© The Authors 2023

1 Introduction

As its core hydrogen supply runs out, a star begins hydrogen thermonuclear fusion in the shell surrounding the central nucleus. During this process, stars are referred to as red giants, with radii ranging from tens to hundreds of times of the radius of our Sun. Red giants emit relatively more light than the Sun, despite their lower surface temperature. The brightness of a red giant branch (RGB) star is about 3000 times that of the Sun. The surface temperature of an M-type RGB star is 3000–4000 K, and the radius is about 200 times that of the Sun. The luminosities of asymptotic giant branch (AGB) stars are similar to those of the brighter RGB stars, and they are up to several times more luminous at the end of the thermal pulsing phase (Sackmann et al. 1993).

Another interesting aspect of these stars are variations in the brightness over long periods that are caused by various groups of cool luminous pulsating variable stars. These long-period variables (LPVs) include the Mira and semiregular types, slow irregular variables, and OGLE small-amplitude red giants (OSARGs). LPVs are seen in both giant and supergiant stars (Soszyński et al. 2009) and have periods from about 100 to more than 1000 days. In some cases, the variations are too poorly defined for the period to be identified, although it is an open question as to whether they are truly nonperiodic. Most LPVs are thermally pulsing AGB stars whose luminosities exceed the solar luminosity several thousand times. Some semiregular and irregular variables are less luminous giant stars, while others are more luminous supergiants, including some of the largest known stars, such as VY CMa.

Low-amplitude and long-period radial velocity (RV) variations are common among evolved K and M giant stars (Hatzes & Cochran 1993; Kürster et al. 2003; Lee et al. 2013; Hatzes et al. 2015). These variations appear on both long (hundreds of days) and short (hours to days) timescales. Short-term variations are most likely caused by Sun-like oscillations excited by turbulent convection and by convective motions in the outer convective zone. Long-term variations can arise from substellar companions, surface inhomogeneities, pulsations, or other intrinsic stellar mechanisms. For giant stars, the surface granulation size is linearly dependent on the stellar radius and mass (Freytag et al. 2002). Thus, the atmosphere of red giants should exhibit a small number of large cells that may cause stochastic low-amplitude RV or light variations. These different timescale variations are detected in K and M giant stars in general and may be associated with complex effects (Larson et al. 1999).

In 2003, we initiated a precise RV survey of nine M giants as part of an ongoing K giant exoplanet survey using the 1.8 m telescope at the Bohyunsan Optical Astronomy Observatory (BOAO). The goal of this paper is to interpret measured low-amplitude and long-period RVs for M giants. In Sect. 2, we describe our observations and data analysis details. In Sect. 3, we present the stellar characteristics of the host stars. The orbital solutions and possible origins of RV variations are presented in Sect. 4. The results of the RV variation measurements taken here are described in Sect. 5. Finally, we discuss and summarize our findings in Sect. 6.

Fig. 1 Long-period RV variations for the standard star τ Ceti from 2003 to 2021.

2 Observations and data reduction

Observations were carried out using the fiber-fed high-resolution Bohyunsan Observatory Echelle Spectrograph (BOES) attached to the 1.8 m telescope at BOAO in Korea (Kim et al. 2007). One exposure with the BOES has a wavelength coverage range of 3500 Å to 10 500 Å, distributed over approximately 75 spectral orders. The BOES is equipped with an iodine absorption (I₂) cell of the type needed for more precise RV measurements. Before starlight enters the fiber, it passes through the I₂ absorption cell regulated at 67°C, which superimposes thousands of molecular absorption lines over the object spectra in the spectral region between 4900 and 6100 Å. Using these lines as a wavelength standard, we simultaneously modeled the time-variant instrumental profile and Doppler shift relative to an I₂ free template spectrum. In order to provide precise RV measurements, we used a fiber with a diameter of 80 μm, which yields a resolving power R = 90 000. Most observations were conducted from 2005 to 2022. The estimated signal-to-noise ratio (S/N) in the I₂ region was approximately 200, and the typical exposure time ranged from 120 to 600 s. The RV standard star τ Ceti, monitored since 2003, was shown to maintain a stable RV value of 7.5 m s⁻¹ for 17 yr, as presented in Fig. 1.

Our stellar samples are the result of the combination of several datasets. In this case, 1) all stars of spectral type M appearing in the HIPPARCOS catalog (Esa 1997), 2) stars from the northern hemisphere (δ > 30 degrees) observed with the BOES at the BOAO, 3) all stars brighter than 6.5 (V magnitude) to attain a sufficient S/N, which are barely observable using 2 m class telescopes with a Doppler precision level of ~ 10 m s⁻¹, and 4) M giants showing high proper motion long-period variation or seminormal variables.

The standard reduction procedures of flat-fielding, scattered light subtraction, and order extraction from raw CCD images were carried out using the IRAF software package. Precise RV measurements using the I₂ method were undertaken using RVI2CELL (Han et al. 2007), which is based on a method used in Valenti et al. (1995) and Butler et al. (1996). However, to model the instrument profile, we used the matrix formula described by Endl et al. (2000). We solved the matrix equation using singular value decomposition instead of the maximum entropy method (Endl et al. 2000).

