Searching for periodic variations in radial velocities after the removal of orbital motions of spectroscopic binaries

ABSTRACT

This study focuses on periodic variations of radial velocities (RVs) after removing the orbital motion of 33 spectroscopic binaries. The RVs were monitored from 2003 to 2012 and published in Katoh et al. (2013, AJ, 145, 41). Their RV precision was determined to be ∼10 m s⁻¹ utilizing an I₂ cell. We investigated the periodic variation using a generalzied Lomb–Scargle algorithm and found periodic variations in the residual velocities of seven binary systems. The residual-velocity variations are mostly generated by stellar activity rather than the orbital motion of a possible companion. For eight binaries, we found significant evidence of a second signal, with velocity dispersions greater than three times the RV uncertainty. We find these residual-velocity variations inconsistent with a Doppler signal induced by the orbital motion of an unknown component. For the remaining 18 binaries, we did not detect significant variations of residual-velocity.

1 Introduction

Observations of multiple star systems can provide valuable information for several important branches of astronomy. Determining the orbit of subsystems in multi-star systems has the potential to improve formation and orbital stability theories (e.g., Tokovinin 2016a, 2016b, 2018a, 2018b, 2019a, 2019b). The first surveys looking for exoplanets often did not include stars known to be in binary systems, especially close binaries with separations <20 au (Eggenberger & Udry 2010). Thus, the number of planets known to be in moderately close binary systems is small.

Recently, exoplanets have been discovered in a binary system with a short separation. Santerne et al. (2014) reported the discovery of a circumstellar planet within the KOI-1257 binary with a separation of 5.3 au. Ortiz et al. (2016) reported the discovery of a giant planet in the system of the giant star HD 59686 A. They also discovered that the HD 59686 system is an eccentric binary with a separation of 3.6 au at periastron. These planets are interesting because of their formation history and orbital stability properties. In a tight binary system, one of the stars tears off the gas and dust from the circumstellar disk around the other star during the planetary formation phase (Artymowicz & Lubow 1994). Model calculations presented by Quintana et al. (2002) indicate that the stability of the planetary embryos decreased because of larger variations in eccentricity caused by Kozai resonance, coinciding with the disk having an inclination relative to the binary plane. Numerical simulation of terrestrial planet formation in a binary–gas planet system shows that an Earth-like planet can form in the habitable zone of the primary star (Haghighipour & Raymond 2007). In realistic radiative cooling models, the disk becomes less eccentric and thus planet formation may be enabled (Müller & Kley 2012). Rafikov (2013) demonstrated that gravity acting on an axisymmetric circumstellar disk reduces planetesimal velocities by an order of magnitude or even more. Silsbee and Rafikov (2015) indicated that self-gravity of an eccentric disk may be efficient at lowering disk eccentricity in the absence of gas drag.

In general, circumstellar planets are subject to gravitational perturbation of the binary components. Holman and Wiegert (1999) noted that binary separation, eccentricity, and mass ratio restrict the gravitationally stable orbits of circumstellar planets. Trifonov et al. (2018) computed the stable orbits of the binaries and one planet of the HD 59686 system. They discovered the existence of stable orbital solutions if both systems have coplanar and prograde orbits or nearly coplanar and retrograde orbits. Therefore, the presence of a planet in the tight binary provides information on their formation process and the dynamical stability in the multiple system.

Several observations of binary systems have revealed the binary fraction of nearby F–G main-sequence stars. Raghavan et al. (2010) showed that the ratio of single : double : triple : quadruple systems is 54 : 34 : 9 : 3. The ratios of triple and quadruple systems are much lower than those of single and double stars. Deep observations of double systems have revealed new multi-star systems. For example, exoplanet surveys discovered that some component stars in visual binaries are in fact spectroscopic binaries (e.g., Gullikson et al. 2015; Katoh et al. 2018). Exoplanet surveys in binary systems may contribute to increasing the ratios of triple and quadruple systems. In our previous work (Katoh et al. 2013), we monitored the radial velocities of 28 single-lined spectroscopic binaries and 5 double-lined spectroscopic binaries with a precision of ∼10 m s⁻¹. This study investigates the periodic variation of the radial velocity (RV) after the removal of orbital motion of the sample binaries in Katoh et al. (2013) to detect low-mass companions.

