A Sanity Check for Planets around Evolved Stars

The number of exoplanets around stars with a post-main-sequence evolution follows an inverted pyramid: as of 2021 May about 4700 exoplanets ¹ have been discovered by different detection methods, about 900 of them via the radial-velocity (RV) technique with only about 120 planet candidates orbiting giant stars. This pictorial viewpoint clearly shows that the number of giants with detected planets is very limited.

Most of the host stars are of about 1 M_⊙ and are covered by the spectral types F8–K1 due to the target selection. This is understandable because their score of narrow absorption lines, which are essential for precise RV measurements, makes them amenable for the Doppler method. Starting from scratch, the similarity to our Sun has established these stars as preferential targets for planet-search surveys. Main-sequence (MS) stars of earlier spectral types, which are hotter and rotate faster, have fewer and more broadened spectral lines. The RV measurements of these more massive stars are less precise, and it is thus more difficult to detect planetary companions.

To overcome this difficulty, one can extend the RV monitoring to giant stars. These seem to be the targets of choice because intermediate-mass (IM) stars (with a median of 1.3 M_⊙) that have evolved onto the giant branch are cool and have lots of stellar lines and low rotation rates, which makes them highly suited for very precise RV studies. Moreover, evolved IM stars are also very luminous and thus appear as very bright targets. Consequently, several RV surveys are searching for planets around giant stars, including the Tautenburg Observatory Planet Search (TOPS) program. Using the 2.0 m Alfred Jensch Telescope and the high-resolution Tautenburg Coudé Échelle Spectrograph (official designation since 2018) at the Thüringer Landessternwarte Tautenburg (TLS), this program, established in 2001, has led to several exoplanet discoveries around giant stars and IM main-sequence stars (e.g., Hatzes et al. 2005, 2006; Döllinger et al. 2007; Guenther et al. 2009; Hartmann et al. 2010).

Others contain the Lick Observatory survey using the Hamilton spectrograph (Frink et al. 2001, 2002; Reffert et al. 2006; Mitchell et al. 2013; Trifonov et al. 2014), the Fiber-fed Extended Range Optical Spectrograph (FEROS) survey at La Silla Observatory (Setiawan et al. 2003a, 2003b, 2005), the survey at Okayama Observatory with the High Dispersion Echelle Spectrograph (HIDES; Sato et al. 2003, 2007, 2008a, 2008b, 2010, 2012), the Penn State Torun planet search with the Hobby–Eberly Telescope (Niedzielski et al. 2007, 2009a, 2009b; Gettel et al. 2012a, 2012b), the planet search at Bohyunsan Observatory using the Bohyunsan Optical Echelle Spectrograph (BOES; Han et al. 2010; Lee et al. 2012a, 2012b, 2013), as well as a search employing FEROS at La Silla Observatory and the Fiber Echelle Spectrograph (FECH) and CHIRON at Cerro Tololo Inter-American Observatory (Jones et al. 2011, 2013, 2014, 2015a). Moreover, Johnson et al. (2010a) monitored a sample of subgiants at Lick Observatory.

Nevertheless, evolved giants are known to be active stars. As a consequence, it is more challenging to reveal the real nature of the RV variability because these stars show additional intrinsic stellar jitter. Despite this fact, choosing giants expands our knowledge about the dependence of planet formation on the stellar mass. In particular, it gives us the possibility to compare the features and occurrence rates of exoplanets around host stars in different evolutionary stages. The planet candidates around giant stars are in this case very important because this small sample already shows properties that are different from planets around Sunlike stars and enables us to have a first insight into the diversity of extrasolar planets.