Fig. 2 Distribution in the H–R diagram of the data used for observations.

3 Stellar characteristics

3.1 Fundamental parameters

The basic stellar parameters were based on the HIPPARCOS catalog (Esa 1997) and Gaia DR2 (Gaia Collaboration 2018). The stellar characteristics of M giants are not well known. The planet mass is subject to some uncertainty because the mass of the host star as measured by different authors and by different methods disagrees. In order to derive the stellar mass, the stellar parameters are required, particularly the effective temperature and gravity. All stellar masses in this work are taken from the literature because the mass estimates are consistent with each other within acceptable error ranges for a given star. Figure 2 shows the position of target stars in the H–R diagram. The sizes of the points are proportional to the stellar radii. Our RV measurements for the nine M giants are listed in Appendix A.

3.2 Rotational velocity

We estimated the stellar rotational velocity using the line-broadening model devised by Takeda et al. (2008). The observed stellar spectra were fit by convolving the intrinsic spectrum model and the total macro-broadening function. To determine the degree of line broadening, we used the automatic spectrum-fitting technique by Takeda (1995) when the spectrum was within the wavelength range of 6080–6089 Å. This technique employs seven free parameters that specify the best-fitting solution in relation to the abundances of six elements (Si, Ti, V, Fe, Co, and Ni). We used the Gray (1989) assumption that the macroturbulence only depends on the surface gravity. We measured the macro-broadening velocity υ_M and estimated the projected rotational velocity υ_rot sin(i) for all stars. In the literature, the υ_rot sin(i) values are taken from various sources obtained by different methods. Massarotti et al. (2008) used the cross correlation of the observed spectra against templates drawn from a library of synthetic spectra calculated by Kurucz (1992) for different stellar atmospheres.

We calculated the rotational velocity for nine targets. However, the line-broadening model we adopted does not apply when the surface temperature is lower than ~3500K (HD 39801, HD 156014, and HD 42995) or for stars with a very weak surface gravity (HD 39801 and HD 156014), and we were able to determine the rotational velocities for only three targets.

Based on the rotational velocities and the stellar radius, we derived the ranges of the upper limits for the rotational periods of 7900 days for HD 6860, 6250 days for HD 18884, and 4200 days for HD 112300. The stellar parameters are listed in Table 1.

4 Orbital solutions and data analysis

We used RVI2CELL (Han et al. 2007) for the best fit to determine the orbital parameters. In order to determine the periodicity in the BOES RV variations, we used the generalized Lomb-Scargle periodogram (GLS; Zechmeister & Kürster 2009). The GLS provides more accurate frequencies, is less susceptible to aliasing, and confers a much better determination of the spectral intensity. All RV measurements are shown in Fig. 3, and the GLS outcomes for all objects are shown in Fig. 4. The GLS false-alarm probability (FAP) was calculated using a bootstrap randomization process (Kürster et al. 2003). The RV data were shuffled 200000 times, keeping the times fixed. The GLS periodogram was used to check the sinusoidal periodicity in the data set for first interpretation of the data. However, to assess the error bars on the parameters and to obtain a more robust fit of the data, we used the Markov chain Monte Carlo (MCMC) algorithm and Exo-Striker (Trifonov 2019) to perform all analysis.

The long-period RV variations in giants are, in general, related to stellar rotation, pulsation, and/or reflex orbital motion by a companion. To uncover the origin of the detected RV variation of our targets, we studied the photometric variations, bisector variations, and stellar activities.

First, the variations in HIPPARCOS photometric data were analyzed to determine the cause of stars showing an RV periodicity. Second, stellar rotational modulations by inhomogeneous surface features can create variable asymmetries in spectral line profiles (Queloz et al. 2001). Two bisector quantities were calculated from the line profile at two flux levels (40% and 80%) (the bisector velocity span BVS ≡ [V_top − V_bottom] and the bisector velocity curvature BVC ≡ [V_top − V_center] − [V_center − V_bottom]).

Finally, we used four types of indicators to check chromo-spheric activities. The EW variations of Ca II H & K, Balmer lines (H_α, H_β), sodium lines, and Ca II 8662 Å lines are frequently used as chromospheric activity indicators because they are sensitive to stellar atmospheric activity. This activity could have strong effects on the RV variations. The efficiency of the short-wavelength region (Ca II H & K) of the BOES spectra is low. Moreover, another activity indicator, the Ca II 8662 Å line, is not suitable either because significant fringing and saturation in our CCD spectra were found at wavelengths longer than 7500 Å. While H_α is sensitive to atmospheric stellar activity (Kürster et al. 2003) and useful for measuring variations, it is difficult to estimate the H line EW due to line blending in the stellar spectra and telluric lines, if any exist. To avoid nearby blending lines (i.e., Ti I 6561.3, Na II 6563.9, and ATM H₂O 6564.0 Å), we measured the H line EWs using a bandpass of ± 1.0 Å centered on the core of the H lines. In the EW calculation of the sodium lines, it is important to avoid nearby blending lines and weak telluric lines. We measured the sodium D lines at 5889.951 Å and 5895.924 Å using a bandpass value of ±0.5 Å centered at the core of the sodium lines.

