up as sharp
peaks at a well-defined value. Periodicities rather appear as scattered
distributions of rotational velocities, which result in a Gaussian
distribution once projected on the frequency axis. This dispersion is due to
complex, poorly constrained effects such as the variable size of starspots and
differential rotation associated with the presence of spots at several
latitudes. Even though the uncertainty on the central periodicity of the
Gaussian observed in the GWPS is very small, the width of this distribution
has to be taken into account to enable fine analysis of the stellar rotation.
This is why the provided uncertainty corresponds to the half width at half
maximum (HWHM) of a Gaussian fit to the highest peak in the GWPS instead of
the statistical error (Table 2).

###  3.3 Dynamical analysis

|  |
---|---|---
|  |
|  |
Figure 3: Phase-folded eclipses and radial velocities for SB2 stars in our sample. For both eclipses, the processed Kepler data is shown in light blue dots and the solid black line corresponds to the fit from JKTEBOP. For the radial velocities, red squares (resp. green diamonds) represent the observed radial velocity of the giant (resp. the companion) and the solid red line (resp. the green line) indicates the fit from JKTEBOP. |  |
---|---|---
|  |
|  |
Figure 4: Phase-folded eclipses and radial velocities for SB1 stars in our
sample. For both eclipses, the processed Kepler data is shown in light blue
dots and the solid black line corresponds to the fit from JKTEBOP. For the
radial velocities, red squares represent the observed radial velocity of the
giant and the solid red line indicates the fit from JKTEBOP.

Table 3:  Orbital parameters from dynamical modeling with JKTEBOP. The
quantity $T_{\mathrm{prim,ecl}}$ stands for the reference time of the primary
eclipses∗ in Kepler Julian date⋆, $\omega$ the argument of periastron, $e$ the
eccentricity, $i$ the orbital plane inclination, $(R_{1},T_{1},L_{1}),$ and
$(R_{2},T_{2},L_{2})$ the RG and companion’s radii, effective temperatures,
and luminosities. The quantities $K_{1},K_{2}$ are the RV semi-amplitudes and
$\gamma_{1}$, $\gamma_{1}$ are the radial velocity offsets. The last two
columns contain the limb-darkening coefficients of the RG component used in
the fit. The least significant digit in brackets after the value indicates the
uncertainty.

KIC | $P_{\mathrm{orb}}$ | $T_{\mathrm{prim,ecl}}$ | $\omega$ | $e$ | $i$ | $\frac{R_{2}}{R_{1}}$ | $\frac{R_{1}+R_{2}}{a}$ | $\left(\frac{T_{2}}{T_{1}}\right)^{4}$ | $\frac{L_{2}}{L_{1}}^{\dagger}$ | $K_{1}$ | $K_{2}$ | $\gamma_{1}$ | $\gamma_{2}$ | $\alpha_{LD,\mathrm{lin}}$ | $\alpha_{LD,\mathrm{quad}}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (days) | (KJD) | (∘) |  | (∘) |  |  |  |  | (km s-1) | (km s-1) | (km s-1) | (km s-1) |  |
4054905 | 274.7306(4) | 670.4562(9) | 35.1(5) | 0.372(2) | 89.387(7) | 0.380(2) | 0.0515(1) | 1.287(5) | 0.1962(2) | 21.6(3) | 22.0(5) | 11.2(3) | 10.7(6) | 0.56 | 0.15
4360072 | 1084.76(1) | 812.17(8) | 307(1) | 0.152(1) | 89.05(1) | 0.052(1) | 0.0215(2) | 1.70(6) | 0.0046(7) | 10.2(5) | … | 57.3(5) | … | 0.55 | 0.18
4473933 | 103.6014(4) | 199.09(1) | 210(4) | 0.279(9) | 84.27(9) | 0.118(2) | 0.147(2) | 6.3(2) | 0.0874(2) | 33.0(7) | … | 5.3(4) | … | 0.50 | 0.00
4663623 | 358.0903(1) | 308.18(8) | 270(1) | 0.399(1) | 88.60(1) | 0.186(3) | 0.0389(5) | 4.1(2) | 0.14400(8) | 22.9(5) | 23.9(5) | -8.5(5) | -7.8(5) | 0.51 | 0.18
5193386 | 21.378310(9) | 136.4272(9) | 312(6) | 0.010(1) | 89.8(2) | 0.3048(7) | 0.1323(3) | 3.59(2) | 0.3334(5) | 48(1) | 56.8(4) | -39.5(3) | -39.5(1) | 0.40 | 0.21
5866138 | 342.259(8) | 436.13(1) | 178(3) | 0.7158(4) | 90.0(7) | 0.056(1) | 0.030(2) | 0.18(1) | 0.00064(5) | 13.3(2) | … | -21.6(2) | … | 0.70 | 0.00
6307537 | 29.74451(3) | 142.643(1) | 209.5(1) | 0.0067(8) | 88.47(2) | 0.2630(7) | 0.1046(2) | 2.74(1) | 0.18956(5) | 41(1) | 50(1) | -17.0(5) | -18(1) | 0.50 | 0.00
6757558 | 421.190(9) | 357.977(6) | 47(7) | 0.22(3) | 88.6(1) | … | … | … | … | 5.7(5) | … | -13.0(5) | … | 0.59 | 0.14
7133286 | 38.51073(5) | 136.332(2) | 271.9(8) | 0.009(3) | 82.99(2) | 0.1717(9) | 0.1763(3) | 3.32(4) | 0.0980(2) | 39.3(6) | 40.5(6) | -54.1(4) | -54.2(4) | 0.50 | 0.00
7293054 | 671.806(3) | 311.384(2) | 70.5(2.6) | 0.80(1) | 87.3(2) | … | … | … | … | 32(4) | 38(4) | -24.2(2) | -23.3(5) | 0.50 | 0.00
7768447 | 122.32(4) | 130.45(4) | 160(8) | 0.322(9) | 88(2) | 0.071(3) | 0.07(2) | 0.6(3) | 0.003(2) | 19.8(2) | … | -59.4(3) | … | 0.55 | 0.13
8435232 | 49.5708(2) | 152.430(5) | 77.5(9) | 0.003(3) | 84.94(8) | 0.0993(5) | 0.191(1) | 4.10(4) | 0.0404(2) | 35.1(3) | 40.5(7) | -25.1(3) | -23.9(4) | 0.50 | 0.00
9153621 | 305.792(5) | 218.24(3) | 314.9(6) | 0.700(3) | 88.82(9) | 0.0978(6) | 0.0472(5) | 2.82(4) | 0.027(2) | 25.7(4) | 30(4) | 37.26(8) | 36(3) | 0.45 | 0.16
9904059 | 102.963(1) | 158.078(4) | 90(3) | 0.32(1) | 86.2(1) | … | … | … | … | 17.0(5) | … | -21.7(5) | … | 0.55 | 0.16
10015516 | 67.69217(9) | 138.533(3) | 271.2(9) | 0.00(1) | 86.91(7) | 0.1584(5) | 0.113(1) | 4.18(9) | 0.1080(2) | 32.7(7) | … | -16.9(4) | … | 0.47 | 0.21
10074700 | 365.6340(6) | 238.984(1) | 94(2) | 0.29(6) | 89.5(1) | 0.1602(7) | 0.017(1) | 0.4(2) | 0.011(6) | … | … | … | … | 0.60 | 0.00
11235323 | 19.668407(8) | 142.3589(7) | 90.4(3) | 0.010(1) | 87.71(1) | 0.4315(6) | 0.1323(2) | 2.90(1) | 0.5056(7) | 48.8(2) | 50.8(4) | -11.43(8) | -11.67(8) | 0.23 | 0.20

101010
∗ We note that the reference time is the epoch of the primary eclipse, whereas
the reference time used in Gaulme et al. (2016a) is the epoch of the
periastron.
⋆ Kepler Julian dates KJD are related to barycentric Julian dates BJD by KJD =
BJD $-$ 2,454,833 days.
† All the values provided in this table were directly fitted on the light
curves with JKTEBOP, except the luminosity ratio which was computed as
$L_{2}/L_{1}=(R_{2}/R_{1})^{2}(T_{2}/T_{1})^{4}$.

We used the JKTEBOP software (Southworth, 2013) to compute the orbital
parameters of the binary systems. This code uses the Levenberg-Marquardt
algorithm to determine the best fit to the data. Error bars are then estimated
with a Monte Carlo algorithm (“task 9” of JKTEBOP). We simultaneously fitted
both the eclipse-photometry light curves and the radial velocities obtained in
section 2. We adopted the same convention as Gaulme et al. (2016a), who
defined the primary component as the giant and the secondary as its companion.
This is why the radii ratios we obtained are smaller than 1. We had to make
two exceptions to this rule for the eccentric systems 7293054 and 9904059, for
which only the eclipse of the companion is visible.

Following Brogaard et al. (2018), we assumed a quadratic limb-darkening law
for the giant components of our binary systems. We used the JKTLD code
(Southworth, 2015) to determine the quadratic coefficient 111111 We remind
that a quadratic limb-darkening law has two coefficients: one quadratic and
one linear. More information can be found in Sing (2010, Eq. 2). . This code
inputs atmospheric parameters, which we got from the APO spectra, and outputs
two coefficients for the spectral passband specified by the user. In JKTEBOP,
we fitted the linear coefficient and used the quadratic coefficient from JKTLD
because of the poor constraints we have on this parameter. We found that the
limb darkening of the companion has negligible influence on the eclipse
photometry. This is most probably because the contribution of this component
to the luminosity of the system is less than 10% and its radius is three to
ten times less than that of the giant. For this reason, we assumed a linear
limb-darkening law for all the companions and fixed its coefficient to 0.5,
which is consistent with the values given by Sing (2010). A more detailed
analysis is required to better characterize the limb darkening of the
companion, which is beyond the scope of the present paper. The limb-darkening
coefficients $\alpha_{LD,\mathrm{lin}}$ and $\alpha_{LD,\mathrm{quad}}$ of the
giants are given in Table 4.

