Search for Exoplanets around Northern Circumpolar Stars. II. The Detection of Radial Velocity Variations in M Giant Stars HD 36384, HD 52030, and HD 208742

The basic stellar parameters were taken from the HIPPARCOS catalog (ESA 1997). The luminosities came from the result of Anderson & Francis (2012), that are computed based on V-band photometry with a bolometric correction supplied by Masana et al. (2006). The stellar atmospheric parameters of temperature (T_eff), metal abundance ([Fe/H]), surface gravity (log g), and micro turbulence (v_micro) were determined using the TGVIT (Takeda et al. 2005). This was based on the Kurucz (1992) atmosphere models using around 130–150 equivalent width (EW) measurements of Fe i and Fe ii lines for each star, which usually require three constraint conditions of excitation equilibrium, ionization equilibrium, and matching the curve of growth shape (Takeda et al. 2002).

HD 52030 has a spectral type of K0 III (ESA 1997). The B–V color index and the T_eff, however, indicate that the star could be a late K- or early M-type giant. The V–K color of 4.08 is more consistent with an M1 III (V–K = 4.05) rather than a K0 III (V–K = 2.31) according to Bessell & Brett 1988. HD 208742 listed as spectral type of K5 with unclassified luminosity class (ESA 1997). The star could be classified as a giant according to the value of the low surface gravity and a large stellar radius compared to that of the dwarf star (see Section 3.2). The HIPPARCOS color index of approximately 1.6 and our estimation of the T_eff indicate that the spectral type of HD 208742 is close to a late K or early M. The V–K color of 3.94 is similar to an M0.5 III in Bessel & Brett (1988). As a result, HD 208742 should be an early M giant star. The basic stellar parameters are summarized in Table 1.

Stellar mass and stellar radius are the major factors in determining the fate of companions in the evolution track of giant stars. We determined the stellar radii and masses from the stellar positions in the color–magnitude diagram using the theoretical stellar isochrones of Bressan et al. (2012). The Bayesian estimation method (Jørgensen & Lindegren 2005; da Silva et al. 2006) was also adopted. We derived R_⋆ = 38.4 ± 3.4 R_⊙ and M_⋆ = 1.14 ± 0.15 M_⊙ for HD 36384, R_⋆ = 53.0 ± 6.1 R_⊙ and M_⋆ = 1.09 ± 0.16 M_⊙ for HD 52030, and R_⋆ = 57.2 ± 7.1 R_⊙ and M_⋆ = 1.18 ± 0.22 M_⊙ for HD 208742.

As stars evolve away from the MS, they become cooler and rotate slower. Low-amplitude and long-period RV variations in evolved stars may arise from the rotational modulation of surface features such as star spots (Lee et al. 2008, 2012). In order to estimate the stellar rotational velocities, we used a line-broadening model (Takeda et al. 2008) and the automatic spectrum-fitting technique (Takeda 1995). We estimated the minimum rotational velocities of 4.5 km s⁻¹ for HD 36384, 4.1 km s⁻¹ for HD 52030, and 5.4 km s⁻¹ for HD 208742. Based on the rotational velocities and the stellar radii, we derived the upper limits for the rotational period of 440 ± 40 days for HD 36384, 650 ± 80 days for HD 52030, and 540 ± 70 days for HD 208742.

We obtained 27 BOES spectra for HD 36384 spanning five years (Table 2), which show clear periodic variations (Figure 1). The Lomb–Scargle (L–S) periodogram (Scargle 1982) results in a peak of 535.1 days. Figure 2 shows the RV data phased to the orbital period superposed on the Keplerian fit. The L–S power of this peak corresponds to a false alarm probability (FAP) of <1 × 10⁻⁵ (top panel in Figure 3), adopting the procedure described in Cumming (2004), which is based on the goodness-of-the-fit statistic for the difference between the Keplerian fit and the linear fit to the data. The FAP is determined by a Monte Carlo method in which fake data sets containing noise are only compared with the observed power or from the analytic distribution of power (Cumming 2004). We found a semi-amplitude K = 302.1 ± 20.4 m s⁻¹ and an eccentricity e = 0.13 ± 0.12 for a Keplerian orbital fit.