The typical occurrence rate of planets with ${m}_{{\rm{p}}}\sin i\gt 1$ M_Jup and P < 2000 days around FGK dwarfs is 4%–5% (see Table 1 and Figure 13 in Cumming et al. 2008). This rate is noticeably smaller in comparison with the frequency of planets around IM stars based on observations of evolved stars (giants and subgiants) showing inconsistent values between 9%–10% and 26% (lower range: Johnson et al. 2007; Döllinger 2008; Döllinger et al. 2009b; Reffert et al. 2015; upper range: Bowler et al. 2010). Moreover, giants tend to harbor more-massive planets (Döllinger et al. 2009b) and show no clear preference for multiplanetary systems. HD 102272 (Niedzielski et al. 2009a), BD+202457 (Niedzielski et al. 2009b), ν Oph (HD 163917; Quirrenbach et al. 2011, 2019; Sato et al. 2012), η Cet (HD 6805; Trifonov et al. 2014), HIP 67851 (HD 121056; Jones et al. 2015a), and, most recently, γ Lib (HD 138905; Takarada et al. 2018) are examples of these rare and often dynamically challenging multiplanet systems.

One hypothesis for the large scatter of the planet frequency of evolved stars might be false positives, i.e., some RV variations of K giants are actually due to intrinsic stellar variability. This assumption is based on additional RV measurements for 42 Dra. This giant star, a member of 62 K giants investigated by Döllinger (2008) within the TOPS program, showed RV variations with a period of 479.1 days consistent with the presence of a substellar companion with a minimum mass of 3.9 M_Jup (Döllinger et al. 2009a). Continued RV measurements, however, are inconsistent with the published planet orbit because the RV amplitude decreased by a factor of about 4, casting serious doubt on the existence of 42 Dra b. However, we cannot exclude a two-planet solution. We suggest that the variable RV signal is very likely due to a yet unknown phenomenon that is intrinsic to the star, resistant to the current standard activity indicators and might be common among evolved stars. These stars have extended atmospheres as well as deep convection zones. Our knowledge about the structure and activity of giants is very limited. Consequently, intrinsic stellar jitter can be caused by rotational modulation (e.g., spots) and/or known short-term and possibly long-period oscillations.

By re-examining other planet candidates, it turned out that γ Dra, not part of the Döllinger sample but included in the TOPS program, behaves similarly to 42 Dra after almost a decade of showing a coherent RV signal in amplitude and phase (Hatzes et al. 2018). A further similar example is α Tau (Aldebaran). Analyzing more than 30 yr of RV data, Hatzes et al. (2015) found evidence for both a planetary companion (P = 628.96 days) and rotational modulation by stellar surface structure (P ≈ 520 days). However, the existence of the planet was later refuted (Reichert et al. 2019). The fact that there is a large number of planet candidates with sparse and incomplete RV data sets (Kürster et al. 2015), for which follow-up RV campaigns are essential to make the planet detection robust, makes the situation more difficult. Thus, it is not surprising that several planet candidates around K giants are questionable, and 42 Dra is only the first example. Therefore, the requirements for planetary candidates have to be verified and improved. Applying only the common earmarks, i.e., checking whether the RV period coincides with the rotation period deduced from activity indicators (e.g., Hipparcos photometry, Hα, and bisectors), seems to be insufficient. In particular, the Hipparcos photometry and the bisectors are only of limited use. While the former is, by and large, not taken contemporaneously with the RV measurements, the latter are almost exclusively derived from spectra taken with a resolving power of less than 100,000.

Our approach is to take more care of the host star identity itself (stellar radius and metallicity) as well as the features of the detected planetary systems (e.g., orbital period). In this way, we can assess how much confidence we can place in the detection of a planet candidate. We will discuss how to verify the true nature of the challenging RV variability of evolved host stars independently of the usual earmarks. Therefore, we will search for common patterns in the stellar and planetary properties and use this as a sanity check.

The identification of striking structures in stellar and planetary features requires comprehensive data material to be evaluated. Additionally, in order to avoid low-number statistics and to guarantee a maximum achievable completeness, these data also have to be consistent. A clear definition is necessary of what is compared and why. This sounds trivial but unfortunately it is not. Subjects of our investigation are single- and multiple-planet systems around G and K giants. We exclude other evolved stars like subgiants to ensure that only stars in an comparable evolutionary stage are investigated, which is crucial to deduce clear findings.