We used the amount of third light from the contamination values given on the
online Kepler catalog. Four values of contamination are provided, including
one for each possible configuration of the satellite. We computed the average
of these values to obtain the amount of third light and fixed it for the
orbital-parameter determination. Since the stars in this study are not
rotating fast, we did not take gravity darkening into account and fixed the
associated coefficients to 1. We also fixed the reflection effect coefficients
to 0.

For SB2 systems, the radial velocity of each component is the sum of two
contributions: a constant offset $\gamma$ due to the systemic radial velocity
of the binary star and a phase-dependent term due to the orbital motion of
amplitude $K$. However, the gravitational redshift (Einstein, 1952) and
convective blueshift (Gray, 2009) lead to different radial velocity offsets
for each component. For instance, the gravitational redshift induces a
wavelength shift,

$\frac{\Delta\lambda}{\lambda}\simeq\frac{GM_{\star}}{R_{\star}c^{2}},$ (4)

where $\lambda$ is the optical wavelength, $G$ the gravitational constant,
$M_{\star}$ the stellar mass, $R_{\star}$ the stellar radius, and $c$ the
speed of light. In the visible domain, the gravitational redshift generates a
radial velocity offset of $v_{\mathrm{offset},\odot}=650$ m s-1 for the Sun
and $v_{\mathrm{offset},\mathrm{RG}}=65$ m s-1 for a 10-$R_{\odot}$ solar mass
giant. Therefore, we fit one systemic radial velocity term per component,
$\gamma_{1}$ and $\gamma_{2}$.

Besides, we do not take into account the ellipsoidal variability of the giants
arising from the tidal interaction with their companion. Modeling this
phenomenon would first require us to disentangle the contributions from
starspots, reflection or beaming effects, which is almost impossible. Then it
would require us to develop and use more complex tools (e.g., Faigler & Mazeh,
2011; Prša, 2018), which could be the aim of future works. Taking this effect
into account would allow us to derive more precise orbital parameters,
especially for systems with $(R_{1}+R_{2})/a\geq 0.1$ (Russell, 1939; Beech,
1985; Morris, 1985). The systems concerned by such ellipsoidal effects are the
closest systems, which are not used to test the asteroseismic scaling
relations.

The dynamical models obtained with JKTEBOP are shown in Fig. 3 for SB2 and
Fig. 4 for SB1 systems. The orbital parameters are reported in Table 3. The
models show an overall good agreement with the data. However, we observe an
enhanced dispersion of the photometric data during the eclipses of the systems
with short periods and large magnetic activity (mainly KIC 5193386, 6307537,
7133286, or 11235323). This artifact originates from the preparation of the
eclipse light curves and was also reported by Gaulme et al. (2014). We do not
to correct these depth variations to avoid altering the eclipse shapes. This
problem actually has very little impact on our study because the data points
are symmetrically distributed around the photometric models, meaning that it
causes no systematic biases on the ratio of radii. Nevertheless, this
dispersion increases the relative error on the radii since errors are computed
with a Monte Carlo algorithm that accounts for data dispersion. This is why
the errors on radii for the shortest-period systems ($P_{\mathrm{orb}}\leq 30$
d) are not smaller in average than for the systems with $P_{\mathrm{orb}}\geq
200$ d, despite a much larger number of eclipses. In any cases, we note that
the systems that show enhanced eclipse-depth dispersion are not used for
testing asteroseismology. They are all very close binaries in which the RG
component shows strong magnetic activity and no oscillations. So, even by
considering that our radii error bars could still be a little underestimated,
it is irrelevant for testing asteroseismology.

###  3.4 Ages from stellar evolution models

We provide proxies of the system ages by fitting the measured parameters of
each binary system individually against theoretical isochrones from the YaPSI
database (see Spada et al., 2017, for details). The YaPSI database covers a
wide range of metallicity and initial helium abundance; the isochrones were
constructed from stellar evolution tracks for stars in the mass range 0.15
$M_{\odot}$ to 5 $M_{\odot}$, covering the evolutionary phases from pre-MS to
the tip of the RGB. It should be noted that the YaPSI tracks and isochrones do
not cover the helium burning phases (horizontal branch and asymptotic giant
branch). Consequently, the uncertainty on the age of the stars whose
evolutionary state is undetermined or classified as RC might be underestimated
by our methodology. Indeed, the observed mass of a RC star may be lower than
its initial mass owing to mass loss near the tip of the RGB (see for instance
Casagrande et al., 2016). This introduces an uncertainty on the age of the
concerned stars. Quantifying this effect in binary stars is out of the scope
of the present paper.

The fit was performed in the mass-radius plane. For the 12 systems for which a
determination of the radius of both the primary and the secondary components
is available, we determined the age range of isochrones that are compatible,
within the error bars, with both stars for a given chemical composition. This
process was repeated for the central value of the metallicity [Fe/H] and for
its minimum and maximum values as determined from the error on the [Fe/H]
measurement. For the remaining systems, our isochrones provide an estimate of
the radius of the secondary component. We note that, since in all these
systems the secondary is a low-mass star on the MS, the radius estimate
obtained in this way is very stringent. The results of this fitting procedure
are summarized in Figs. 16, and 17. The age ranges are given in Table 4. We
obtained the values of this table by computing the arithmetic mean of the
smallest and largest age possible for each system (e.g., for KIC 4054905, 6.32
Gyr and 9.4 Gyr, see Fig. 16). The uncertainties reported correspond to the
half difference between these two boundaries.

##  4 Results and discussions

In this section, we first give an overview of the variety of systems that we
identified. We then check the accuracy of the seismic scaling relations using
our extended sample and we propose new reference values. Next, we present the
oscillation properties of the giants we characterized and analyze how they are
impacted by close binarity. Finally, we study the tidal circularization of the
systems presented in this work and compare these to the other binaries hosting
a RG from the literature.

###  4.1 Nature of the systems

As shown in Figs. 3 and 4, among the 17 binaries studied in this work nine are
SB2s and eight are SB1s. To determine the mass and radius of the components of
SB2 systems, we used the dynamical results from the analysis of Sect. 3.3. In
the SB2 case, determining the masses of the components and semimajor axis of
the system is straightforward through the following relations:

$\displaystyle M_{1}^{\mathrm{(SB2)}}$
$\displaystyle=\frac{P_{\mathrm{orb}}}{2\pi\
G\sin^{3}i}\left(1-e^{2}\right)^{3/2}(K_{1}+K_{2})^{2}K_{2},$ (5)
$\displaystyle M_{2}^{\mathrm{(SB2)}}$
$\displaystyle=\frac{P_{\mathrm{orb}}}{2\pi\
G\sin^{3}i}\left(1-e^{2}\right)^{3/2}(K_{2}+K_{1})^{2}K_{1},$ (6)
$\displaystyle a^{\mathrm{(SB2)}}$
$\displaystyle=\frac{\sqrt{1-e^{2}}}{2\pi\sin
i}(K_{1}+K_{2})P_{\mathrm{orb}},$ (7)

where $K_{1}$ and $K_{2}$ are the radial velocity semi-amplitudes of the giant
and its companion, respectively. The radii of the components can then be
determined from the semimajor axis, the sum of the fractional radii, and the
radius ratio of the system. For the SB1 systems, we computed the mass, radius,
and effective temperature of the companion by combining the RG mass and radius
obtained through seismic analysis (see Sect. 3.1 and 4.2) with the orbital
parameters given by JKTEBOP. In this case, the value of $K_{2}$ is unknown so
it is impossible to apply the relations (5), (6), and (7). The mass function
$f(m)$ of the system can however be determined. This quantity is defined as

$f(m)=\frac{\left(M_{2}\sin i\right)^{3}}{\left(M_{1}+M_{2}\right)^{2}},$ (8)

and is linked to the observable orbital parameters of the system through the
following relation:

$f(m)=\frac{P_{\mathrm{orb}}K_{1}^{3}}{2\pi\ G}\left(1-e^{2}\right)^{3/2}.$
(9)

The mass ratio of the system, $q$, can then be determined by solving the
following third-degree equation:

$q^{3}-\alpha q^{2}-2\alpha q-a=0,$ (10)

where

$\alpha=\frac{f(m)}{M_{1}\sin^{3}i}.$ (11)

Finally, the radius of the secondary component can be computed from the
seismic radius of the giant and the radius ratio of the binary star. The
equations given in this paragraph are obtained by studying the dynamics of a
two-body system in gravitational interaction. A clear presentation of this
computation can be found in the lecture notes of Benacquista (2013). The
masses and radii of the stars in our sample are given in Table 4. Overall, we
identify four classes of systems: 1) four SB2s with a pulsating giant; 2) five
SB2s with a non-oscillating giant; 3) two SB1 with a hot MS companion; and 4)
six SB1s with a red-dwarf companion. We now describe each group in more
detail.