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Observations for HD 52030 with the BOES took place between 2010 December and 2016 March. We gathered a total of 27 spectra during five and half years (Figure 4 and Table 3). Figure 4 shows more obvious linear secular change, which may come from an unknown long-term period binary. The RV measurements phased to the orbital period are shown in Figure 5. The L–S periodogram shows a peak at 484 days (Figure 6). The RV variations could be fitted with a Keplerian orbit with a period of 484.3 ± 4.2 days, a semi-amplitude of 329.0 ± 21.8 m s⁻¹, and an eccentricity of 0.14 ± 0.14.

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Since 2010 February, we have gathered 24 spectra for HD 208742 as displayed in Figure 7 and listed in Table 4. The L–S periodogram of the RV measurements for HD 208742 shows a significant peak at a period of 602.8 days (top panel in Figure 9). The L–S power of this peak corresponds to an FAP of less than 1 × 10⁻⁴. We found semi-amplitude K = 303.0 ± 16.6 m s⁻¹ and eccentricity e = 0.06 ± 0.13 for a Keplerian fit and Figure 8 shows the phase folded RV orbit for HD 208742.

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The residual RV variations after removing the Keplerian orbital fit are 73.1 m s⁻¹ for HD 36384, 82.1 m s⁻¹ for HD 52030, and 55.4 m s⁻¹ for HD 208742. They are significantly larger than the RV precision for the RV standard star τ Ceti (∼7 m s⁻¹) and the typical internal error of individual RV precisions of ∼10.9 m s⁻¹ (HD 36384), ∼11.7 m s⁻¹ (HD 52030), and ∼14.4 m s⁻¹ (HD 208742), respectively. We searched for periodic variations in the residual RV measurements using the L–S periodogram. These show no additional periodic signals (dashed lines in the top panels of Figures 3, 6, and 9). Large residual RVs can be the typical features of evolved stars (Setiawan et al. 2003; Hatzes et al. 2005; Döllinger et al. 2007; de Medeiros et al. 2009), which tend to increase toward later type stars (Hekker et al. 2006). They are most likely to arise from stellar oscillations. These can be stochastic so they may not appear as periodic signals, particularly due to the sparse sampling of the data. The scaling relationships of Kjeldsen & Bedding (1995) yield expected RV amplitudes from stellar oscillations of ∼80 m s⁻¹ for HD 36384, ∼186 m s⁻¹ for HD 52030, and ∼194 m s⁻¹ for HD 208742 comparable or greater than the observed residuals after removing the Keplerian fit. Thus, these residuals may be related to the stellar oscillations.

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To search for possible brightness variations that might be caused by the rotational modulation of large star spots, we analyzed the HIPPARCOS photometry data. The data were obtained from 1989 December to 1993 February (HD 36384), from 1989 December to 1993 March (HD 52030), and from 1989 December to 1993 February (HD 208742): a total of 177, 226, and 141 HIPPARCOS measurements were made for HD 36384, HD 52030, and HD 208742, respectively. All stars showed rms scatters of 0.012–0.014 mag. This corresponds to a variation over the time span of the observations of 0.19%, 0.22%, and 0.18% for the three stars, respectively. The L–S of the photometric variations for the stars are shown in Figures 3, 6, and 9. All three stars exhibit certain level of periodic variations. HD 36384 especially shows periodic photometric variations close to the 535 day period seen in RV variations.

Large spots, produced by the chromospheric activity, crossing the stellar surface can create a spectroscopic signature that might be misinterpreted as the presence of a companion. When searching for exoplanets using the RV technique, thus, the possibility of variations caused by chromospheric activity must be considered. The EW variations of Ca ii H and K, H_β, Mg i b triplet, He i D₃, Na i D₁, and D₂, H_α, and Ca ii infrared triplet (IRT) lines are, in general, used as optical chromospheric activity indicators. Of these, the Na i D₁ and D₂ and Mg i b triplet lines are excluded from the study due to their location inside the I₂ molecular region. The Ca ii IRT lines are not suitable either due to significant fringing and saturation of our CCD spectra at wavelengths longer than ∼7500 Å.