In section 2 we describe the observations and data reduction. In section 3, we report on the RVs after the removal of the binary orbital motion for the observational samples. Finally, we discuss the RV variations of the individual objects in section 4.

2 Observations and data reduction

2.1 Target stars and observations

We searched for the RV variations generated by the companions around 33 spectroscopic binaries, the orbital elements of which were redetermined by Katoh et al. (2013); see table 1. Katoh et al. (2013) observed these 33 binaries using the precise Doppler method (also known as the precise radial velocity method) with measurements every one or two months between 2003 and 2009. In the previous study, we utilized the 1.88 m telescope at the Okayama Astrophysical Observatory (OAO) and HIgh Dispersion Echelle Spectrograph (HIDES; Izumiura 1999). Until 2007 November, HIDES was equipped with a single 2K × 4K CCD and the observational wavelengths ranged from 5000 to 6100 Å. As of 2007 December, when HIDES was upgraded to three CCDs, the observational range expanded to 3750–7500 Å

with a RED cross-disperser. The spectral resolution (R = λ/Δλ) was ∼60000 with a 200 μm (⁠|${0{^{\prime \prime }_{.}}76}$|⁠) slit width. Exposure times were 120–1800 s, depending on the target luminosity and weather conditions. The typical signal-to-noise ratio is 100–200 for a sixth-magnitude star with an exposure time of less than 1800 s. The RVs monitored until 2009 were presented in Katoh et al. (2013).

We took additional RV data of eight binaries (HD 82674, HD 105982, HD 131511, HD 139461, HD 150680, HD 153597, HD 163840, and HD 178428) every one or two months from 2010 to 2012. From 2010, HIDES has been equipped with a high-efficiency fiber-link mode (HIDES-F; Kambe et al. 2013). We obtained the spectra of HD 131511 and HD 139461 using both HIDES-F and the conventional slit mode (HIDES-S). For the HIDES-F observations, R (resolution) was 50000, with a |${1{^{\prime \prime }_{.}}05}$|-wide image sliced by an image slicer. The exposure times were 600 s and 1200 s for the HIDES-F observations. We obtained typical signal-to-noise ratios of 150–200 for the binary systems. We also observed ι Per as an RV standard star between 2005 and 2012.

We measured the RVs using an iodine absorption cell (I₂ cell; Kambe et al. 2002), which is a glass chamber filled with I₂ gas. The iodine absorption lines are superimposed onto the stellar spectra through the I₂ cell. We also derived a photon-weighted central exposure time using a photon monitor, which records the intensity of the object in the HIDES slit every 3 s. We used the TEMPO program¹ to calculate and correct for an apparent RV caused by the Earth’s movement.

2.2 Data reduction

The spectral data was reduced using the IRAF software package in the standard manner. We reduced the data within the spectral range 3800–6000 Å.

3 Results

3.1 RV offset

Any change or upgrade of the instrument makes a systematic RV offset (e.g., Lo Curto et al. 2015; Trifonov et al. 2020). We derived the RV offset before and after the CCD upgrade using the Exo-Striker exoplanet toolbox.² The RV of ι Per is shown in figure 1. We calculated an offset that gives the smallest weighted root mean square (wrms) to the RV data. The offsets of the single-CCD and three-CCD data are −5.4 ± 2.9 m s⁻¹ and −1.6 ± 3.1 m s⁻¹, respectively. Therefore, the RV offset between the single-CCD and three-CCD data is 3.8 ± 6.0 m s⁻¹. The fiber upgrade of HIDES also induced a systematic RV offset. The RV offset between the HIDES-S and HIDES-F data is 5.4 ± 2.8 m s⁻¹. These RV offsets are as low as the wrms of the RV data of ι Per, so we did not consider the systematic RV offsets in this work.