Table 4: Physical properties of the 17 systems studied in this paper.

| Red Giant |  | Companion |  | Spin/orbit |  |
---|---|---|---|---|---|---|---
KIC | Evol | $M_{1,\mathrm{dyn}}$ | $M_{1,\mathrm{seis}}$ | $R_{1,\mathrm{dyn}}$ | $R_{1,\mathrm{seis}}$ | $\log g_{\mathrm{dyn}}$ | $\log g_{\mathrm{seis}}$ | $T_{\mathrm{eff,1}}$ | [Fe/H] |  | $M_{2}$ | $R_{2}$ | $\textsl{T}_{\mathrm{eff},2}$ |  | $e$ | $P_{\mathrm{orb}}$ | $P_{\mathrm{rot}}$ | Age | Notes
|  | ($M_{\odot}$) | ($M_{\odot}$) | ($R_{\odot}$) | ($R_{\odot}$) | (dex) | (dex) | (K) | (dex) |  | ($M_{\odot}$) | ($R_{\odot}$) | (K) |  |  | (days) | (days) | (Gyr) |
Double-line spectroscopic binaries (SB2)
4054905 | RC | 0.95(4) | 0.91(6) | 8.19(8) | 8.2(2) | 2.589(9) | 2.571(9) | 4790(190) | -0.7(3) |  | 0.93(1) | 3.11(3) | 5100(197) |  | 0.37 | 274.7 | … | 7.9(1.6) |
4663623 | … | 1.41(8) | 1.52(6) | 9.8(2) | 10.0(1) | 2.60(1) | 2.623(5) | 4812(92) | -0.13(6) |  | 1.41(10) | 1.83(5) | 6827(140) |  | 0.40 | 358.1 | … | 2.0(0.2) |  $l=1$ depleted
5193386 | RGB | 1.39(3) | … | 4.49(5) | … | 3.274(4) | … | 4780(100) | -0.36(6) |  | 1.17(5) | 1.37(1) | 6622(127) |  | 0.01 | 21.4 | 26(2) | 2.5(0.6) | Flares, Ca H&K em
6307537 | RGB | 1.29(7) | … | 4.45(6) | … | 3.25(1) | … | 4960(240) | -0.0(4) |  | 1.06(4) | 1.17(2) | 6387(306) |  | 0.01 | 29.7 | 78(6) | 5.3(3.0) | Flares, Ca H&K em
7133286 | … | 1.05(3) | … | 9.21(8) | … | 2.532(7) | … | 4500(110) | -0.6(2) |  | 1.02(3) | 1.58(1) | 6075(148) |  | 0.01 | 38.5 | 38(3) | 5.4(0.9) | Flares, Ca H&K em
7293054 | … | 1.6(1) | 1.56(10) | … | 11.4(2) | … | 2.518(8) | 4790(160) | 0.1(3) |  | 1.4(1) | 4.0(3) | 5900(374) |  | 0.80 | 671.8 | … | 0.9(0.3) | Cmp eclipsed
8435232 | … | 1.20(4) | … | 12.9(2) | … | 2.297(8) | … | 4460(130) | -0.1(2) |  | 1.04(3) | 1.28(2) | 6347(174) |  | 0.00 | 49.6 | 48(3) | 5.3(1.7) | Ca H&K em
9153621 | … | 1.1(2) | 1.16(8) | 10.4(6) | 10.4(2) | 2.45(4) | 2.470(9) | 4760(190) | -0.3(2) |  | 0.93(10) | 1.02(6) | 6170(235) |  | 0.70 | 305.8 | … | 7.8(5.2) |
11235323 | RGB | 1.03(1) | … | 3.578(9) | … | 3.342(4) | … | 4840(200) | -0.4(2) |  | 0.989(2) | 1.544(4) | 6319(254) |  | 0.01 | 19.7 | 24(2) | 7.2(1.7) | Flares, Hα em.,
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | Ca H&K em
Single-line spectroscopic binaries (SB1)
4360072 | RC | … | 1.05(8) | … | 10.7(2) | … | 2.402(9) | 5020(210) | -0.1(2) |  | 0.71(3) | 0.5(1) | 5923(530) |  | 0.15 | 1084.8 | … | 11.5(5.0) |
4473933 | … | … | … | … | … | … | … | 4530(220) | -0.4(3) |  | … | … | 7172(344) |  | 0.28 | 103.6 | 68(6) | … | Ca H&K em
5866138 | RC | … | 1.57(7) | … | 8.1(1) | … | 2.820(6) | 4960(120) | 0.1(1) |  | 0.49(2) | 0.456(10) | 3252(93) |  | 0.72 | 342.3 | … | 2.0(0.6) |
6757558 | RGB | … | 0.88(3) | … | 4.96(6) | … | 2.992(5) | 4590(110) | -0.0(1) |  | 0.217(9) | … | … |  | 0.22 | 421.2 | … | 12.1(3.5) | RG eclipsed
7768447 | RGB | … | 1.12(7) | … | 8.3(2) | … | 2.650(8) | 4760(160) | 0.2(2) |  | 0.63(3) | 0.59(3) | 4115(555) |  | 0.32 | 122.3 | … | 8.8(3.2) |
9904059 | RGB | … | 0.98(6) | … | 4.96(8) | … | 3.039(7) | 4830(160) | 0.0(3) |  | 0.46(2) | … | … |  | 0.32 | 103.0 | … | 9.9(4.0) | Cmp eclipsed
10015516 | RC | … | 1.75(9) | … | 9.6(2) | … | 2.716(7) | 4830(130) | -0.4(2) |  | 1.33(6) | 1.52(3) | 6909(177) |  | 0.00 | 67.7 | 66(6) | 0.8(0.2) | Ca H&K em
10074700 | … | … | 0.84(4) | … | 3.53(5) | … | 3.267(6) | 5070(100) | -0.4(1) |  | 0.6(3) | 0.56(1) | 4020(520) |  | 0.29 | 365.6 | … | 13.9(3.9) | Faint

121212The parameters $M$, $R$, $\log g$, $T_{\mathrm{eff}}$, and [Fe/H] refer
to stellar masses, radii, surface gravities, effective temperatures, and
metallicities, respectively. The subscripts “dyn” and “seis” stand for
dynamical modeling and asteroseismic scaling relations, respectively. In the
comment column, em. stands for spectral “emission”; Ca H & K indicate the
calcium lines at 3968.5 and 3933.7 Å, respectively, and Hα the hydrogen Balmer
line at 6562.8 Å. The comments “RG eclipsed” and “Cmp eclipsed” indicate that
only one type of eclipse is visible in the light curve, either the RG is
eclipsed (RG) or the companion (Cmp). For SB1 systems, the parameters of the
companion stars are deduced by combining asteroseismic masses and radii of the
RG with the mass function obtained from light curve and radial velocity
modeling. For RC stars, the age uncertainty may be underestimated (see
discussion in Sect. 3.4). We could not determine the mass, radius, and age of
the giant component of KIC 4473933 because this binary is an SB1 (see Fig. 4)
and its power spectrum has no detectable oscillations (see Fig. 15). The
values of $T_{\mathrm{eff}}$, [Fe/H], $P_{\mathrm{orb}}$, and $e$ are reported
to provide a view of each system at a glance. The exact values with
uncertainties are shown in Tables 1 and 2.

####  4.1.1 SB2 systems with a pulsating giant

This group is interesting because it can be used to test the accuracy of the
seismic scaling relations (Sect. 4.2). These four systems are KIC 4054905, KIC
4663623, KIC 7293054, and KIC 9153621.

KIC 4054905 is composed of two nearly identical-mass stars ($M\approx
0.95\leavevmode\nobreak\ M_{\odot}$) on a 275-day eccentric orbit ($e=0.37$).
The primary component is a giant with a radius of 8 $R_{\odot}$ and its
companion is a subgiant with a radius of 3 $R_{\odot}$. We only detect the
oscillations of the largest component. The mixed-mode analysis reveals that
the giant component belongs to the RC, which means that it has already
traveled through the tip of the RGB, where its radius was on the order of 180
$R_{\odot}$. Knowing the eccentricity and that the semimajor axis of the orbit
is 1 AU, the distance in between the two components at the periastron is 137
$R_{\odot}$. This means that this system has likely experienced mass exchanges
during the evolutionary phase where its primary component was at the tip of
the RGB. This star is one of the very few eccentric binary systems that
contain a helium core-burning star. While the existence of such binary systems
was disputed by Verbunt & Phinney (1995), Beck et al. (2018b) show that such
systems do exist. Such systems are also relevant to determine the efficiency
of the equilibrium tide.

KIC 4663623 is a system composed of two $\approx 1.5\leavevmode\nobreak\
M_{\odot}$ stars on a 358-day eccentric orbit ($e=0.4$). The giant component
has a radius of 10 $R_{\odot}$ whereas its companion lies close to the MS with
a radius of 1.8 $R_{\odot}$. The $l=1$ modes are severely, although not
totally depleted, which makes the mixed-mode analysis inconclusive. While
Gaulme et al. (2014) conclude it was a RGB, our analysis suggests it is a RC,
which is supported by the measurements of Kallinger et al. (2018). The
evolutionary tracks that we ran to determine the age of the system are
compatible with the RG on the RGB and the companion on the MS, but the error
bars are very large. The 180-$R_{\odot}$ distance in between the two
components at periastron suggests that the stars exchanged mass earlier in
their evolution if the giant is on the RC.

The system KIC 7293054 is composed of a 1.6 $M_{\odot}$ RG and a 1.4
$M_{\odot}$ companion orbiting in about 672 days on a very eccentric orbit
($e=0.8$). While the asteroseismic analysis indicates an 11.6 $R_{\odot}$ for
the giant, it is impossible to determine the radius of the companion because
this binary has no secondary eclipse (Fig. 3). Moreover, since we found no
mixed modes in the power spectrum of the giant, it is difficult to accurately
determine its evolutionary state. The high eccentricity of this system makes
it an interesting test case for testing tidal theory. While the orbital
semimajor axis is 500 $R_{\odot}$, the distance between the two components at
periastron is less than 80 $R_{\odot}$.