Moreover, the exact mass boundary for the discrimination between planets and brown dwarfs (BDs) is still under debate (Burrows et al. 2001; Schneider et al. 2011; Hatzes & Rauer 2015), providing different input numbers for statistical investigations and producing contrary results. Therefore, we follow a suggested definition for giant planets based on the mass–density relationship by Hatzes & Rauer (2015), which represents a more complete and uniform approach. Similar to the MS of stars, objects on the upper end of the giant planet sequence (BDs) can simply be referred to as high-mass giant planets, while planets with masses near that of Jupiter can be called low-mass giant planets.

The other important point is the authenticity of the data. We deliberately choose the original releases of the planet detections to exclude transmission errors. Our suggestions can only improve the comparability of the data sets because the data were in general taken at different observational facilities (e.g., telescopes, spectrographs, and corresponding spectral resolution) and treated with different determination (e.g., pipelines, models, line lists) and calibration methods (e.g., iodine cell, simultaneous ThAr).

To be aware of this fact can nevertheless be the first step to explaining and resolving the aforementioned issues of inconsistent occurrence rates and the validity of the planet–metallicity correlation for giants. Special attention is drawn to the stellar radius and metallicity of the host star as well as the orbital period. It should be verified if the behavior of 42 Dra and γ Dra are individual cases of evolved stars with larger radii or the rule for this kind of star, which would have a big influence concerning statistics and planet formation theories.

Following these specifications, Table 1 contains essential properties of the known RV planets and their G- and K-giant host stars to investigate correlations that are crucial to revealing the real nature of their RV variability. In summary, we consider 18 G giants and 80 K giants with a single planet (including 5 K giants from our TLS survey), 1 G/K giant and 11 K giants with multiple/double planets as well as 13 further TLS planet candidates (not included in Table 1) in the subsequent analysis, giving 135 planets/candidates in 123 systems altogether. We note that four of the systems (HD 11977, HD 122430, HD 47636, and HD 110014) have entries from two references. For the analysis and figures in this paper, we used the values from the references that are listed first.