The most common indicators of chromospheric activity are the Ca ii H and K lines, which are well studied for F- to K-type stars (Montes et al. 1995; Kürster et al. 2003; Hatzes et al. 2015; Lee et al. 2015). However, the BOES does not provide a sufficient S/N ratio to estimate EW variations in the Ca ii H and K line region. We used the Ca ii H line because this spectral region was of higher quality than for the Ca ii K feature. Figure 10 shows the Ca ii H line region of four BOES spectra, and the chromospherically active star HD 201091 (K5 V) is shown for comparison. Unfortunately, the spectra are of too poor quality to resolve any emission feature that might be present. Possible weak features are visible in the center of the Ca ii H line for all three stars, though not strong enough to guarantee the presence of the chromospheric activity in the sample. We thus measured variations in H_α and H_β EW for the sample. Specifically, the H_α line is sensitive to the chromospheric structure and conditions in giant stars (Cram & Mullan 1985; Smith et al. 1989). Recently, Lee et al. (2016) found that two hydrogen lines of μ UMa show periodic variations (∼473 days) consistent with the secondary RV period of 471 days, whose origin is probably a stellar activity. We measured the EWs using a band pass of ±1.0 Å for H_α and ±0.8 Å for H_β centered on the core of the lines to avoid nearby blending lines and ATM H₂O absorption lines. The individual chromospheric activity measurements of the H lines in L–S periodograms are shown in the third panel of Figures 3, 6, and 9. They do not show any significant periodic variations.

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In order to investigate other causes that may produce apparent RV variations, such as stellar rotational modulations or pulsations rather than the orbital motion, a spectral line shape analysis was performed using high-resolution stellar lines (Hatzes et al. 1998; Queloz et al. 2001). Two bisector quantities were calculated: the velocity span (BVS) and the velocity curvature (BVC). The former is the velocity difference between the two flux levels of the bisector and the latter is the difference of the velocity span of the upper half and lower half of the bisectors.

To avoid contaminations, unblended spectral features with high flux levels and free of the I₂ absorption lines were chosen. The BOES iodine cell has negligible absorption lines beyond about 6200 Å. So, we selected 11 spectral lines of V i 6251.8, Fe i 6262.6, Ti i 6325.2, Cr i 6330.1, Fe i 6335.3, Fe i 6411.6, Fe i 6421.4, Ca i 6499.7, Fe i 6574.2, Fe i 6593.9, and Ni i 6767.8 Å. The difference between the bisectors of the profiles at flux levels of 0.8 and 0.4 of the central depth were used as velocity spans, which thereby avoid the spectral core and wing where errors of the bisector measurements are large. The average BVS and BVC were computed using the bisector measurements of all 11 spectral lines after subtracting the mean value for each spectral line. Figures 3, 6, and 9 (bottom panel) show L–S periodograms of BVS and BVC for each star, respectively. None of them exhibit any meaningful periodic variations.

Analyses of rotational periods, H line EW variations, and line bisector measurements of all three stars do not show any obvious evidence of the RV variations caused by a rotational modulation of surface features. However, several strong periods were found in the HIPPARCOS photometric data, which suggests the possibility of stellar pulsations. In particular, the period of ∼570 days in HD 36384, close to a 535 day period in RV variations, strengthens the possibility. We further checked for any changes in the amplitude of RV variations as a function of time for HD 36384. Although the sampling of the RV data is not sufficient for this analysis, the WWZ analysis hints a secular decrease of the amplitude of RV variations over five years. In addition, HD 36384 is classified as a variable star in the SIMBAD database. Even though the mechanism to produce such low-amplitude, long-period pulsation modes is not well understood, we suspect that the current RV variations seen in HD 36384 is more likely to be the result of stellar pulsations rather than an orbiting companion.