3.2 Binary orbital motions

The RVs of 33 spectroscopic binaries are shown in figures 2–10. For HD 131511 and HD 219420, we present the HIDES velocities and the published velocities of Fischer, Marcy, and Spronck (2014). The offsets between the HIDES velocities and the published ones are +5039.8 m s⁻¹ for HD 131511 and −1703.7 m s⁻¹ for HD 219420. For HD 131511 and HD 139461, these spectra were obtained using both HIDES-S and HIDES-F. For HD 210763, RV data with an uncertainty larger than 600 m s⁻¹ were omitted. Katoh et al. (2013) determined the binary orbits of HD 82674, HD 105982, HD 131511, HD 139461, HD 150680, HD 153597, HD 163840, HD 178428, HD 210763, and HD 219420. We redetermined the orbital elements of the eight binaries with the additional RV data and the published data in Katoh et al. (2013) and Fischer, Marcy, and Spronck (2014). The orbital elements of the binaries were determined by the least-squares fitting. We used the orbital elements from Katoh et al. (2013) as the initial values. We weighted the RVs according to their errors and sought the best-fitting Keplerian elements. The uncertainty of each orbital element was estimated by using a Markov chain Monte Carlo method (Foreman-Mackey et al. 2013). The new orbital elements of the eight binaries are listed in table 2. For other binary systems, we used the orbital elements determined in Katoh et al. (2013). We calculated the RV variations caused by the binary orbital motion from the orbital elements (see figures 2–10).

3.3 Residual variations

We investigated the periodic variation of the residual velocity with a generalized Lomb–Scargle periodogram algorithm (GLS; Zechmeister & Kurster 2009). We used the Exo-Striker exoplanet toolbox, which includes a GLS periodogram functionality with analytical false alarm probability (FAP) levels for the periodic signal. We regard periodic signals with FAP ≤ 0.1|$\%$| as significant.

We show the periodograms of the 33 targets in figures 11–16. This work assumed the period with the strongest peak in the periodogram to be the periodic signal. The best-fitting double Keplerian motion was determined

with the binary orbit and a low amplitude of the periodic signal as the initial values of the fitting tools routine (Trifonov et al. 2019). The double Keplerian orbits of the 33 binary sysytems are shown in figures 17–25. Figures 26–28 show the RV plots and double Keplerian models to be folded with the phase of the RV curve for the binary. For the 33 targets, we also made periodograms (see figures 17–25) about the residual variations, which is the RV after the removal of the binary orbital motion determined with the double Keplerian fitting. The nine FAPs of HD 9312, HD 35956, HD 36859, HD 92000, HD 131511, HD 139461, HD 143333, HD 150680, and HD 178428 are lower than 0.1|$\%$|⁠.

We optimized the maximum likelihood of the best-fitting model of the RV data. We followed the method of Baluev (2009) and derived the best-fitting model of the RV data to include the RV jitter as an additional parameter. Following the analytic formulations given by Ortiz et al. (2016), we calculated the RV jitter of the primary star for the 33 binary systems. The values of ln |$\mathcal {L}$| were derived from the best-fitting model of the binary orbit only, and of double Keplerian orbit including the RV jitter, respectively. If the difference of both solutions, Δln |$\mathcal {L}$|⁠, is smaller than 5, we think that the binary system does not have a significant third-body (or stellar activity) signal. The RV jitter, ln |$\mathcal {L}$|⁠, of the binary orbit only and the double Keplerian orbit including the RV jitter, and Δln |$\mathcal {L}$| are listed in table 3.

The seven binary systems of HD 35956, HD 92000, HD 131511, HD 139461, HD 143333, HD 150680, and HD 178428 exhibit a significant signal in the residual-velocity variations. We determined the best-fitting Keplerian motions by the least-squares fitting for the residual variations in the seven binaries (figures 29 and 30). The best-fitting Keplerian elements are listed in table 4. The periods of residual variations of HD 35956 and HD 131511 are 1.27 d and 1.58 d. However, these periods are not the one-day alias of another signal. The causes of the residual-velocity variations are discussed in subsection 4.1. The Δln |$\mathcal {L}$| of each of HD 9939, HD 14214, HD 15814, HD 43587, HD 43821, HD 54563, HD 77247, HD 79028, HD 105982, HD 137052, HD 153597, HD 163840, HD 210763, HD 213429, HD 219420, and HD 220007 is larger than 5. We discuss the cause of their residual-velocity variations in subsection 4.2. For the other ten binaries (Δln |$\mathcal {L}$| < 5), we concluded that the residual variations do not exhibit a significant signal. We determine the mass detection limit of a circumstellar component around the primary star for each binary in subsection 4.3.