Table 1. Properties of Published Planetary Systems of G and K Giants

Star	Spectral Type	V	B − V	MV	Mass	Radius	[Fe/H]	Teff	log g	${m}_{{\rm{p}}}\sin i$	Period	References
		(mag)	(mag)	(mag)	(M⊙)	(R⊙)	(dex)	(K)		(MJup)	(days)
G giants with a single planet (18 host stars)
HD 11755	G5	6.87	1.22	+0.05	0.90	27.30	−0.74	4313	1.67	6.5	433.7	1
HD 11977	G8.5III	4.68	0.93	+0.57	1.91	10.09	−0.21	4970	2.90	6.54	711	2
					2.31	13.00	−0.16			6.5	621	3
HD 12648	G5	6.98	0.90	+1.00	1.20	9.20	−0.57	4836	2.18	2.9	133.6	1
HD 14067	G9III	6.53	1.03	+0.33	2.40	12.40	−0.10	4815	2.61	7.8	1455	4
HD 15779	G3III	5.36	1.00	+0.73	2.49	10.50	+0.00	4846	2.63	3.0	691.9	5
HD 16400	G5III/K0III	5.65	1.02	+0.63	2.40	11.00	−0.06	4785	2.35	5.3	952.7	6
HD 71369	G4II–III	3.35	0.86	−0.40	3.09	14.10	−0.09	5242	2.64	4.1	1630	5
HD 100655	G9III	6.45	1.01	+0.96	2.40	9.30	+0.15	4861	2.89	1.7	157.57	7
HD 104985	G9III	5.78	1.03	+0.74	1.60	11.00	−0.35	4786	2.62	8.3	199.51	8
HD 107383	G8III	4.74	0.99	−0.48	2.70	19.90	−0.35	4742	2.31	19.4	326.03	9
HD 112410	G8III	6.86	1.02	+0.99	1.54	9.41	−0.31	4830	2.53	9.18	124.6	10,11
HD 119445	G6III	6.30	0.88	−1.03	3.90	20.50	+0.04	5083	2.40	37.6	410.2	12
HD 120084	G7III	5.91	1.00	+0.96	2.39	9.12	+0.09	4892	2.71	4.5	2082	13
HD 141680	G8III/K0IV	5.21	1.02	+0.49	2.17	12.30	−0.24	4770	2.32	1.7	277.02	13
HD 173416	G8III	6.06	1.04	+0.41	2.00	13.50	−0.22	4683	2.48	2.7	323.6	14
HD 175679	G8III	6.14	0.96	+0.52	2.70	11.60	−0.14	4844	2.59	37.3	1366.8	15
HD 188310	G9III/K0III	4.71	1.02	+0.63	2.20	12.00	−0.21	4780	2.66	2.8	136.75	16
HD 199665	G6III	5.51	0.93	+1.15	2.30	8.50	−0.05	4979	2.82	10.3	993.3	16
K giants with a single planet (80 host stars)
BD+15 2375	KIII	10.31	1.05	+0.80	1.08	8.95	−0.22	4649	2.61	1.06	153.22	17
BD+15 2940	K0	9.19	1.00	+0.40	1.10	14.70	+0.28	4796	2.80	1.11	137.48	18
BD+20 274	K5III	9.36	1.36	+0.00	0.80	17.30	−0.46	4296	1.99	4.2	578.2	19
BD+48 738	K0III	9.14	1.25	+0.00	0.74	11.00	−0.20	4414	2.24	0.91	392.6	20
BD+48 740	K2III	8.69	1.25	⋯	1.50	11.40	−0.13	4534	2.48	1.6	771.3	21
BD+49 828	K0	9.38	1.13	+0.00	1.52	7.60	−0.19	4943	2.85	1.6	2590	22
HD 1690	K1III	9.17	1.35	+1.70	1.09	16.70	−0.32	4393	2.12	6.1	533	23
HD 2952	K0III	5.93	1.04	+0.44	2.54	12.02	+0.00	4844	2.67	1.6	311.6	13
HD 5583	K0	7.60	0.94	+0.65	1.01	9.09	−0.50	4830	2.53	5.78	139.35	17
HD 5608	K0III–IV	5.99	1.00	+2.11	1.55	5.50	+0.06	4854	3.03	1.4	792.6	5
HD 11343	K2III–IV	7.88	1.08	+1.80	1.17	7.83	−0.15	4670	2.7	5.5	1560.2	24
HD 13189	K2II	7.57	1.47	−3.80	4.50	50.39	−0.58	4365	1.74	14.0	471.6	25
HD 17092	K0III	7.73	1.25	+0.80	2.30	10.90	+0.22	4650	3.0	4.6	359.9	26
HD 24064	K0	6.75	1.51	−0.40	1.00	38.0	−0.49	4053	1.44	9.4	535.6	1
HD 28305	K0III	3.53	1.01	+0.15	2.70	13.70	+0.17	4901	2.64	7.6	594.9	27
HD 29139 a (Aldebaran)	K5III	0.85	1.52	−0.65	1.13	45.1	−0.27	4055	1.2	6.47	628.96	28
HD 32518 b	K1III	6.44	1.11	+1.08	1.13	10.22	−0.15	4580	2.10	3.04	157.54	29
HD 40956	K0	6.58	1.01	+1.20	2.00	8.56	+0.14	4869	3.02	2.7	578.6	30