KIC 9153621 is composed of a giant of mass 1.1 $M_{\odot}$ and radius 10
$R_{\odot}$ and a MS star of mass 0.9 $M_{\odot}$ and radius 1 $R_{\odot}$.
The high uncertainty on the primary dynamical mass is due to the poor
constraint on $K_{2}$. The relation between these two quantities is given in
Eq. (5). The absence of mixed modes in the power spectrum does not allow us to
determine the evolutionary state of the primary component. Because of its
large orbital eccentricity ($e=0.7$) and semimajor axis of 1 AU, the distance
at periastron (65 $R_{\odot}$) is small enough that mass exchange either has
happened or will happen during the RGB ascension of the primary component.

####  4.1.2 SB2 systems with a non-oscillating giant

These five EBs (KIC 5193386, KIC 6307537, KIC 7133286, KIC 8435232, and KIC
11235323) have similar characteristics. They constitute the systems with the
shortest orbital periods of the sample and their values range from 20 days to
50 days. The masses and radii of the primary components range from 1.03
$M_{\odot}$ to 1.38 $M_{\odot}$ and from 3.6 $R_{\odot}$ to 12.9 $R_{\odot}$,
respectively. The mass ratios $M_{2}/M_{1}$ are very homogeneous and range
from 0.82 to 0.96. Finally, their orbits are all circular and their giant
components are active. These properties are further discussed in Sect. 4.3.

####  4.1.3 SB1 systems with a hot MS companion

These two systems (KIC 4473933 and KIC 10015516) are challenging because they
are SB1s despite luminosity ratios of 9% and 11%, respectively. They are both
composed of an active RG and a MS star with
$\textsl{T}_{\mathrm{eff},2}\simeq$ 7 000 K. The non-detection of these two
companions, despite favorable fractional light ratios, is most probably due to
the broadening of their spectral lines resulting from their rapid rotation. We
note that, in the two systems, the rotation period of the giant component is
equal to the tidal pseudo-synchronization period predicted by Hut (1981).
Despite these similarities, their orbital configurations are slightly
different, which we detail in this section.

KIC 4473933 is the only non-oscillating RG that does not belong to an SB2
among the 36 known RGs in EBs. Both the photometric and spectroscopic data
allow us to affirm that KIC 4473933 is composed of a giant and a hot MS star.
First, since the deepest eclipse has a flat bottom and the shallowest has a
round bottom, the component with the biggest radius is the coldest, which
indicates that it is an evolved star that has left the MS. This is confirmed
by the analysis of its disentangled optical spectrum, which showed that its
surface gravity and effective temperature were those of a RG (see Table 1). As
mentioned above, this giant is active and its rotation is pseudo-synchronized
as predicted by Hut (1981), which indicates that this binary has experienced
tidal interaction. We note that the orbital period of this system,
$P_{\mathrm{orb}}\simeq$ 104 d, is significantly longer than those of the
other systems with no detectable oscillations. We also note that this system
has a significant nonzero eccentricity ($e$ = 0.279), which is further
discussed in paragraph 4.3.

The system KIC 10015516 is particularly interesting because it is composed of
an oscillating RG and a pulsating $\gamma$ Doradus ($\gamma$ Dor) star.
Although analyzing the pulsations of the companion is out of the scope of the
present work, we estimate the mass and radius of the $\gamma$ Dor by combining
the seismic mass and radius of the giant with the orbital parameters of the
system. The resulting parameters are fully compatible with a $\gamma$ Dor
variable star (see Table 4). Another interesting feature of this system is
that its giant is active and its rotation is synchronized to the orbit. It is
the only binary in the sample presented in this work whose primary component
is active and has detectable oscillations. We show in Sect. 4.4 that this
system is a precious test case for tidal evolution theories.

Figure 5: Radii of M and K dwarfs as a function of their masses. The gray dots
correspond to the measurements obtained by Parsons et al. (2018) by compiling
catalogs and observing new targets. Among the values presented by these
authors, only those with a relative uncertainty less than 10% are shown. We
note that the uncertainty on the radius (resp. mass) of the companion of KIC
4360072 (resp. KIC 10074700) is greater than 10%. We however decided to keep
them on the plot to allow for comparison with the most up-to-date scatterplot.

####  4.1.4 SB1 systems with a red-dwarf companion

The six binaries of this group (KIC 4360072, KIC 5866138, KIC 6757558, KIC
7768447, KIC 9904059, and KIC 10074700) are composed of an oscillating RG and
an MS star less massive than 0.7 $M_{\odot}$. As noted by, for example,
Parsons et al. (2018), characterizing such low-mass stars is important since
they are priority targets for the search for habitable planets. These authors
also noted that the mass and radius of these objects were generally poorly
constrained because of their low luminosity. Since the number of known M or K
dwarfs for which the mass and radius are measured within an uncertainty less
than 10% is about 40, any new star is a precious addition.

We characterize the dwarf companions from the seismic properties of the giant
and the orbital parameters from JKTEBOP. Since KIC 6757558 and KIC 9904059
have no secondary eclipse, the radius of the dwarf component cannot be
determined. We also note that we could not measure any radial velocity for KIC
10074700 because of its low luminosity. Consequently, the secondary star in
this system was only characterized using photometric data.

Concerning KIC 4360072, the very high effective temperature of the companion
is surprising given its mass and radius ($\textsl{T}_{\mathrm{eff},2}$ = 5730
K, $M_{2}=0.68\,M_{\odot}$, $R_{2}=0.54\,R_{\odot}$, see Table 4). The most
probable cause for this discrepancy is the surface activity of the giant in
this system, which can be seen in Fig. 4. Because of the very long orbital
period of this system (1084 d), only one primary eclipse and two secondary
eclipses were observed by Kepler. As a result, the surface activity signal was
not averaged out in the phase-folded light curve, which might have biased the
dynamical analysis. A more detailed investigation is required to better
characterize the companion of this system, which is out of the scope of the
present work.

We compare our results with the known mass–radius relationship for this type
of objects. In Fig. 5, we plot the radius of the 40 stars published by Parsons
et al. (2018) as a function of their masses and add the dwarf companions of
our sample. It appears that our stars are in the middle of the already known
distribution. The large uncertainty on the mass of the secondary component of
KIC 10074700 is a consequence of the absence of radial velocity measurements
for this system. We also plotted the three dwarf companions of the sample of
Gaulme et al. (2016a). Whereas two of these are in good agreement with the
mass–radius relationship, the secondary of KIC 5179609, with
$M=0.60\leavevmode\nobreak\ M_{\odot}$ and $R=0.37\leavevmode\nobreak\
R_{\odot}$, lies significantly below this value. This most likely results from
an underestimation of the ratio of the radii. Since this EB displays very
shallow secondary eclipses, modeling these secondary eclipses is challenging
because they are difficult to disentangle from the other signals present in
the light curve such as the variability caused by the oscillations. This makes
errors on their depth and width more probable and, as a consequence, can cause
significant errors on the radius and luminosity ratios of the system.

Figure 6: Comparison between the asteroseismic estimates and dynamical
measurements of the mean density and surface gravity. Left panel: The ratio of
the seismic mean density, $\bar{\rho}_{\mathrm{seis}}$, divided by the
dynamical mean density, $\bar{\rho}_{\mathrm{dyn}}$, as a function of the
dynamical mean density. Right panel: The ratio of the seismic surface gravity,
$g_{\mathrm{seis}}$, divided by the dynamical surface gravity,
$g_{\mathrm{dyn}}$, as a function of the dynamical surface gravity. Each dot
corresponds to an SB2 EB with an oscillating RG component. The blue dots
represent those published by Gaulme et al. (2016a), the black dot, the star
discovered by Themeßl et al. (2018) and the red dots, those published in this
paper, to which we added KIC 4663623, the star from Gaulme et al. (2016a) that
we reanalyzed in this study. The correspondence between the letters and the
KIC indices are given in Tables. 1 and 6. KIC 7293054 is not shown in this
figure because its radius could not be determined dynamically. The seismic
estimates for the points shown were obtained with the correction described in
subsection 4.2. The dotted gray and black lines represent the means obtained
with the reference values of Mosser et al. (2013) and Themeßl et al. (2018),
respectively. The black plain line indicates a ratio of 1.

###  4.2 Testing the accuracy of the asteroseismic scaling relations

One of the main interests of studying solar-like oscillators in EBs is to
check whether the stellar masses and radii obtained with asteroseismology
agree with the dynamical quantites. Since the latter method relies on basic
physical principles, it can be considered a robust and unbiased method to
determine the mass and radius of a star. The dynamical and seismic analyses
have already been compared in previous works, in particular by Frandsen et al.
(2013), Gaulme et al. (2016a), Brogaard et al. (2018), and Themeßl et al.
(2018). Based on a sample of ten RGs, Gaulme et al. (2016a) found that the
asteroseismic scaling relations tend to overestimate the masses and radii by
about 15% and 5%, respectively. Such a discrepancy is significant and may
cause large biases when studying the evolution of stellar populations.

A subsample of three of these stars were studied a second time by Brogaard et
al. (2018), who obtained new radial velocity measurements and new effective
temperatures and metallicities. Beyond small discrepancies, these authors
confirmed the mass and radius overestimation reported by Gaulme et al. (2016a)
when employing the asteroseismic scaling relations. In addition, for the first
time, they tested the online software PARAM (Rodrigues et al.,
2017)131313http://stev.oapd.inaf.it/cgi-bin/param, which uses grids of stellar
evolution models to retrieve RG masses and radii from $\nu_{\mathrm{max}}$,
$\Delta\nu$, $\textsl{T}_{\mathrm{eff}}$, and [Fe/H]. They observed a good
agreement between the PARAM results and the dynamical measurements. Finally,
Themeßl et al. (2018) led a similar study with the ten systems studied by
Gaulme et al. and a new system that had not been published before. For the new
system and two others, Themeßl et al. (2018) measured new radial velocities
and determined the dynamical mass and radius. To circumvent the mass and
radius overestimation, they proposed an adjustment of reference values
(${\Delta\nu}_{\mathrm{ref}}$, $\nu_{\mathrm{max,ref}}$,
$\textsl{T}_{\mathrm{eff,ref}}$) which provides a better agreement between the
asteroseismic and dynamical stellar properties.