4 Discussion

4.1 Periodic signal

In the following we discuss whether the periodic residual variation in the individual binaries is caused by the orbital motion of a third body or by the stellar activity.

4.1.1 HD 139461

If the residual-velocity variation of HD 139461 is caused by the orbital motion of a third body, the component would be a circumstellar planet with a minimum mass (m_thirdsin i, with the orbital inclination i) of 0.98 M_Jupiter, a semimajor axis of 0.54 au, and an eccentricity of 0.41. However, stellar oscillation could also generate the observed RV variations. The radial variation of the photosphere contributing to the oscillation could cause variations in luminosity. If those oscillations occur in HD 139461, the integration of the Keplerian fit within half the period would provide the total amount of stellar radius variation. The stellar radius was determined to be 1.79 R_|$\odot$| (McDonald et al. 2017). If this number is indeed the average radius, we calculate that the stellar radius varies between 1.63 R_|$\odot$| and 1.95 R_|$\odot$|. Assuming no change in effective temperature, the magnitude variation is expected to be 0.4 mag. The variations of Hipparcos photometric data for HD 139461 are shown in figure 31. The photometric data with dispersion <3 σ taken within 1 d on average were combined through averaging. We computed the periodogram with the photometric data, using the code provided by the NASA Exoplanet Archive³ (see figure 31). The Hipparcos photometric data for HD 139461 show significant variations with a period of 58.4 d and a magnitude variation of 0.3 mag.

4.1.2 HD 150680

If the residual-velocity variation of HD 150680 is caused by the orbital motion of a third body, the component would be a circumstellar planet with m_thirdsin i of 2.05 M_Jupiter, a semimajor axis of 1.02 au, and an eccentricity of 0.40. However, in this case stellar oscillation could also generate RV variations. The radial variation of the photosphere contributing to the oscillation could cause variations in luminosity. If oscillations occur in HD 150680, the integration of the Keplerian fit within half the period would reveal the total amount of the stellar radius variation. According to McDonald, Zijlstra, and Watson (2017), its stellar radius is 2.78 R_|$\odot$|. If this radius presents the average value, we calculate that the stellar radius varies between 2.47 R_|$\odot$| and 3.10 R_|$\odot$|. Assuming no change in the effective temperature, the magnitude variation is expected to be 0.45 mag. The Hipparcos photometric data of HD 150680 show no such significant variations (figure 33). Hence, we reject the possibility that oscillations explain the residual-velocity variation of HD 150680.

Moreover, co-rotation of the cool spots with the star causes variations in the luminosity. We present a periodogram with the Hipparcos photometric data of HD 150680. The photometric data taken within one day was combined through averaging. The periodogram and the phased light curve are shown in figure 36. The periodogram has the strongest peak at 14.9 d, and the phased light curve appears periodic. The luminosity variations of HD 150680 may indicate the presence of co-rotating cool spots. The stellar rotational velocity (⁠|$v$|_rotsin i) of HD 150680 is 6.2 km s⁻¹ (Luck 2017). Therefore, we derived a maximum rotational period of 22.7 d. If the period of the luminosity variation indicates the rotational period, the stellar inclination of HD 150680 is 47°. However, the period of the luminosity variations is not consistent with those of typical residual-velocity variations. Therefore, we infer that co-rotating spots are not the cause of the residual-velocity variations in HD 150680.