Fig. 3 Radial velocity variations for nine M giants. The names of individual targets are labeled in the upper right corners of each panel.

5 Results

5.1 HD 6860 (β And)

HD 6860 (β And) is a bright star in the northern constellation of Andromeda and has an average apparent visual magnitude of 2.06. It is approximately at 60 parsecs from the Sun, according to its Gaia parallax (Gaia Collaboration 2018). The total extinction toward this star in the visual band is about 0.06 mag. This star has a low RV of 0.7 km s⁻¹ compared to the high tangential velocities from the proper motion values. HD 6860 is known to be a single red giant of spectral type M0 III. It is suspected of being a semiregular variable star, and its apparent visual magnitude varies by a magnitude of 0.014.

We obtained 44 spectra in total for HD 6860 from December 2005 to December 2021. The Keplerian fit to the RV data yields the following orbital parameters of the HD 6860 system: an orbital period of ${663.87}_{-4.31}^{+4.61}$ days, a semi-amplitude of ${373.97}_{-27.86}^{+22.63}\text{\hspace{0.5em}m\hspace{0.5em}}{\text{s}}^{-1}$, and an eccentricity of ${0.28}_{-0.09}^{+0.10}$. Figure 5 shows RV variations for HD 6860. The RV measurements phased to the orbital period are shown in Fig. 6. When we assume 2.49 M_⊙ (Dehaes et al. 2011) for the mass of HD 6860, the companion has a minimum mass of ${28.26}_{-2.18}^{+2.06}$ M_J. In order to ensure the reliability of our GLS periodogram analysis, we computed the FAP. For the prominent peak at 661 days in the RV power spectrum, we computed the preliminary FAP, finding it to be lower than 1 × 10⁻⁶% level in the GLS periodogram of the RVs. Figure B.1 shows the posterior distribution and correlations between all parameters sampled with our MCMC.

The HIPPARCOS photometric data contain 59 observations for HD 6860. The data have an RMS scatter that is smaller than the magnitude of 0.014. The GLS periodogram of the HIPPARCOS measurements shows a significant period of 41 days. However, the short apparent periodicity of 41 days for HD 6860 is too short to originate from an orbiting planet as the semimajor axis would then be inside the stellar photosphere. To search for variations in the spectral line shape, we selected the V1 6039.722 line, which is an unblended spectral feature with a high flux level located beyond the I₂ absorption region, meaning that contamination should not affect our bisector measurements. We carried out GLS period analyses of the bisectors, and no significant peaks were found, as shown in panele of Fig. 7.

The RMS values of the H_α and H_β EWs indicate less than 0.4% variation. The GLS periodogram of the H line EW variations for HD 6860 are shown in panel f of Fig. 7. Significant peaks at 1200 days similar to those of the H_α and H_β lines were found and judged to be unrelated to the RV period. The RMS value s in the sodium line D1 EWs and D2 EWs shows less than 0.1% variation in both stars. The GLS periodograms of the sodium D EW variations are shown in Fig. 7g for HD 6860. The sodium lines of HD 6860 show strong periоds at about 1190 days, very similar to those shown in the H lines (1200 days). Therefore, the 1200-day period is quite likely to be related to chromospheric activity.

Fig. 4 Generalized Lomb–Scargle periodogram power for nine M giants. The horizontal lines in each panel correspond to an FAP of 1%.

Fig. 5 Radial velocity measurements (top panel) and the residuals (bottom panel) for HD 6860 from December 2005 to December 2021. The solid line shows the orbital solution with a period of 664 days.

Fig. 6 Phase diagram for HD 6860.

Fig. 7 Generalized Lomb-Scargle periodograms for RVs, photometric variations, bisector variations, and stellar activities of HD 6860. (a) Priodogram for RVs, (b) the same GLS periodogram for the residual RVs after subtracting the strong peak at 664 days, (c) GLS periodogram of our time sampling (window function), (d) GLS periodogram of the HIPPARCOS photometric data, (e) GLS periodograms of the BVS and the BVC, (f) H EW variations, and (g) sodium line EW variations. The vertical dashed lines indicate orbital periods of 664 days. The horizontal lines in each panel correspond to a 1% FAP.

5.2 HD 18884 (α Cet)

HD 18884 is a cool luminous red giant about 77 parsecs away from the Sun and is known to be an LPV. It is at the AGB evolutionary stage, during which hydrogen and helium are exhausted at the core (Eggen 1992), and will most likely become a highly unstable star similar to Mira, before finally shedding its outer layers and forming a planetary nebula, leaving a relatively large white dwarf remnant.

Over the 15-yr period from October 2006 to December 2021, a total of 75 spectra for HD 18884 were collected. The RV periodic variations and a phase diagram of HD 18884 are shown in Figs. 8 and 9. The GLS periodogram of the RV measurements shows a significant peak at 885 days. The orbital parameters of the system were derived as the semi-amplitude of 287 ± 53 m s⁻¹ and the eccentricity of 0.4 ± 0.2. A relatively large residual (RMS of 150 m s⁻¹) corresponding to the characteristics of late-type stars was also noted, although no secondary significant peak was found. When we adopt a mass of 2.3 M_⊙ for HD 18884 (Wittkowski et al. 2006), the best-fit Keplerian model yields a minimum mass of 21 M_J for its companion.