We performed a similar experiment with all the binaries that have been
published and the new systems presented in this work. In other words, the
total sample now comprises 14 systems, including the following: 1) the ten
binaries that were already published in 2016 (Frandsen et al., 2013; Rawls et
al., 2016; Gaulme et al., 2016a; Brogaard et al., 2018); 2) KIC 5640750
(Themeßl et al., 2018); and 3) KIC 4054905, KIC 7293054, and KIC 9153621 from
the present study.

First of all, our results are consistent with the conclusions of Gaulme et al.
(2016a). Indeed, when we apply the same asteroseismic scaling relations, that
is, when we use the approach and solar reference values of Mosser et al.
(2013), seismic masses are overestimated by approximately 15 % $\pm$ 10 %, and
radii by 5% $\pm$ 3 %. The correction of Mosser et al. (2013) consists of
multiplying the observed value of $\Delta\nu$ by a correcting factor (equal to
1.038 for RGs) and using solar reference values provided in their paper
($\Delta\nu_{\odot,\mathrm{M13}}$ = 138.8 $\mu$Hz,
$\nu_{\mathrm{max},\odot,\mathrm{M13}}$ = 3104 $\mu$Hz)141414 Appropriately
applying the correction of Mosser et al. (2013) actually involves a
recalibration of the solar global seismic parameters $\Delta\nu_{\odot}$ and
$\nu_{\mathrm{max},\odot}$ to ensure these reference values are consistent
with the used seismic analysis pipeline. We decided however not to proceed to
this calibration because our pipeline is very similar to that of Mosser et al.
(2013). . Secondly, when we apply the latest corrections of the scaling
relations proposed by Themeßl et al. (2018), the seismic masses and radii
match the dynamical values within the error bars. We observe a slight
underestimation of 1% for both masses and radii on average, with a dispersion
of 9% and 3%, respectively. We thus confirm that their proposed tuned
reference values reduce the biases in mass and radius 151515 It should be
noted that a suitable application of the Themeßl et al. (2018) correction
would require us to tune the solar reference values so as to cancel the
average deviation between seismic and dynamical masses and radii in the
14-benchmark star sample. In this work, we directly used the values they
reported for two reasons. First, the point of this section is to show that a
proper calibration of the reference values has to be done using the stellar
mean density and surface gravity instead of mass and radius. Second, since
directly using their reference values already gave a satisfying result,
recalibrating these values was not necessary to show the improvement they
yielded. .

Figure 7: Comparison between the asteroseismic estimates of the stellar masses
and radii and their dynamical measurements. The seismic estimates for the
points shown were obtained using the unbiased correction described in
subsection 4.2. Left panel: Comparison in mass. Right panel: Comparison in
radius. See Tables. 1 and 6 for the correspondence between the letters and the
KIC indices.

However, a proper comparison between the dynamical method and the seismic
scaling relations should be done in terms of mean density and surface gravity
instead of stellar mass and radius (e.g., Kallinger et al., 2018). Indeed, the
scaling relations connect the global seismic parameters to the stellar mean
density $\bar{\rho}$ and the surface gravity $g$. When we compare the
dynamical measurements of these quantities ($g_{\mathrm{dyn}}$,
$\bar{\rho}_{\mathrm{dyn}}$) to their seismic estimates ($g_{\mathrm{seis}}$,
$\bar{\rho}_{\mathrm{seis}}$), we observe that the reference values used by
Gaulme et al. (2016a) lead to overestimating the surface gravity by 4% $\pm$
6% and underestimating the mean density by 2% $\pm$ 5%. We note that, although
both density and gravity agree within the error bars, the masses and radii do
not. This is because of the opposite signs of the biases in $g$ and
$\bar{\rho}$, and the strong dependence of stellar mass as a function of
gravity and density ($M\propto g^{3}/\bar{\rho}^{2}$). In contrast, using the
reference values of Themeßl et al. (2018) leads to overestimating both the
surface gravity and the mean density by 2% $\pm$ 6% and 3% $\pm$ 5%,
respectively, which leads to an unbiased result on $M$ and $R$.

In this work, we propose to calibrate the seismic reference values
${\Delta\nu}_{\mathrm{ref}}$, $\nu_{\mathrm{max,ref}}$, and
$\textsl{T}_{\mathrm{eff,ref}}$ directly from mean density and surface
gravity. The principle is to choose these references so that the average value
over the sample of 14 RGs of the seismic-to-dynamical density and gravity
ratios, $<\bar{\rho}_{\mathrm{seis}}/\bar{\rho}_{\mathrm{dyn}}>$ and
$<g_{\mathrm{seis}}/g_{\mathrm{dyn}}>$, are both equal to 1. The value of
${\Delta\nu}_{\mathrm{ref}}$ is determined by the constraint on
$<\bar{\rho}_{\mathrm{seis}}/\bar{\rho}_{\mathrm{dyn}}>$, while the constraint
on $<g_{\mathrm{seis}}/g_{\mathrm{dyn}}>$ fixes the value of the product
$\nu_{\mathrm{max,ref}}\sqrt{\textsl{T}_{\mathrm{eff,ref}}}$. Consequently,
there is one degree of freedom in the choice of $\nu_{\mathrm{max,ref}}$ and
$\textsl{T}_{\mathrm{eff,ref}}$. We decide to fix
$\textsl{T}_{\mathrm{eff,ref}}$ = 5771.8 K, which is a recent solar effective
temperature estimate used by Themeßl et al. (2018). In these conditions, the
new seismic reference values are given as

$\displaystyle{\Delta\nu}_{\mathrm{ref}}$
$\displaystyle=132.9\leavevmode\nobreak\ \mu\mbox{Hz},$ (12)
$\displaystyle\nu_{\mathrm{max,ref}}$ $\displaystyle=3227\leavevmode\nobreak\
\mu\mbox{Hz}.$ (13)

With these new reference values, the dispersion of the mismatch between
seismic and dynamical values is 5% for both the mean density and surface
gravity (Fig. 6). With these values of ${\Delta\nu}_{\mathrm{ref}}$ and
$\nu_{\mathrm{max,ref}}$, the stellar masses and radii too are unbiased (the
overstimation is precisely $1.9\times 10^{-3}$ for the mass and $5.6\times
10^{-5}$ for the radius, see Fig. 7). These results are comparable to those of
Kallinger et al. (2018), who developed a correction based on the mean density
and surface gravity. The dispersion is 9% for the mass and 3% for the radius,
following the correction from Themeßl et al. (2018). This plot confirms that
these new reference values allow us to correct the biases of the seismic
scaling relations. Ensuring that seismic estimates of masses and radii are
unbiased is important because such quantities can be used to determine other
properties of stars and stellar populations (see for instance Miglio et al.,
2012; Silva Aguirre et al., 2018; Sharma et al., 2020). The recent studies of
Hall et al. (2019) and Zinn et al. (2019) also focused on the accuracy of the
scaling relations. In Table 4, we used the global seismic parameters of Table
2 and the reference values of Eqs. (12) and (13) to estimate the mass and
radius of each of the pulsating stars in our sample. With these estimates, we
can characterize all the systems including the SB1s for which only a mass
ratio can be determined from the orbital dynamics.

We note that the reference values of Eqs. (12) and (13) are not strictly
universal. They are specific to our seismic pipeline and should in principle
be recomputed if another analysis software is used. With a different pipeline,
the observed $\nu_{\mathrm{max}}$ and $\Delta\nu$ may be slightly different,
which would bias the outcome. In addition, we note that these reference values
are obtained with a reference effective temperature of
$\textsl{T}_{\mathrm{eff,ref}}$ = 5771.8 K. Another choice of reference
effective temperature (e.g., 5777 K as for Gaulme et al. 2016a) would lead to
different values of ${\Delta\nu}_{\mathrm{ref}}$ and $\nu_{\mathrm{max,ref}}$.
Finally, this correction is valid in the range of mass and evolutionary state
covered by the sample used in this paper. Our approach does not allow us to
extrapolate outside this parameter space.

Developing a more generalizable correction would require us to take into
account more accurately the stellar structure and the influence of the
evolutionary state on the global seismic parameter. With this in mind, we
compared the results of the method proposed by Sharma et al. (2016) with those
of the dynamical method161616 The routine developed by Sharma et al. (2016) is
publicly available at http://www.physics.usyd.edu.au/k2gap/Asfgrid/). . This
correction is based on searching in a grid of stellar models the synthetic
star that best matches the observed asymptotic $\Delta\nu$,
$\nu_{\mathrm{max}}$, metallicity, evolutionary state, effective temperature,
and surface gravity. In our sample, the method of Sharma et al. (2016) yielded
an average overestimation of 10% on mass and 3% on radius, which is a slight
improvement compared to the method used by Gaulme et al. (2016a). These
results suggest that more accurate mass and radius estimates can be obtained
if more parameters (e.g., metalicity and evolutionary state) are taken into
account. This is supported by Pinsonneault et al. (2018), who showed that RGB
and RC stars may have different reference values.

The dependence of the seismic reference values on the evolutionary state
implies that empirical corrections that treat RGB and RC stars equally, for
example, those from Mosser et al. (2013), Themeßl et al. (2018), and the
present paper, introduce systematic uncertainties at the few percent level on
mass and radius. This is an additional reason why future corrections to the
seismic scaling relations will benefit from taking the evolutionary state into
account. However, testing such corrections with precision requires knowledge
of the evolutionary state of the benchmark stars, which is not always the
case. For example, in this paper, the absence of mixed modes in the spectra of
KIC 7293054 and KIC 9153621 prevented us from determining the evolutionary
state (see Sect. 3.1.3). Moreover, a larger sample of stars will be required
to draw significant conclusions regarding the influence of the evolutionary
state on the seismic-relation calibration. These issues are out of the scope
of the present paper.