HD 44385	K0	6.77	1.27	−0.10	1.80	19.50	+0.10	4440	2.0	5.9	473.5	31
HD 54719	K2III	4.41	1.26	−0.56	2.30	26.80	+0.14	4388	1.96	20.6	305.5	32
HD 59686	K2III	5.45	1.13	+0.52	1.90	13.20	+0.15	4658	2.49	6.92	299.36	33
HD 62509	K0III	1.14	1.00	+1.08	1.70	8.80	−0.07	4850	2.96	2.3	589.64	34
HD 66141	K2III	4.39	1.26	−0.15	1.10	21.40	−0.32	4323	1.92	6.0	480.5	35
HD 69267	K4III	3.52	1.48	−1.30	1.70	47.20	−0.29	4092	1.4	7.8	605.2	36
HD 73108 b (4 UMa)	K1III	5.79	1.20	+0.15	1.23	18.11	−0.25	4415	1.80	7.1	269.3	37
HD 76920	K1III	7.80	1.11	+1.47	1.17	7.47	−0.11	4968	2.94	3.93	415.4	38
HD 81688	K0III–IV	5.40	0.99	+0.57	2.10	13.00	−0.36	4753	2.22	2.7	184.02	16
HD 85503	K2III	3.88	1.22	+1.00	1.50	11.40	+0.36	4538	2.4	2.4	357.8	36
HD 86950	K1III	7.46	1.09	+1.30	1.66	8.80	+0.04	4805	2.66	3.6	1270	39
HD 95127	K0	8.15	1.28	+0.80	1.20	20.00	−0.18	4218	1.78	5.01	482	22
HD 96127	K2III	7.43	1.50	−1.23	0.91	35.00	−0.24	4152	2.06	4.0	647.3	20
HD 97619	K0	7.04	1.32	+0.20	1.30	19.50	−0.07	4355	2.33	3.5	665.9	31
HD 104358	K0III	7.77	1.14	⋯	1.27	7.40	+0.08	4631	2.80	69.3	281.1	40
HD 106574	K2III	5.88	1.18	+0.10	1.20	20.40	−0.43	4501	2.18	8.5	1065.7	31
HD 111591	K0III	6.59	1.00	+1.40	1.94	8.03	+0.07	4884	3.10	4.4	1056.4	30
HD 113996	K5III	4.92	1.48	−0.10	1.49	25.11	+0.13	4181	1.86	6.3	610.2	30
HD 117253	K0III	6.75	1.00	+1.10	2.50	8.93	+0.16	5000	2.9	6.0	1084.5	41
HD 118904	K2III	5.67	1.22	+0.40	1.50	14.80	−0.11	4469	2.13	3.1	676.7	31
HD 120457	K1III	6.44	0.99	+1.20	2.41	8.69	+0.15	4985	2.85	11.1	2556.5	42
HD 122430 a	K3III	5.50	1.33	−0.20	1.68	22.90	−0.09	4300	2.0	2.1	455.1	43
										3.71	344	44
HD 131873	K4III	2.08	1.47	−0.90	1.40	38.30	−0.27	4126	1.5	6.1	522.3	36
HD 133086	K0	6.83	0.99	+0.95	1.80	9.90	−0.03	4847	2.57	1.5	93.4	1
HD 135760	K1III	7.05	1.05	+2.20	1.74	5.77	+0.20	4850	3.1	2.4	822.3	24
HD 136512	K0III	5.51	1.02	+0.84	2.13	10.50	−0.29	4749	2.34	1.5	187.83	5
HD 136726 b (11 UMi)	K4III	5.02	1.40	−0.37	1.80	24.08	+0.04	4340	1.60	10.50	516.22	29
HD 137759	K2III	3.29	1.17	+0.81	1.05	12.8	+0.15	4445	1.15	8.82	510.72	45
HD 139357 b	K4III	5.98	1.20	+0.61	1.35	11.47	−0.13	4700	2.90	9.76	1125.7	46
HD 142091	K0III–IV	4.79	0.99	+2.29	1.51	5.00	+0.10	4877	3.21	1.6	1251	5
HD 143107	K2III	4.14	1.23	+0.00	1.70	21.00	−0.32	4406	1.94	6.7	417.9	47
HD 145457	K0III	6.57	1.04	+0.97	1.90	9.90	−0.14	4757	2.77	2.9	176.3	48
HD 145934	K0	8.50	1.05	+0.00	1.75	5.38	⋯	⋯	3.23	2.28	2730	49
HD 155233	K1III	6.81	1.03	+2.40	1.50	5.03	+0.10	4845	3.21	2.0	885	24,40
HD 158996	K5III	5.80	1.50	−1.50	1.80	50.30	−0.20	4069	1.2	14.0	820.2	50
HD 164058 a (γ Dra)	K5III	2.23	1.53	−1.93	2.14	50.03	−0.14	3930	1.55	10.7	702.47	51
HD 164428	K5	6.39	1.45	−0.80	1.50	35.40	−0.07	4119	1.62	5.7	599.6	31
HD 170693 a , b (42 Dra)	K1.5III	4.83	1.19	−0.09	0.98	22.03	−0.46	4200	1.71	3.88	479.1	46
HD 175370	K2III	7.19	1.27	+0.02	1.02	23.50	−0.52	4301	1.70	4.6	349.5	52
HD 180314	K0	6.61	1.00	+0.93	2.60	9.20	+0.20	4917	2.98	22.0	396.03	48