The 57 observations of HIPPARCOS photometric data were used for HD 18884, which shows an RMS scatter of less than a magnitude of 0.014. No significant peak was found from the GLS periodogram. To search for variations in the spectral line shape, we selected the V1 6039.722 Å line. GLS period analyses show no significant peaks (Fig. 10).

The RMSs in the H_α and H_β EWs indicate less than 0.4% variation. The GLS periodogram of the H line EW variations for HD 18884 are shown in panel f of Fig. 10. Significant peaks at 880 days similar to those of the RV variation were found. The RMS value in the sodium line D1 EWs and D2 EWs shows less than 0.1% variation in both stars. The GLS periodograms of the sodium D EW variations are shown in Fig. 10g. Because the 870-day period found in HD 18884 nearly coincides with the H lines and RV period, the main cause of the RV period probably is stellar atmospheric activities.

Fig. 8 Radial velocity measurements (top panel) and the residuals (bottom panel) for HD 18884 from December 2005 to December 2021. The solid line is the orbital solution with a period of 885 days.

Fig. 9 Phase diagram for HD 18884.

5.3 HD 39801(α Ori)

The M2 Iab supergiant HD 39801 (α Ori) is an ideal laboratory to search for exoplanets around massive stars and to study their properties. The star is classified as a semiregular variable with an SRC subclassification with a period of 2335 days (6.39 yr) (Samus’ et al. 2017). The absolute luminosities and photospheric radii are now sufficiently well determined to warrant a new investigation of the constraints on models for this star. The list in the Catalog of Components of Double & Multiple stars (CCDM) contains at least four combined celestial bodies, all of which are within three arcminutes of the star. However, little is known about them, except for their position angles and apparent magnitudes (Dommanget & Nys 2002). Thus, HD 39801 has no known orbital companions, and its mass has therefore not yet been determined with any certainty. A pulsating semiregular variable star such as HD 39801 is subject to multiple cycles of increasing and decreasing brightness caused by changes in its size and temperature. This star is usually considered to be a runaway star without any companion (van Loon 2013). The presence of companions has been suggested from spectroscopic and polarimetric observations (Karovska et al. 1986).

Over the 13-yr period from January 2008 to April 2021, we collected 92 spectra for HD 39801. The resulting power spectrum displays a broad, highly significant peak centered at a period of 2245 days (Fig. 4). This period is very similar to the 2335 days presented by Samus’ et al. (2017). When we assume a stellar mass of 16.5–19 M_⊙, HD 39801 has a companion of approximately one solar mass at a distance of 8.5–9.0 AU. This result is similar to that in earlier work (Samus’ et al. 2017).

From November 2019 to March 2020, HD 39801 experienced a historic dimming in its visible brightness. The apparent brightness decreased to about 1.6 magnitudes, and the southern hemisphere of HD 39801 was ten times darker than the northern hemisphere in the visible spectrum during its great dimming in February 2020 (Montargès et al. 2021). Unfortunately, we could not confirm the great dimming because it was not observed in February 2020 using the BOES.

Fig. 10 Generalized Lomb-Scargle periodograms for RVs, photometric variations, bisector variations, and stellar activities of HD 18884. (a) GLS periodogram for RVs, (b) the same GLS periodogram for the residual RVs after subtracting the strong peak of 885 days, (c) GLS periodogram of our time sampling (window function), (d) GLS periodogram of the HIPPARCOS photometric data, (e) GLS periodograms of the BVS and the BVC, (f) H EW variations, and (g) sodium line EW variations. The vertical dashed lines indicate orbital periods of 885 days. The horizontal lines in each panel correspond to a 1% FAP.

5.4 HD 42995 (η Gem)

HD 42995, an RGB, is a triple system composed of a primary M-type giant and a close companion, as spectroscopically confirmed. This star has been classified as a semiregular variable with SRa-type variability. This variability closely approximates Mira variables, but the amplitude is lower. Many long-period variables show long secondary periods that are typically ten times longer than the main period, with an amplitude up to one magnitude at visual wavelengths. However, no such changes were detected for HD 42995. The main period is known to average of 234 days (Percy et al. 2008), which is very close to the 235-day period from HIPPARCOS photometric data. Little is known about the companion, although HD 42995 is a sixth-magnitude bright star. It is assigned a G0 spectral type and is giant on the basis of its brightness (Hunsch et al. 1998). The orbit calculated in 1944 is essentially unchanged today, with a period of 2983 days and an eccentricity of 0.53. Observers have found signs of an eclipse corresponding to the derived orbit. However, the evidence was considered inconclusive (McLaughlin & van Dijke 1944). On the other hand, the companion is suspected to be an M-type star based on the appearance of its spectrum (Hunsch et al. 1998).

We obtained 48 spectra from October 2006 to April 2021. The power spectrum displays a broad, highly significant peak centered at a period of 3001 ± 11 days and an eccentricity of 0.53 ± 0.05 (Fig. 4), very similar to the 2983 days and 0.53 found by McLaughlin & van Dijke (1944). When we assume a mass of 2.5 M_⊙ (Hunsch et al. 1998), HD 42995 has a companion of 1.2 M_⊙ (minimum mass) at a distance of 5.5 AU.