There is recent evidence that long-period variations in K giant stars that mimic a planet signal may in fact be intrinsic stellar variability (Reffert et al. 2015; A. P. Hatzes 2017, private communication). Such RV amplitude change is obviously not compatible with orbiting companions, and the periodic RV variations in such systems are more likely due to the long-period stellar pulsations, known to occur in giant stars. These findings warn us that the usual diagnostic tests for orbiting planets such as comparison of variations of chromospheric activity indicators and BVS/BVC against those of RV spanning less than three to five years may not be conclusive as previously believed, especially for giant stars. Follow-up observations over a longer timescale will help to select out such "fake planet" systems.

The physical parameters from the Keplerian fit for HD 52030 b and HD 208742 b place the minimum mass of the companions in the planetary mass region. Figure 12 shows the distribution of the stellar radii versus the planetary masses. Of the ∼3000 host stars harboring companions with known stellar radii, 97% are smaller than the subgiant phase of 5 R_⊙ (∼0.025 au; within an orbit of a 3 day hot Jupiter). The stars crossing the subgiant branch do not undergo significant expansion. The largest host stars discovered so far to have companions are HD 208527 (51.1 R_⊙) and HD 13189 (50.39 R_⊙). HD 52030 and HD 208742 in our study may be the largest stars with a substellar companion at a radius of 53.0 R_⊙ (0.25 au) and 57.2 R_⊙ (0.27 au), respectively. Approximately 65% of companions resided inside 0.25 au from host stars and most companions around dwarfs will undergo an ineluctable destiny during the evolutionary process.

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The fate of planets around evolved stars may be dramatically altered as the host star evolves off the MS stage. The companions may have been engulfed or moved outward by the expanding host stars when the latter increases its radius as it ascends the red giant branch (RGB) and the asymptotic giant branch (AGB). When the Sun climbs the AGB stage with its largest radial extent of 213 R_⊙ (0.99 au); however, the Earth would move out to 1.69 au, narrowly escaping being engulfed only in the presence of mass loss (Sackmann et al. 1993). Recent studies showed that planets with masses smaller than 1 M_Jup do not survive during the planetary nebula phase if located initially at an orbital distance closer than 3–5 au (Villaver & Livio 2007; Kunitomo et al. 2011; Mustill & Villaver 2012; Mustill et al. 2014), whereas planets more massive than 2 M_Jup survive down to orbital distances of ∼3 au. For 1.5–5 M_⊙, planets in orbits within 0.5 au around RGB stars could have been engulfed by the host stars at the tip of the RGB due to the tidal force from the host stars (Sato et al. 2008). Johnson et al. (2007) also considered the possibility that the lack of close-in planets around giants may be attributable to engulfment by the expanding atmospheres of the host stars.

Figure 13 shows HD 36384, HD 52030, and HD 208742 in the H–R diagram along with their theoretical evolution tracks (Girardi et al. 2000). The diagram indicates the evolution of 1.5 M_⊙ and 1.6 M_⊙ stars according to the stellar evolution models with Z = 0.008 (HD 52030 and HD 208742) and Z = 0.019 (HD 36384). The stars are located at the AGB stage on the H–R diagram after having undergone the helium flash leaving the giant clump. It is unclear what happens to the companions when they interact with the atmosphere of their expanding host stars. Thus, if companions exist within 0.25 au around HD 52030, and HD 208742 in the beginning, there are two possible scenarios for their fate. First, low-mass planets may be engulfed. Second, companions more massive than 2 M_Jup may be pushed out to close distance. The companions at 1.2–1.5 au detected in this paper are probably impervious to the effect of the evolutionary process. There may be unusual cases in which a short-period substellar companion survives the engulfment as its parent star evolves into a white dwarf (Maxted et al. 2006).

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The current knowledge of the evolutionary tracks for evolved stars is not sufficient enough to predict the fate of these systems. We need to understand the dynamics of planetary systems around the largest evolving giants. Furthermore, the number of large stars with planetary companions is limited. Future surveys will provide us with more candidates, allowing us to better trace the shape of the companion mass function and offer us some understanding of the origin and history of these systems.