HD 181342	K0III	7.55	1.02	+2.30	1.89	5.12	+0.20	5040	3.3	2.9	562.1	24
HD 186641	K0	7.34	1.00	+2.20	1.93	5.34	+0.29	5020	3.26	20.0	1058.8	53
HD 202432	K2	7.05	1.21	+1.00	1.20	11.10	+0.16	4549	2.42	1.9	418.8	31
HD 203949	K2III	5.64	1.19	+1.10	2.12	10.07	+0.31	4780	2.94	8.2	184.2	10,54
HD 205478	K1III	3.74	0.99	+2.02	1.61	5.81	+0.18	4860	3.12	2.4	417.4	55
HD 207229	K1III	5.62	1.02	+0.50	2.42	11.60	+0.00	4890	3.2	1.98	144.3	53
HD 208897	K0	6.51	1.01	+2.46	1.25	4.98	+0.21	4860	3.13	1.4	352.7	56
HD 210702	K0III/K1IV	5.93	0.95	+2.14	1.68	5.10	+0.01	4967	3.19	1.9	354.8	5
HD 216536	K0	9.23	1.19	⋯	1.36	12.50	−0.17	4639	2.36	1.47	148.6	22
HD 219415	K0III	8.94	1.00	⋯	1.00	2.90	−0.04	4820	3.51	1.0	2093.3	19
HD 219449	K0III	4.24	1.11	+0.93	1.40	11.00	−0.03	4665	2.52	3.2	181.4	32
HD 221345	K0III	5.22	1.03	+0.67	2.20	11.00	−0.24	4813	2.63	4.8	185.84	6
HD 222076	K0III	7.48	1.03	+2.87	1.07	4.14	+0.05	4806	3.31	1.56	871	39
HD 233604	K5	10.4	1.01	⋯	1.50	10.90	−0.36	4791	2.55	6.58	192	18
HD 238914	K7	8.79	1.02	+3.10	1.47	12.73	−0.25	4769	2.37	6.0	4100	57
HD 240210 c	K3III	8.33	1.65	+2.60	0.82	10.50	−0.18	4297	2.31	5.21	501.75	58,59
HD 240237	K2III	8.19	1.68	+0.00	1.69	32.00	−0.26	4361	2.49	5.3	745.7	20
SAND 364	K3III	9.80	1.36	⋯	1.35	21.80	−0.02	4284	2.20	1.54	121.71	60
SAND 978	K4	9.71	1.37	+0.00	1.37	⋯	⋯	4200	1.80	2.18	511.21	61
TYC 3318-1333-1	KIII	9.90	1.23	⋯	1.19	5.90	−0.06	4776	2.97	3.42	562	57
TYC 3667-1280-1	K1	9.86	1.00	+0.99	1.87	6.26	−0.08	5130	3.11	5.4	26.47	62
TYC 4282-605-1	K	10.58	1.16	+1.35	0.97	16.21	−0.07	4300	2.0	10.78	101.54	63
G/K giants with multiple planets (1 host star)
HD 138905	G8.5III/K0III	3.91	1.01	+0.45	1.47	11.10	−0.30	4822	2.56	1.02	415.2	64
										4.58	964.6	64
K giants with multiple planets (11 host stars)
BD+20 2457	K2II	9.75	1.25	+3.20	2.80	49.00	−1.00	4137	1.51	21.42	379.63	58
										12.47	621.99	58
HD 6805	K1III	3.46	1.16	+0.68	1.70	14.30	+0.12	4529	2.36	2.60	407	65
										3.30	740	65
HD 33844	K0III	7.29	1.04	⋯	1.78	5.29	+0.27	4861	3.24	1.96	551.4	66
										1.75	916	66
HD 47366	K1III	6.11	0.99	+1.51	1.81	7.30	−0.02	4866	2.97	1.75	363.3	67,68
										1.86	684.7	67,68
HD 47536 d	K0III	5.25	1.18	−0.17	0.98	23.47	−0.68	4380	1.72	5.00	430	69
										7.00	2500	69
							−0.61	4352	2.10	4.00	434.9	43
HD 89484 d	K0III	2.01	1.13	−0.92	1.23	31.88	−0.51	4330	1.59	8.78	428.5	70
										2.14	1340.	70
HD 102272	K0	8.69	1.02	+0.90	1.9	10.1	−0.26	4908	3.07	5.9	127.58	71
										2.6	520	71
HD 110014 d	K2III	4.66	1.24	−0.11	2.09	20.90	+0.14	4702	2.53	10.70	882.6	43
										3.10	130.0	43
					2.17		+0.19			11.10	835.47	72
HD 121056	K0III	6.17	1.01	+2.10	1.63	5.92	+0.00	4890	3.15	1.38	88.9	53
										5.98	2131.8	53
HD 163917	K0III	3.32	0.99	−0.19	2.70	14.62	+0.06	4886	2.56	22.20	530.02	73
										24.67	3183	73
TYC 1422-614-1	K2	10.21	0.95	+0.81	1.15	6.85	−0.20	4806	2.85	2.51	198.44	74
										10.10	569.2	74