4.1.3 HD 178428

If the residual-velocity variation of HD 178428 is caused by the orbital motion of a third body, the component would be a circumstellar planet with m_thirdsin i of 0.15 M_Jupiter, a semimajor axis of 0.13 au, and an eccentricity of 0.27. We calculated S_MW of HD 178428 and found the strongest peak at 10.7 d in the periodogram. The phased variation of S_MW is shown in figure 37. The correlation coefficient between S_MW and the residual velocity is 0.292 with a significance of 82.5% (figure 38). We note that in this case the two quantities may be correlated. We computed the periodogram with the Hipparcos photometric data of HD 178428; the photometric data taken within one day was averaged. The periodogram and the phased light curve are shown in figure 39. The periodogram has the strongest peak at 11.9 d. The phased light curve appears periodic. The stellar rotational velocity (⁠|$v$|_rotsin i) is 5.1  s⁻¹ (Luck 2017) and the stellar radius is 1.13 R_|$\odot$| (Wright et al. 2011). We derived the maximum rotational period of 11.2 d. Co-rotating cool spots within HD 178428 are suspected to be the cause of the luminosity variations.

Radial variation of the photosphere arising from oscillation can act as a generator of variations in the luminosity. If photospheric oscillation occurs in HD 178428, the asymmetry of the spectral line is correlated with the RV. We calculated the line bisectors of the absorption lines in the HD 178428 spectra using the spectral analysis tool provided by the Esac Science Data Center (VOSpec).⁴ The bisector of an absorption line is the midpoint of the blue and red sides of the profile at the same flux level. The asymmetry of the absorption line is determined by connecting bisector points from the wings toward the core of the line. We calculated the bisector of the Fe i line at 4788.7627 Å, which is not blended with other lines (Dravins et al. 1981). At this wavelength, the iodine spectrum does not heavily contaminate the stellar spectrum. Twenty-six line bisectors were calculated from the observed spectra between 2008 April and 2010 August. One of the line bisectors is shown in figure 40. The bisector velocity span is the difference between the average velocities in the wing and core zones of the spectral line. The flux widths in the wing and core zones are 0.15 (see figure 40). The periodogram and the phased variation of the bisector velocity span are shown in figure 41. The periodogram has the strongest peak at 12.6 d. The phased variation seems periodic. However, the correlation coefficient between the bisector velocity span and the residual velocity is 0.132 and the significance is 48.2|$\%$|⁠. Because the correlation of the two quantities is weak, we consider that the residual-velocity variation of HD 178428 is generated by the chromospheric activity rather than the photospheric oscillation.

4.1.4 Periodic variations

The residual velocity of HD 131511 has a periodic variation of 1.59 d. HD 131511 is an RS CVn-type binary showing the intense chromospheric activity. The HIDES spectra of HD 131511 shows strong emission lines of Ca ii H and K. The periodogram of the S_MW index has the strongest peak at 1.54 d (figure 44). The Hipparcos data of HD 131511 shows a periodic variation of 10.3 d (figure 45). The stellar rotational velocity (⁠|$v$|_rotsin i) is 4.5 km s⁻¹ and the stellar radius is 0.84 R_|$\odot$| (Marsden et al. 2014). We calculated a maximum rotational period of 9.4 d. We consider that cool spots co-rotating with the stellar surface are causing the photometric and spectroscopic variations.

The residual velocities of HD 35956 and HD 143333 show periodic variations of 1.27 d and 2.29 d. The photometric variations indicate periods of 1.04 d and 1.68 d (figure 46). We do not reject the possibility that the residual-velocity variations are correlated with the photometric variations.

4.2 Possible variations

For HD 9939, HD 14214, HD 15814, HD 43587, HD 43821, HD 54563, HD 77247, HD 79028, HD 105982, HD 137052, HD 153597, HD 163840, HD 210763, HD 213429, HD 219420, and HD 220007, their sixteen Δln |$\mathcal {L}$|’s are larger than 5. The dispersions of the residual velocities of HD 15814, HD 43587, HD 43821, HD 79028, HD 163840, HD 210763, HD 213429, and HD 220007 are larger than three times the RV uncertainty. These large variations may indicate the existence of circumstellar or circumbinary planets with an orbital period longer than the observational period. However, Katoh et al. (2013) claimed that HD 15814, HD 163840, HD 210763, and HD 213429 show spectral features in both the primary and secondary stars. The secondary star features prevent the RV of the primary star from being calculated precisely, and only provide false variations in the RVs.