5.5 HD 44478 (μ Gem)

HD 44478 is a slow irregular-type variable in the AGB stage of spectral type M3 III. Its brightness in the V band varies between magnitudes +2.75 and +3.02 over a 27-day period, along with a 2000-day period in its long-term variation (Percy et al. 2001).

We determined an orbital period of 560 days from the RV measurement for HD 44478 over 15 yr (see Fig. 4). The FAP is estimated to exceed 5%. This usually means that it is unlikely to be a statistically significant signal. There was no evidence for a 27-day period or a long-term variation of 2000 days. However, the GLS periodogram for the HIPPARCOS photometric data shows a 27-day period with a brightness change of 0.04, as was reported by Percy et al. (2001). This suggests that it is probably due to low-order radial pulsation (Percy et al. 2001), and the long-term variation may be due to rotation or to convection-induced oscillatory thermal modes in red giants, known as a new type of stellar oscillation proposed by Wood (2000).

5.6 HD 112300 (δ Vir)

HD 112300 is an M1 III star with a mass of 1.4 solar masses and an effective temperature of ~3660 K (McDonald et al. 2017). This star exhibits semiregular variability with a very small amplitude, showing a magnitude of approximately 0.04 according to HIPPARCOS photometric data. A frequency analysis of the observed optical curve shows pulsations of several cycles. The known periods found by Tabur et al. (2009) are 13.0 days, 17.2 days, 25.6 days, 110.1 days, and 125.8 days. HD 112300 may be a binary star with a K-type dwarf companion, and it may have an orbital period exceeding of 200 000 yr, but this has not been confirmed.

For HD 112300, 35 spectra in total were collected from June 2006 to December 2021. The best-fit model yielded a period of ${466.63}_{-1.28}^{+1.47}$ days, a semi-amplitude of ${353.99}_{-23.04}^{+13.63}$ m s⁻¹, and an eccentricity of $e={0.36}_{-0.11}^{+0.06}$. The RV also clearly shows a linear trend. Thus, we included the linear slope as an unknown parameter in the orbital solution. Assuming a stellar mass of 1.4 ± 0.3 M_⊙, we derived a minimum mass of a planetary companion $m\sin \left(i\right)={15.83}_{-2.74}^{+2.34}$ M_Jup at a distance $a={1.33}_{-0.11}^{+0.09}$ AU from the host. Figure 11 shows the periodic variations for HD 112300, and the RV phase diagram of the orbit is shown in Fig. 12. The posterior distribution and correlations between all parameters for HD 112300 sampled with our MCMC is shown in Appendix B.2.

The HIPPARCOS photometric data contain 93 observations for HD 112300. They reveal considerable scatter with a magnitude of 0.022. GLS periodogram analyses indicate strong peaks at 138 days, 251 days, and 693 days for HD 112300, which are inconsistent with the RV period of 467 days. To search for variations in the spectral line shapes, the Ba II 6141.713 Å line was used. The GLS analysis of the barium time series produces no significant signals (panel e of Fig. 13).

The RMS in the H_α and H_β EWs indicate less than 0.4% variation. The GLS periodogram of the H line EW variations for HD 112300 is shown in panel f of Fig. 13. There is no significant peak. The RMS value in the sodium line D1 EWs and D2 EWs shows less than 0.1% variation in both stars. The GLS periodograms of the sodium D EW variations are shown in Fig. 13g. The significant peak is below 30 days for HD 112300. This short period has nothing to do with the existence of planets around giants, but is rather related to the stellar activity.

Fig. 11 RV measurements (top panel) and the residuals (bottom panel) for HD 112300 from June 2006 to December 2021. The solid line is the orbital solution with a period of 467 days.

Fig. 12 Phase diagram for HD112300.

Fig. 13 Generalized Lomb-Scargle periodograms for RVs, photometric variations, bisector variations, and stellar activities of HD 112300. (a) GLS periodogram for the RVs, (b) the same GLS periodogram for the residual RVs after subtracting the strong peak of 467 days, (c) GLS periodogram of our time sampling (window function), (d) GLS periodogram of the HIPPARCOS photometric data, (e) GLS periodograms of the BVS and the BVC, (f) H EW variations, and (g) sodium line EW variations. The vertical dashed lines indicate orbital periods of 467days. The horizontal lines in each panel correspond to a 1% FAP.

5.7 HD 146051 (δ Oph)

The high-proper-motion star HD 146051 has a stellar classification of M0.5 III. It is currently on the AGB. The measured angular diameter of this star, after correction for limb darkening, is 10.47 ± 0.12 mas (Richichi et al. 2005). This yields a physical size of about 54 times the radius of the Sun. The effective temperature of the outer atmosphere is relatively cool at ~3800 K (McDonald et al. 2017). It is listed as a suspected variable star that may change by a magnitude of 0.03 in the visual band.

We obtained 39 spectra from June 2006 to March 2021. GLS results show no significant peak in the RV measurements (Fig. 4).