As a final comparison, we used the PARAM online tool (Rodrigues et al., 2017),
which was successfully tested by Brogaard et al. (2018)171717 In addition,
Brogaard et al. (2018) also find good agreement between asteroseismic and
dynamical estimates of mass and radius after application of standard scaling
relations with $\Delta\nu$ corrections from Rodrigues et al. (2017).  on three
systems, to estimate the masses and radii of all 14 of our systems. The
principle, similar to that of White et al. (2011) and Sharma et al. (2016),
consists of fitting a stellar evolution model to the available data set. The
basic set is the pair ($\Delta\nu$, $\nu_{\mathrm{max}}$), which can be
complemented by the effective temperature, metallicity, period spacing of the
mixed modes, and absolute luminosity. We observed a strong discrepancy in the
results of the new target KIC 4054905, one of the few systems that belong to
the RC, when we opted to provide ${\Delta\Pi}$ as a constraint. The PARAM code
estimates the mass at $1.03\pm 0.05M_{\odot}$ without ${\Delta\Pi}$ and
$2.06\pm 0.02M_{\odot}$ with ${\Delta\Pi}$, whereas the dynamical value is
$M_{\mathrm{dyn}}=0.95\pm 0.04M_{\odot}$. An explanation to this specific case
could be the fact that the RG belongs to the RC and may have experienced mass
transfer with its companion at the tip of the RGB, which could have altered
its structure and evolution, thus making the output of the stellar evolution
models irrelevant. Other sources of discrepancy between the predicted and
observed values of ${\Delta\Pi}$ were studied by Constantino et al. (2015).
Their work constitutes a useful reference to investigate this question in
detail. Regarding the other systems, including a prior on the evolutionary
state in the PARAM optimization allows us to get masses and radii
overestimated only by 5% and 0.5%, which is very encouraging. Meanwhile a
simple empirical approach that is model free, as we propose, remains
competitive for deriving accurate RG parameters.

###  4.3 Oscillation suppression and surface activity in close-in systems

Figure 8:  Properties of rotational modulations and radial ($l=0$) modes near
the frequency at maximum amplitude $\nu_{\mathrm{max}}$. Top panel: The
photometric magnetic activity level proxy $S_{\mathrm{ph}}$ (%) as a function
of orbital period (days). The $S_{\mathrm{ph}}$ values are given in Tables 6
and 4. Middle panel: The relative difference in between expected and measured
oscillation amplitudes (%) as a function of orbital period $P_{\mathrm{orb}}$
(days). The red line indicates 0, i.e., stars whose oscillations are not
detected. The two dashed blue lines represent the region in which relative
mode amplitude lies for systems with orbital periods longer than 180 days
within two sigma. Bottom panel: The mode width $\Gamma_{\mathrm{max}}$
($\mu$Hz) as a function of orbital period $P_{\mathrm{orb}}$ (d). In all
panels the size of each symbol represents the amplitude of stellar variability
$S_{\mathrm{ph}}$ and the gray scale indicates the pulsation mode amplitude
(white-no modes; black-large amp.).

In their sample of 19 binaries, Gaulme et al. (2014) found that four giants
were active and had no detectable pulsations. These four systems displayed
strong pseudoperiodic modulations due to surface activity (hereafter called
rotational modulations) and all had orbital periods shorter than 50 days, sums
of fractional radii $(R_{1}+R_{2})/a$ larger than 15 %, and companions hotter
than the giant component ($T_{2}>T_{1}$). Shortly after that publication, some
concerns about the existence of such a mode suppression were raised in the
community for the following reasons. Firstly, the oscillation signal could
have been diluted because of the contribution of the companion to the light of
the binary system. The relatively small fraction of the luminosity of the
companion ($L_{2}/L_{1}<15\,\%$) makes that option extremely unlikely. This
was further confirmed by Rawls et al. (2016), who characterized the
oscillations of two pulsating RGs that form a 171-day orbital period eclipsing
binary system with a luminosity ratio close to 1; and more recently by the
numerical simulations of Sekaran et al. (2019), who showed that in RG binaries
with a luminosity ratio on the order of 10 %, the determination of the seismic
parameters of the more luminous component was not biased by light dilution.
Secondly, the oscillation frequencies could be out of the range covered by
Kepler. Despite mass and radius estimates of the companions based on orbital
parameters and asteroseismic properties of the giant, such an option needed to
be checked. Gaulme et al. (2016a) confirmed the original conclusion of Gaulme
et al. (2014) based on radial velocity measurements: given their masses and
radii, all large companions were RGs and all should have been displaying
detectable oscillations.

Table 5: Predicted $\Delta\nu$ and $\nu_{\mathrm{max}}$ for the non-
oscillating RGs in SB2 systems

KIC |  $\Delta\nu$ ($\mu$Hz) |  $\nu_{\mathrm{max}}$ ($\mu$Hz)
---|---|---
5193386 | 16.51 $\pm$ 0.29 | 233.6 $\pm$ 7.7
6307537 | 16.18 $\pm$ 0.52 | 218 $\pm$ 14
7133286 | 4.902 $\pm$ 0.087 | 43.5 $\pm$ 1.6
8435232 | 3.162 $\pm$ 0.080 | 25.5 $\pm$ 1.2
11235323 | 20.05 $\pm$ 0.12 | 272.9 $\pm$ 6.4
181818 Since no uncertainty on the effective temperature of the primary
component of KIC 5193386 was available, we computed the error bar on its
$\nu_{\mathrm{max}}$ parameter using $\sigma_{\textsl{T}_{\mathrm{eff}}}$ =
100 K, which is the typical order of magnitude of the uncertainty for this
parameter. We note that the APOGEE DR14 rather suggests an uncertainty of 70 K
(Abolfathi et al., 2018; Pinsonneault et al., 2018). However, given the low
luminosity of this system (visible magnitude of 14.7, while the typical value
for the rest of the sample is 13), its high luminosity ratio
($L_{2}/L_{1}=0.33$), and the uncertainties for the other binaries studied in
this work (typically 150 K), we suspect this value to be underestimated. For
the other stars, we used the uncertainty provided in Table 1.

The present work adds seven more systems with clear rotational modulations,
including six with totally suppressed oscillations and one with partially
suppressed oscillations (KIC 10015516). We computed the expected global
seismic parameters of the five non-oscillating giants that belong to SB2
systems from their dynamical mass and radius, and $\textsl{T}_{\mathrm{eff}}$
(Table 5) by inverting the asteroseismic scaling relations. These estimates
confirm that the oscillations frequencies of the non-oscillating RGs in EBs
lie in the frequency range accessible by Kepler. The sixth system with an
active and non-oscillating RG is KIC 4473933. This binary is different because
it is not circular ($e$ = 0.279) and its 103.6 d orbital period is
significantly longer than that of the other systems with a non-oscillating
giant. The rotation period of its RG component is close to the pseudo-
synchronization period predicted by Hut (1981, see also ), which suggests that
this binary has already undergone significant tidal synchronization 191919 It
should be noted that the ab initio modeling of the dissipation of the
equilibrium tide of Remus et al. (2012) can lead to a dependence of the tidal
torque on the rotation and orbital periods similar to those of the Hut model
(see also Sect. 4.4).  .

Figure 9: Orbital configurations of the systems. Top: Orbital period vs.
relative radii for the 35 systems from (Gaulme et al., 2014) and this paper.
The size of each symbol represents the amplitude of stellar variability and
the gray scale indicates the pulsation mode amplitude (white – no modes; black
– large amp.) Bottom: The same but for the eccentricity of the binary system.
This figure is an updated version of Fig. 6 from Gaulme et al. (2014). Figure
10: Orbital period vs. the rotation period for the 17 systems (out of the set
35 RG/EBs studied by Gaulme et al. (2014) and this paper), where significant
surface activity is detected. The size of each symbol represents the amplitude
of stellar variability and the gray scale indicates the pulsation-mode
amplitude (white—no modes; black—large amp). The parallel lines indicate
isolevels of the ratio $P_{\mathrm{rot}}/P_{\mathrm{orb}}$. This figure is an
updated version of Fig. 5 from Gaulme et al. (2014).

Beyond an almost doubled number of systems of RGs in EBs with respect to
Gaulme et al. (2014), there are two main improvements regarding the study of
rotational modulations and oscillation properties in close binary systems.
Firstly, instead of measuring the peak-to-peak amplitude of stellar
variability from the time series, we compute the photometric magnetic activity
index $S_{\mathrm{ph}}$ as defined by Mathur et al. (2014). It is the standard
deviation of the light curve over five times the rotation period
$P_{\mathrm{rot}}$ when surface activity is detected. In the absence of
photometric modulation, we compute the mean of the running standard deviation
of the light curve in five-day ranges. These stars correspond to the smallest,
darkest symbols in Figs. 8 and 9. The values of $S_{\mathrm{ph}}$ used in this
section are reported in Tables 2 and 6. Secondly, we properly measure the
amplitude of radial modes by employing a peak-bagging method (Sect. 3.1.2). In
the former work, the height of the largest peak of the oscillation power
spectra was used as a proxy of mode amplitude. It was actually inaccurate as
modes of the same amplitude may have different heights and widths 202020For a
single-sided PSD, the amplitude of a given mode is defined as
$A=\sqrt{HW\pi/2}$ (Appourchaux et al., 2015), where $H$ and $W$ are its
height and width.. The current approach is better as it entails fitting each
oscillation mode with a Lorentzian function. That way, we are able to look for
unusual mode widths, which are inversely proportional to the mode lifetime:
the wider a mode, the shorter its lifetime. We also reanalyzed the sample of
19 RG/EBs characterized by Gaulme et al. (2014) to ensure consistency between
the studies. Our goal is to emphasize the link in RG binaries between
oscillation suppression, magnetic activity, and tidal interactions. We combine
the results from the dynamical modeling, rotational modulations, and peak-
bagging in Figs. 8, 9, and 10. Our conclusions are summarized at the end of
this section.