Residual-velocity variations may be caused by the magnetic activity on the stellar surface. We monitored the S indexes of the eight binaries. The measured S index values and the correlation parameters of the S index and residual velocity are listed in table 5. The two quantities may be correlated for HD 15814, HD 43587, and HD 163840. For HD 43821, HD 79028, HD 210763, and HD 220007, the correlations of the two quantities are weak. This study measured only one S index of HD 213429.

The Hipparcos photometric data of HD 43821 show variations with a period of 33.7 d and an amplitude of 0.004 mag (figure 47). HD 43821 is a giant star with an effective temperature of 5124 K, a luminosity of 31.6 L_|$\odot$|, and a radius of 7.13 R_|$\odot$|. If radial oscillation occurs in HD 43821, the integration of the Keplerian fit within half the period gives the total amount of the stellar radius variation. If 7.13 R_|$\odot$| represents the average radius, we calculate that the stellar radius varies between 7.12 R_|$\odot$| and 7.14 R_|$\odot$|, assuming no change in the effective temperature. Further, the magnitude variation is expected to be 0.006 mag, which is consistent with the Hipparcos data.

The period of the residual variation is longer than the binary orbital period in HD 79028. If the orbital motion of the third companion generates the residual variation, then the companion is necessarily a circumbinary planet. The circumbinary component is discussed in subsection 4.4.

The residual variation of HD 220007 seems periodic (see figure 10). In recent years, Gaia DR2 has provided an effective temperature of 3907 K and stellar luminosity of 611 L_|$\odot$| of HD 220007’s primary star (Gaia Collaboration 2018). Hence, the primary star is a late giant. RV variations of a giant star can be caused by either a low-mass companion or stellar activities such as oscillation and rotational modulation due to the surface inhomogeneity. Specifically, K giant stars are known to have long-period variations in the RV due to such stellar activities (e.g., Hatzes & Cochran 1998).

For HD 9939, HD 14214, HD 54563, HD 77247, HD 105982, HD 137052, HD 153597, and HD 219420, their residual velocity dispersions are smaller than three times the RV uncertainty. We think that their small variations do not indicate the orbital motion of a third body.

4.3 Mass detection limit of the circumstellar component

4.4 Circumbinary components

In this work, the separations of the 14 individual binaries are all shorter than 1 au. For HD 137052, Holman and Wiegert (1999) calculated the shortest period of stable orbits of a circumbinary component to be 1900 d. However, the observation period of this work was only 1504 d. For the other 13 binaries, the observation period was longer than the shortest period calculated by Holman and Wiegert (1999). We investigated the RV variation generated by the orbital motion of a circumbinary component in 13 samples. Four samples, HD 9939, HD 15814, HD 153597, and HD 210763, show spectral features of both the primary and secondary stars. The residual variations of the other two samples, HD 131511 and HD 178428, are generated by stellar activity. For HD 9312, HD 160346, and HD 170829, their Δln |$\mathcal {L}$|’s are smaller than 5. We did not detect significant residual-velocity variations with the orbital motion of a circumbinary planet or stellar activity for these three samples. For HD 9312, HD 9939, HD 14214, HD 54563, HD 77247, HD 153597, HD 160346, and HD 170829, the dispersion of the residual velocity is smaller than three times the RV uncertainty. We think that their small variations do not indicate the orbital motion of a circumbinary component.

HD 79028 shows its Δln |$\mathcal {L}$| to be larger than 5 and the dispersion of residual velocity to be larger than three times the RV uncertainty. The periodogram has the strongest peak at 80.50 d. Its FAP is 10|$\%$|⁠. If the orbital motion of a third companion generates the residual variation of HD 79028, the companion would be a circumbinary planet with a semi-major axis of 0.43 au and a mass of 0.74 M_Jupiter. For HD 79028, the values for the S index and the Hipparcos photometric data vary with periods of 1.69 d and 2.25 d, respectively (figure 49). The luminosity variations indicate the existence of co-rotating cool spots. The variations of the S index suggest inhomogeneity in cool spots on the surface of HD 79028. We do not reject the possibility that the residual-velocity variation of HD 79028 is generated by surface inhomogeneities or cool spot co-rotation. We derived a maximum rotational period of ∼13 d from the stellar radius of 1.64 R_|$\odot$| (Gaia Collaboration 2018) and a minimum rotational velocity of 6.5 km s⁻¹ (Luck 2017). If the period of the luminosity variation correlates with the rotational period, the stellar inclination of HD 79028 would be 13°.