5.8 HD 156014 (α Her)

The AGB star HD 156014 (M5 Ib-II) is an LPV that is the primary star of a triple system. The primary star forms a visual binary pair with a second star, which is itself a spectroscopic binary (Moravveji et al. 2013). HD 156014 A and B are more than 500 AU apart, with an estimated orbital period of approximately 3600 yr. HD 156014 A is a relatively massive red bright giant; however, RV measurements suggest a companion with a period of about a decade (according to the Washington Double Star Catalog). The full range of its brightness is from magnitude 2.7 to magnitude 4.0 (Samus’ et al. 2017). However, it usually varies within a much smaller range of around 0.6 magnitude (Percy et al. 2001). The two components of HD 156014B are a primary yellow giant star and a secondary yellow-white dwarf star in a 51.578-day orbit.

We obtained 25 measurements of HD 156014 spanning more than 9 yr from June 2010 to October 2019. There is no significant power in the RV data and only a period of 497.6 days with an FAP of 5% that is not related to the brightness variation.

5.9 HD 183030 (λ UMi)

HD 183030 is an AGB star showing semiregular variability. HIPPARCOS photometric data show that HD 183030 is an LPV star with a period of 647 days. Its brightness varies by a magnitude of approximately 0.1 in the visual band.

A total of 30 spectra were taken from June 2010 to January 2022 using the BOES. Precisely measured RV data reveal no significant signals (Fig. 4). Perhaps the data are insufficient to provide meaning with which to reach a reliable scientific conclusion regarding an LPV for HD 183030.

6 Discussion

We selected nine bright M giants in the RGB or AGB stage and observed them for more than a decade to find low-amplitude and long-period RV variations using high-resolution spectroscopy. Generally, most giant stars have intrinsic RV variations, pulsations, and/or surface activities. In order to determine the nature of the RV variabilities, we comprehensively conducted all relevant analyses. A better understanding of how RV modulations behave as stars evolve during the RGB or AGB stage can also be gained by a detailed study of all possible star-induced signals.

In general, giants reveal pulsation periods of a few days in the form of radial pulsations. We estimated the fundamental periods, that is, the radial pulsation periods, and the expected amplitudes for HD 6860 and for HD 112300 using the relations devised by Kjeldsen & Bedding (1995) in Table 2. The periods are far too short to explain the RV variations we observed. However, the expected RV amplitudes from the stellar oscillations are consistent with the RMS scatter in the RV orbital fits. Thus, the significant RV scatter observed with regard to the orbital solution can easily be explained by these stellar oscillations. We note that both stars are expected to have the smallest RV amplitudes attributable to stellar oscillations, and indeed have the smallest amounts of observed RV scatter. The best-fit orbital parameters of the planetary signals in the final MCMC model are listed in Table 3.

As a result of the long-term RV observations of the nine M giants, two long-term stellar companions were verified for HD 39801 and for HD 42995. In addition, low-amplitude and long-period RV periods were found around three M giants. Among them, the 885-day variations discovered for HD 18884 are strongly suspected to be due to stellar chromospheric activity, and the remaining two M giants HD 6860 and HD 112300 are found to harbor substellar companions.

The variable M giant HD 6860 (CSV 100088, NSV 414) and the M giant HD 112300 (NSV 6026) have been observed for photometric and spectroscopic variations since the early twentieth century. A history of RV determinations of both stars recorded before the development of precise RV techniques is listed in Tables 4 and 5. However, there are few observed RV results for HD 6860 and HD 112300 despite the long interval. The RV values have been found to vary in the range of ~ 1.07 km s⁻¹ for HD 6860 and ~0.94 km s⁻¹ for HD 112300, which indicates possible periodic RV variations.

The M giant HD 6860 reveals different long-term variations in its spectroscopic and chromospheric activity measurements. Four types of chromospheric activity indicators were used to verify the cause of the RV origin. Interestingly, all indications show a nearly identical period of 1190–1200 days, unrelated to the RV period of 661 days. This can be interpreted as a strong evidence that the cause of the RV variation at 1200 days is chromospheric activity.

The M giant HD 112300 also shows different long-term variations in the spectroscopic and photometric measurements. HD 112300 was discovered to be a variable with a long period of ~693 days according to HIPPARCOS measurements. These variations are similar to those of a semiregular variable among late-type supergiants (SRC) or a long secondary-period variable (LSPV). SRCs are M supergiants that show semiregular multi-periodic photometric variations ranging from several dozen to several thousand days (i.e., BC Cyg, α Ori, and μ Cep). However, unlike one magnitude variation in the V band that is usually observed in an SRC variable, HD 112300 only shows a variation magnitude of 0.22 in the photometric measurements.

On the other hand, Kiss et al. (2006) showed that ~25% of pulsating red supergiants show periodic brightness changes that are characterized by two distinct timescales: a few hundred days (first-period mode), and more than approximately 1000 days (secondary-period mode), known as LSPVs. Our analyses show that for HD 6680, the first period is caused by a substellar companion, and the long secondary period can be attributed to chromospheric activity. The first period for HD 112300 is also related to a substellar companion, and the long secondary period may stem from the rotational modulation in the surface activities. Further RV observations of these pulsating red supergiants will show whether these distinct timescales generally have different origins as in HD 6860 and HD 112300.