Figure 8 (top panel) shows the photometric magnetic activity level proxy
$S_{\mathrm{ph}}$, that is, the amplitude of the photometric signal caused by
the presence of spots on the RG surfaces, as a function of the orbital period.
The correlation is clear: for orbital periods longer than 180 days,
$S_{\mathrm{ph}}$ never exceeds 0.1%. At shorter orbital periods,
$S_{\mathrm{ph}}$ becomes larger, reaching 10% of the relative stellar flux.
This analysis is consistent with the conclusions of Mathur et al. (2019) who
studied the correlation of surface activity and oscillation detection for a
sample of 2,000 MS stars observed by Kepler. These authors report that stars
with $S_{\mathrm{ph}}$ larger than 0.2 % have almost no chance of having
oscillations detected (98.3% probability). We detect oscillations with
$S_{\mathrm{ph}}\approx 1\,\%$ but our sample consists of RGs, which may
explain the difference with Mathur et al. (2019).

High $S_{\mathrm{ph}}$ values are correlated with suppressed oscillations.
This can be seen in Fig. 8 (middle panel), in which we compare the amplitude
of the closest radial mode to $\nu_{\mathrm{max}}$ with the empirically
expected maximum radial mode amplitude predicted by Corsaro et al. (2013).
This estimated mode amplitude is essentially a scaling law based on the
amplitude of solar oscillations, which is a function of $\nu_{\mathrm{max}}$,
$\Delta\nu$, $T_{\mathrm{eff}}$ and the solar mode amplitude. It arises that
the relative amplitudes of oscillations are fairly uniform (dispersion
standard deviation of $12\,\%$) for systems with $P_{\mathrm{orb}}\geq 180$ d.
We note a small offset: the average mode amplitude of RGs should be 0 instead
of $-14\,\%$ in the RGs that are not suppressed. It could either mean that
even for longer orbits modes are partially suppressed or that the peak-bagging
algorithms used by Corsaro to draw the amplitude scaling law and by Gaulme
provide slightly different results. We favor the second option because an
offset of that order of magnitude was reported by Gaulme et al. (2016b) when
both Corsaro code and Gaulme measured the amplitude of solar oscillations in
SOHO photometric time series. In any case, all RGs in systems with orbits
shorter than 100 days display significant mode suppression. In between 100 and
180 days, both situations (suppressed and not) are met.

In shorter-period systems, partially suppressed oscillations also have a
shorter lifetime. This is visible in Fig. 8 (bottom panel), where we plot the
mode width as a function of $P_{\mathrm{orb}}$ where it clearly appears that
modes with a suppressed amplitude are also wider, that is, with shorter
lifetimes. The mean width of the largest radial modes is about 0.15 $\mu$Hz
for systems with $P_{\mathrm{orb}}\geq 180$ d, but can reach about 1 $\mu$Hz
in the most extreme case. This shorter mode lifetime suggests that the surface
activity prevents the pressure waves from forming long-lived standing modes.

Figures 9 and 10 are updates of Figs. 5 and 6 from Gaulme et al. (2014), where
we confirm that oscillations and surface activity are both correlated with the
orbital configuration of the systems, that is, to tidal interactions. All
systems with relative distance $(R_{1}+R_{2})/a\leq 7\,\%$ show no significant
rotational modulations, regular oscillation amplitudes, and random
eccentricities. Among the 35 confirmed RGs in EBs that have been studied with
radial velocity measurements by Frandsen et al. (2013), Gaulme et al. (2016a),
and Themeßl et al. (2018), a total of 18 meet this low surface activity
threshold. When $7\,\%\leq(R_{1}+R_{2})/a\leq 15\,\%$ rotational modulations
get higher ($S_{\mathrm{ph}}>0.1\,\%$) and $e\leq 0.4$. For all systems with
$(R_{1}+R_{2})/a\geq 15\,\%$ (that is, orbits shorter than about 50 days)
orbits are circular, rotational modulations are maximum ($1\leq
S_{\mathrm{ph}}\leq 10\,\%$), and only one RG displays (weak) oscillations out
of six. Figure 10 shows that all active systems with partially or totally
suppressed oscillations are either synchronized and circularized, or pseudo-
synchronized.

In this section, we first showed that, for RGs in binary systems, the
photometric magnetic activity level proxy, $S_{\mathrm{ph}}$, was linked to
the orbital period: the shorter the period, the higher the value of
$S_{\mathrm{ph}}$. We then used $S_{\mathrm{ph}}$ and the mode-amplitude
predictor of Corsaro et al. (2013) to confirm on a larger sample the result of
Gaulme et al. (2014, 2016a), who showed that active RGs in binaries had
suppressed or partially suppressed oscillations. We also demonstrated a
correlation between orbital and rotation period, as shown in Fig. 10, which
suggests that the most active giants in our sample were spun up by tidal
interactions. We finally showed evidence for tidal circularization in our
sample: close-in systems with $(R_{1}+R_{2})/a$ ¿ 15 % all have an orbital
eccentricity smaller than 0.1. Taken together, these elements support the
scenario proposed by Gaulme et al. (2014) to explain the suppression of
oscillations in the shorter-period systems of their sample: in these binaries,
tidal interactions act to accelerate the rotation of the giant; as a
consequence, this component becomes more active, which results in its
oscillations being suppressed.

Recently, Gaulme et al. (2020) went further in analyzing the link between
tidal interactions and surface activity. In particular, they studied a sample
of 4 500 RGs among which 370 displayed rotational modulations and showed that
RGs members of binary systems had higher surface activity levels than single
RGs with the same rotation periods. This suggests that tidal interactions
enhance the magnetic activity of RGs. Investigating these observations will be
the goal of a future work. More discussion about tidal circularization is
described in the next section.

###  4.4 Observational constraints on tidal circularization

Figure 11: Orbital eccentricity as a function of the circularization proxy,
$\varepsilon_{r}=\log_{10}(-\Delta\ln e/f)$. The vertical dashed line
represents the critical value $\varepsilon_{\mathrm{crit}}=\log_{10}(3)$
predicted by Zahn (1989) and confirmed by Verbunt & Phinney (1995) and Beck et
al. (2018b).

Several teams have exploited the Kepler data to study the tidal
circularization of binary systems. The two main observational works dedicated
to test theoretical predictions were those of Van Eylen et al. (2016) and Beck
et al. (2018b). Van Eylen et al. investigated the influence of the spectral
type of the components of binary systems on their circularization timescale,
denoted $\tau_{\mathrm{circ}}$. These authors first computed the orbital
period and $e\cos\omega$ for 945 stars in the KEBC. They then used the
photometric effective temperatures given in the catalog of Armstrong et al.
(2014) to divide their sample into three groups: the systems composed of two
hot stars, those composed of two cool stars, and those composed of a hot star
and a cool star. The boundary between hot and cool was set at
$\textsl{T}_{\mathrm{eff}}$ = 6250 K, which approximately corresponds to the
limit separating late-type MS stars with a convective envelope from earlier-
type MS stars with a radiative envelope. These authors found that, among the
hot–hot binaries, the fraction of eccentric short-period systems was higher
than in the other two groups. This result suggests that the tidal dissipation
is more efficient in late-type stars, as predicted by Zahn (1975) and Zahn
(1977). However, as noted by the authors, this feature in the eccentricity
distribution could be caused by other effects, which is why the interpretation
above should be reinvestigated by more detailed studies on smaller samples.

Beck et al. (2018b) focused on a sample of 59 binary systems with at least one
RG component, which had been characterized by Verbunt & Phinney (1995), Beck
et al. (2014, 2018a), and Gaulme et al. (2014, 2016a). Beck et al. (2018b)
tested the equilibrium tide212121The equilibrium tide is the large-scale flow
induced by the hydrostatic adjustement of a star induced by the presence of a
companion (Zahn, 1966a; Remus et al., 2012). This flow is completed by the so-
called dynamical tide (Zahn, 1975), which is constituted by oscillation
eigenmodes that are excited by the tidal force, that is, tidal gravity waves
in stably stratified radiation zones (e.g., Zahn, 1975) and tidal inertial
waves in convective regions (Ogilvie & Lin, 2004). model of Zahn (1966a, b,
1977, 1989) by investigating if the eccentricity variations predicted by these
theoretical calculations allowed them to explain the orbital eccentricity
distribution in their sample. Beck et al. (2018b) found a good agreement
between theory and observations, which we explain in more detail in the next
paragraphs. The approaches of Van Eylen et al. (2016) and Beck et al. (2018b)
are complementary because they implemented observational tests of the tidal
theoretical results through two independent methods. In this subsection, we
explain why the 16 binaries characterized in this work222222That is, all our
sample except from KIC 4473933. complete the sample of 59 systems of Beck et
al. (2018b).