5 Summary

We computed the residual velocity as the RV after the removal of the orbital motion of a spectroscopic binary. This study investigated the periodic variations in the residual velocities of 33 spectroscopic binaries with the orbital elements predetermined by Katoh et al. (2013) to detect low-mass companions. For eight samples, we monitored the radial velocities every one or two months since 2010. The RV precision was determined to be ∼10 m s⁻¹ for all 33 binaries. We computed the primary period of the residual variation with the generalized Lomb–Scargle algorithm.

We found periodic variations in the residual velocities of HD 35956, HD 92000, HD 131511, HD 139461, HD 143333, HD 150680, and HD 178428. The residual variations of HD 139461 may correlate with the luminosity variations in the Hipparcos data. We propose that stellar oscillations of HD 139461’s primary star generate the measured residual variations. The residual velocities of HD 150680 correlate with the S index, indicating the chromospheric activity. Moreover, in HD 178428, the chromospheric activity and residual-velocity variations may be correlated. Co-rotating cool spots in HD 178428 are suspected to be the cause of luminosity variations. Consequently, we conclude that the residual-velocity variation of HD 178428 is generated by the chromospheric activity. For HD 92000, the residual variation and S index are correlated. HD 131511 shows large chromospheric activity. The period of the luminosity variations may be consistent with the rotational period for HD 131511. We consider that cool spots caused by the magnetic activity are co-rotating on the surface of HD 131511. For HD 35956 and HD 143333, we consider that the residual-velocity variations are correlated with the luminosity variations. The period of the residual variations is longer than the binary orbital period in HD 79028. The variation of the S index suggests an inhomogeneous distribution of cool spots on the surface of HD 79028. The luminosity variation indicates the existence of co-rotating cool spots. Thus, this study argues that surface inhomogeneities are the primary generator of the residual-velocity variation in HD 79028. For the other two binaries, their Δln |$\mathcal {L}$|’s are larger than 5 and the residual velocity dispersions are larger than three times the RV uncertainty. The S index and the residual velocity may be correlated in HD 15814, HD 43587, and HD 163840. For HD 43821, the Hipparcos amplitude approximates the magnitude variation caused by the radial oscillation. For the other 18 binaries, we did not detect significant RV variations generated by the orbital motion of the third component in the residual velocity.

For 33 binaries, this work does not detect any circumstellar components with a mass heavier than Jupiter. On the other hand, some previous observations found circumstellar planets in binaries with separations of over 1 au. This study showed that only 19 binaries have a separation of over 1 au. If the probability for the existence of a gas planet is less than 5|$\%$| for a binary with this separation range, the expected value for circumstellar planet detection is less than one planet in this work. Future studies need to monitor the radial velocities of 40 binary systems with separations >1 au in order to reveal whether 5|$\%$| is the upper or lower limit of the detection rate of circumstellar planets.

Acknowledgements

This research is based on data collected at the Okayama Astrophysical Observatory (OAO), operated by the National Astronomical Observatory of Japan. We thank all of the staff members at the OAO for their support during the observations. This paper makes use of the periodogram calculation code and EXOFAST (Eastman et al. 2013) as provided by the NASA Exoplanet Archive, which is operated by the California Institute of Technology under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research has made use of VOSpec, which is provided by the Esac Science Data Center, TOPCAT, an interactive graphical viewer and editor for tabular data (Taylor 2005), and the SIMBAD database and the VizieR Service, which are operated by the CDS, Strasbourg, France. This work has made use of data from the European Space Agency mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

Appendix. Radial velocity list

We display the RVs of HD 82674, HD 105982, HD 131511, HD 139461, HD 150680, HD 153597, HD 163840, HD 178428, and HD 219420 in table 7.

Footnotes

References