As of January of 2022, approximately 100 giant planets have been discovered around (super)giant stars. These giant planets are more massive than the giant planets found around solar-type stars. The reason might be that giant stars are more massive than the Sun, and more massive stars are expected to have more massive planets. However, the masses of the planets that have been found around giant stars do not correlate with the masses of the stars. Therefore, the planets could be growing in mass during the red giant stage of the hosting stars. This type of growth in planet mass could be partly due to accretion from stellar wind, although a much stronger effect would be Roche-lobe overflow, causing a mass-transfer from the star to the planet when the giant expands out to the orbital distance of the planet (Jones et al. 2014).

To summarize, we observed nine bright M red giants since 2005 and found significant periodic RV signals on HD 6860 and HD 112300 that originate from substellar companions. The best Keplerian fit and MCMC simulation yield an orbital period of ${663.87}_{-4.31}^{+4.61}$ days, a semi-amplitude of ${373.97}_{-27.86}^{+22.63}$ m s⁻¹, an eccentricity of ${0.28}_{-0.09}^{+0.10}$ for HD 6680, and an orbital period of ${466.63}_{-1.28}^{+1.47}$ days, a semi-amplitude value of ${353.99}_{-23.04}^{+13.63}$ m s⁻¹, and an eccentricity of ${0.36}_{-0.11}^{+0.06}$ for HD 112300. Thus, we obtain a minimum companion mass of ${28.26}_{-2.18}^{+2.06}$ M_J and a semimajor axis of ${2.03}_{-0.01}^{+0.01}$ AU for HD 6680, as well as a minimum companion mass of ${15.83}_{-2.74}^{+2.34}$ M_J and a semimajor axis of ${1.33}_{-0.11}^{+0.08}$ AU for HD 112300. The radius of the M giant HD 6860 is 86 R_⊙, which at the time of this study makes the largest star with a substellar companion.

After we removed the RV signal attributed to the companions, the remaining RV variations are 123.7 m s⁻¹ for HD 6860 and 93.6 m s⁻¹ for HD 112300. The variations are larger than those expected for the stellar activity, given the errors of the measurements. Additional periodic variations can be considered and duly weighed because the values are significantly higher than the RV precision for the RV standard star т Ceti (7.5 m s₋¹), and they are higher than the typical internal error of the individual RV accuracy rate of ~12 m s⁻¹. Hatzes et al. (2005) demonstrated that a high RMS of the residuals (~51 m s⁻¹) can be found in the K1 giant HD 13189, showing significant short-term RV variability on a timescale of days that is most likely due to stellar oscillations. Lee et al. (2013) showed that the RMS values of the RV residuals of the M2 III giant HD 220074 have a median value of 57 m s⁻¹. Recently, Lee et al. (2017) found that the RMS values of the RV residuals of the M1 III giant HD 52030 and M0.5 III HD 208742 have medians of 82 m s⁻¹ and 55 m s⁻¹, respectively. This behavior is typical for K and M giant stars, regardless of whether they are periodic, and it tends to increase toward later spectral types.

It is very meaningful and rare in itself that substellar companions were discovered through RV observations around M (super) giants with a greatly expanded and active stellar atmosphere. In particular, the fact that substellar companions survived RGB and AGB upheaval events presents another viable research topic related to the problem of planet survival. Hon et al. (2023) recently carried out follow-up observations and an analysis of the red giant 8 UMi, which had been an exoplanet system in the RGB stage (Lee et al. 2015). They showed that 8 UMi b survived the RGB phase, and this case is expected to be common. The system shows that a core-helium burning red giant can accommodate close planets, and it provides evidence for the role of nonstandard stellar evolution in the extended survival of late-stage exoplanet systems. To understand this late evolutionary stage of exoplanet systems such as those in this work will certainly become one of the main topics in future research on exoplanets.

Acknowledgements

B.C.L. acknowledges partial support by the KASI (Korea Astronomy and Space Science Institute) grant 2023-1-832-03 and acknowledges support by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A2C1009501). M.G.P. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1I1A3A02062242) and KASI under the R&D program supervised by the Ministry of Science, ICT and Future Planning. H.Y.C. was supported by a National Research Foundation of Korea Grant funded by the Korean government (NRF-2018R1D1A3B070421880) and Basic Science Research Program through the NRF of Korea funded by the Ministry of Science, ICT and Future Planning (No. 2018R1A6A1A06024970). B.L. and J.R.K. acknowledge support by the NRF grant funded by MSIT (Grant No. 2022R1C1C2004102). This research made use of the SIMBAD database, operated at the CDS, Strasbourg, France.

Appendix A Radial velocity measurements

In this appendix, we present all observational data collected with the BOES. We list the observation dates as the Julian date (JD), the RVs, and the uncertainty (±σ).

Appendix B Corner plots

We present posterior distributions of the parameters sampled from the model MCMC fit.