Beck et al. (2018b) followed the approach of Verbunt & Phinney (1995), which
relies on linking the orbital eccentricity variations undergone by binary
systems to their current orbital and structural parameters. After adapting the
equations of Zahn (1977) to the case of detached binaries with a RG, Verbunt &
Phinney (1995) obtained the following relation:

$\frac{\Delta\ln e}{f}=-1.3\times
10^{4}\left(\frac{M_{1}}{M_{\odot}}\right)^{-11/3}\left(\frac{R_{1}}{R_{\odot}}\right)^{6.51}q(1+q)^{-5/3}\left(\frac{P_{\mathrm{orb}}}{\mathrm{day}}\right)^{-16/3},$
(14)

where $\Delta\ln e=\ln(e_{\mathrm{today}})-\ln(e_{\mathrm{ZAMS}})$ is the
variation of the logarithmic eccentricity undergone by the binary, $f$ is a
dimensionless factor that accounts for the effects of the turbulent friction
applied by the convection on the equilibrium tide, and $q=M_{2}/M_{1}$ is the
mass ratio of the system. The crucial parameter in this formula is the value
of the multiplicative constant $f$. This factor is predicted by Zahn (1989) to
be on the order of 1, which implies that systems for which $(-\Delta\ln
e/f)>3$ are circularized and that the only circular systems with $(-\Delta\ln
e/f)<3$ formed circular.

Beck et al. (2018b) computed $\varepsilon_{r}=\log_{10}(-\Delta\ln e/f)$ for
each binary in their sample. When these authors plotted the orbital
eccentricities of their binaries as a function of $\varepsilon_{r}$, they
found that the value $\varepsilon_{\mathrm{crit}}=\log_{10}(3)$ was a relevant
boundary between circularized and non-circularized systems. Thus, they
confirmed the results that Verbunt & Phinney (1995) obtained on a smaller
sample. In addition, Beck et al. (2018b) demonstrated that the dissipation of
tidal inertial waves in the deep convective envelopes of RG can be neglected
(Ogilvie & Lin, 2007; Mathis, 2015; Gallet et al., 2017) because these stars
are close to the configuration of a full convective sphere where this
mechanism becomes less efficient (Wu, 2005). They also showed that this
$\varepsilon_{\mathrm{crit}}$ marked the separating line between oscillating
and non-oscillating systems, indicating that the non-oscillating binaries are
those with short circularization timescales.

To extend the sample presented by Beck et al. (2018b), we compute
$\varepsilon_{r}$ for the 16 new systems as well as for the two recent RG
binaries published by Themeßl et al. (2018) and Kuszlewicz et al. (2019). The
updated picture is shown in Fig. 11, where the orbital eccentricity is plotted
as a function of $\varepsilon_{r}$ for the whole sample. Among the 18 new
binaries, the eccentric systems all verify
$\varepsilon_{r}<\varepsilon_{\mathrm{crit}}$, as predicted by the theory of
the equilibrium tide. However, only two out of six new circular binaries have
$\varepsilon_{r}>\varepsilon_{\mathrm{crit}}$, whereas almost all the circular
systems considered by Beck et al. (2018b) verified this condition.

Among our sample, the four circular binaries with
$\varepsilon_{r}<\varepsilon_{\mathrm{crit}}$ are KIC 5193386, KIC 6307537,
KIC 11235323, and KIC 10015516. The first three systems have an active, non-
oscillating RG, as explained in paragraph 4.3. The latter, KIC 10015516, is
composed of an active RG and a hot MS companion with $\gamma$ Dor oscillations
(Sect. 4.1). Several scenarios could explain the position of these four
binaries in Fig. 11. First, these stars could have formed circular. This
hypothesis can not be discarded with the data available to date. The second
possibility is that they have undergone some circularization due to the
dissipation of the dynamical tide during the MS phase of their giant
component. The dissipation of tidal gravity waves resulting from their
breaking during the subgiant and RG phases could be another mechanism to study
(Barker & Ogilvie, 2010; Weinberg et al., 2017; Sun et al., 2018). Finally,
these systems could also have been circularized during the pre-MS phase of the
primary component. Two theories could explain this pre-MS circularization:
first, the dissipation of the equilibrium tide during this phase because of
the important thickness of the convective envelope (see Zahn & Bouchet, 1989)
and second, the dissipation of tidal inertial waves over this period (see for
instance Mathis, 2015; Gallet et al., 2017). Testing these hypotheses requires
secular evolution models of binary stars, similar to those developed for star-
planet systems developed by Benbakoura et al. (2019), which is beyond the
scope of this paper. In this context, the four systems mentioned in this
paragraph are the most interesting cases to test evolution scenarios involving
multiple tidal mechanisms.

Figure 11 also shows a dearth of binaries with eccentricities between 0.5 ¡
$e$ ¡ 0.6. This was first discovered by Beck et al. (2018b) in their RG binary
analysis and is further discussed by Beck et al. (submitted). To this point,
no theoretical explanation has been suggested.

##  5 Conclusions and prospects

In this paper, we reported the identification of 16 new EBs hosting a RG
observed by the Kepler main mission. Thus, this paper brings the number of
confirmed stars that belong to EBs from the original Kepler mission from 20 to
36 (Hekker et al., 2010; Gaulme et al., 2013, 2014; Themeßl et al., 2018;
Kuszlewicz et al., 2019, and this paper). We presented the result of ground-
based high-resolution spectroscopic observations of these 16 systems plus KIC
4663623, which was observed with a poor sampling by Gaulme et al. (2016a). For
each system, we obtained 15 radial velocity measurements on average that we
combined with the Kepler light curve to perform a photometric, seismic, and
spectroscopic analysis. From this study, we divided the sample into four
groups: four SB2 with a pulsating giant, five SB2 with a non-oscillating
giant, two SB1 with a hot MS companion, and six SB1 with a red-dwarf
companion.

The first group, composed of KIC 4054905, KIC 4663623, KIC 7293054, and KIC
9153621, is useful to test the asteroseismic scaling relations232323 Among
these four systems, one (KIC 4663623) had already been studied by Gaulme et
al. (2016a). The other three binaries are novel detections. . Our study brings
three new systems to the 11 already known EBs that allow for such a test. In
Sect. 4, we compared the dynamical masses and radii of these 14 benchmarks to
their seismic estimates and confirmed the discrepancy that was reported in
previous works (Huber, 2015; Gaulme et al., 2016a; Brogaard et al., 2018;
Themeßl et al., 2018). We determined a set of empirical reference values for
$\nu_{\mathrm{max}}$ and $\Delta\nu$ for RG stars that allowed us to compute
unbiased seismic estimates of stellar masses and radii on our sample. The
values provided in Eqs. (12) and (13) are specific to our seismic pipeline but
can easily be recomputed for any other seismic analysis code.

We are aware that a sample of 14 stars is still small in a statistical sense
for providing robust empirical calibrations and we suggest looking for more of
these systems. Three RG/EB candidates, which were not studied in this paper,
have been identified in the targets of the original Kepler mission by Gaulme &
Guzik (2019) during a systematic search for pulsating stars in all of the
known Kepler data. In addition, there are promising data sets from the K2
(Howell et al., 2014) and TESS (Ricker et al., 2014) missions, even though the
frequency resolution of TESS is significantly worse. However, early results
about RG seismology with TESS are encouraging (Silva Aguirre et al., 2019).
Alternative types of systems should be explored as well. It is possible to
measure the mass of stars belonging to “heartbeat” binaries (e.g., Welsh et
al., 2011), hierarchical triple systems (e.g., Borkovits et al., 2016), and
visual binaries (e.g., Marcadon et al., 2018) with the help of complementary
high-resolution spectroscopy.

Regarding radial velocity measurements, we note that gravitational redshift
and convective blueshift should be taken into account ab initio in the
dynamical modeling of the binary systems. With JKTEBOP, the best method to
account for these two phenomena is to allow the systemic radial velocity of
the companion to differ from to that of the giant (see Sect. 3.3). Since their
effects can both yield a difference on the order of 500 m s-1, they are
responsible for an uncertainty of 1% to 3% on the dynamical masses, which
would be suppressed if they were not treated as free parameters. Whereas the
gravitational redshift can easily be computed from the mass and radius of a
star, the convective blueshift is still poorly understood. Useful references
concerning this phenomenon are the papers of Gray (2016), Meunier et al.
(2017a, b), and Dai et al. (2019).

Our work confirms the inverse relation between surface magnetic activity and
amplitude of the modes. The stars shown the largest surface magnetism do not
show visible modes in the PSD.

The systems analyzed in this work are also precious test cases for
understanding how binarity impacts the internal structure of stars and how
tidal interaction shapes the systems. In these evolved binaries, the angular
momentum exchange associated with tidal interaction arises simultaneously to
the structural evolution of their components. Therefore, they lie beyond the
theoretical framework of Hut (1981), which has been used as a reference by
observational studies of tidal evolution (e.g., Lurie et al., 2017; Zimmerman
et al., 2017). This work adds six non-oscillating giants to the four already
published by Gaulme et al. (2014, 2016a). Such stars are very helpful to
understand the tidal pseudo-synchronization of the components of binary
systems. Moreover, the whole sample we considered represents a significant
contribution to the study led by Beck et al. (2018b) on tidal circularization
of evolved binaries. It confirms the importance of the dissipation of the
equilibrium tide and highlights in some cases the necessity to explore other
tidal dissipation mechanisms.

Consequently, the present work shows the necessity of secular evolution models
of binary systems taking into account the structural and rotational evolution
of the components simultaneously to the tidal angular momentum exchanges.
Significant theoretical advances have been done by Siess et al. (2013) and
Davis et al. (2014) for intermediate-mass and massive stars by Fleming et al.
(2019) for MS solar-like stars and by Benbakoura et al. (2019) in the case of
star-planet systems. Understanding the tidal interactions that occur in binary
systems is of great importance to explain the stellar rotational distributions
and their link to stellar dynamics, structure, and evolution (Mathis, 2019).

###### Acknowledgements.

The authors thank the referee for their careful reading and constructive
comments which allowed us to improve this article. We also thank B. Mosser and
T. Appourchaux for verifying the mixed-mode analysis of KIC 4663623. This
paper includes data collected by the Kepler mission. Funding for the Kepler
mission is provided by the NASA Science Mission directorate. Some of the data
presented in this paper were obtained from the Mikulski Archive for Space