Fig. B.1 Corner plot showing the posterior distributions of the main internal structure parameters of HD 6860 b. The titles of each column correspond to the median and 1σ, which are also shown with dashed lines. This displays the results of the MCMC analysis, and the corrected RV time-series is presented. This analysis involves fitting a model that consists of an offset, an RV jitter, the semi-amplitude (Kb), the orbital period (Pb), the orbital eccentricity (eb), the periastron angle (ωb), the mean anomaly (MAb), the slope (RV lin.tr), the mean longitude λb, the minimum mass (m sin i), and the semimajor axis (ab).

Fig. B.2 Corner plot showing the posterior distributions of the main internal structure parameters of HD 112300 b. The titles of each column correspond to the median and 1 σ, which are also shown with dashed lines. This displays the results of MCMC analysis, and the corrected RV time-series is presented. This analysis involves fitting a model that consists of an offset, an RV jitter, the semi-amplitude (Kb), the orbital period (Pb), the orbital eccentricity (eb), the periastron angle (ωb), the mean anomaly (MAb), the slope (RV lin.tr), the mean longitude λb, the minimum mass (m sin i), and the semimajor axis (ab).

References

All Tables

All Figures

	Fig. 1 Long-period RV variations for the standard star τ Ceti from 2003 to 2021.
In the text

	Fig. 2 Distribution in the H–R diagram of the data used for observations.
In the text

	Fig. 3 Radial velocity variations for nine M giants. The names of individual targets are labeled in the upper right corners of each panel.
In the text

	Fig. 4 Generalized Lomb–Scargle periodogram power for nine M giants. The horizontal lines in each panel correspond to an FAP of 1%.
In the text

	Fig. 5 Radial velocity measurements (top panel) and the residuals (bottom panel) for HD 6860 from December 2005 to December 2021. The solid line shows the orbital solution with a period of 664 days.
In the text

	Fig. 6 Phase diagram for HD 6860.
In the text

Fig. 7 Generalized Lomb-Scargle periodograms for RVs, photometric variations, bisector variations, and stellar activities of HD 6860. (a) Priodogram for RVs, (b) the same GLS periodogram for the residual RVs after subtracting the strong peak at 664 days, (c) GLS periodogram of our time sampling (window function), (d) GLS periodogram of the HIPPARCOS photometric data, (e) GLS periodograms of the BVS and the BVC, (f) H EW variations, and (g) sodium line EW variations. The vertical dashed lines indicate orbital periods of 664 days. The horizontal lines in each panel correspond to a 1% FAP.

In the text

	Fig. 8 Radial velocity measurements (top panel) and the residuals (bottom panel) for HD 18884 from December 2005 to December 2021. The solid line is the orbital solution with a period of 885 days.
In the text

	Fig. 9 Phase diagram for HD 18884.
In the text

Fig. 10 Generalized Lomb-Scargle periodograms for RVs, photometric variations, bisector variations, and stellar activities of HD 18884. (a) GLS periodogram for RVs, (b) the same GLS periodogram for the residual RVs after subtracting the strong peak of 885 days, (c) GLS periodogram of our time sampling (window function), (d) GLS periodogram of the HIPPARCOS photometric data, (e) GLS periodograms of the BVS and the BVC, (f) H EW variations, and (g) sodium line EW variations. The vertical dashed lines indicate orbital periods of 885 days. The horizontal lines in each panel correspond to a 1% FAP.

In the text

	Fig. 11 RV measurements (top panel) and the residuals (bottom panel) for HD 112300 from June 2006 to December 2021. The solid line is the orbital solution with a period of 467 days.
In the text

	Fig. 12 Phase diagram for HD112300.
In the text

Fig. 13 Generalized Lomb-Scargle periodograms for RVs, photometric variations, bisector variations, and stellar activities of HD 112300. (a) GLS periodogram for the RVs, (b) the same GLS periodogram for the residual RVs after subtracting the strong peak of 467 days, (c) GLS periodogram of our time sampling (window function), (d) GLS periodogram of the HIPPARCOS photometric data, (e) GLS periodograms of the BVS and the BVC, (f) H EW variations, and (g) sodium line EW variations. The vertical dashed lines indicate orbital periods of 467days. The horizontal lines in each panel correspond to a 1% FAP.

In the text

Fig. B.1 Corner plot showing the posterior distributions of the main internal structure parameters of HD 6860 b. The titles of each column correspond to the median and 1σ, which are also shown with dashed lines. This displays the results of the MCMC analysis, and the corrected RV time-series is presented. This analysis involves fitting a model that consists of an offset, an RV jitter, the semi-amplitude (Kb), the orbital period (Pb), the orbital eccentricity (eb), the periastron angle (ωb), the mean anomaly (MAb), the slope (RV lin.tr), the mean longitude λb, the minimum mass (m sin i), and the semimajor axis (ab).

In the text

Fig. B.2 Corner plot showing the posterior distributions of the main internal structure parameters of HD 112300 b. The titles of each column correspond to the median and 1 σ, which are also shown with dashed lines. This displays the results of MCMC analysis, and the corrected RV time-series is presented. This analysis involves fitting a model that consists of an offset, an RV jitter, the semi-amplitude (Kb), the orbital period (Pb), the orbital eccentricity (eb), the periastron angle (ωb), the mean anomaly (MAb), the slope (RV lin.tr), the mean longitude λb, the minimum mass (m sin i), and the semimajor axis (ab).

In the text