Notes.

^a Stars with a questionable planet. ^b Stars of our TLS sample (green symbols in Figures 1, 3, 4). ^c Three possible two-planet solutions found in (65). ^d Stars with a questionable second planet.

References. (1) Lee et al. (2015), (2) Soto et al. (2015), (3) Setiawan et al. (2005), (4) Wang et al. (2014), (5) Sato et al. (2012), (6) Sato et al. (2008b), (7) Omiya et al. (2012), (8) Sato et al. (2003), (9) Liu et al. (2008), (10) Jones et al. (2011), (11) Jones et al. (2013), (12) Omiya et al. (2009), (13) Sato et al. (2013), (14) Liu et al. (2009), (15) Wang et al. (2012), (16) Sato et al. (2008a), (17) Niedzielski et al. (2016a), (18) Nowak et al. (2013), (19) Gettel et al. (2012b), (20) Gettel et al. (2012a), (21) Adamów et al. (2012); (22) Niedzielski et al. (2015b), (23) Moutou et al. (2011), (24) Jones et al. (2016), (25) Hatzes et al. (2005), (26) Niedzielski et al. (2007), (27) Sato et al. (2007), (28) Hatzes et al. (2015), (29) Döllinger et al. (2009b), (30) Jeong et al. (2018b), (31) Jeong et al. (2018a), (32) Mitchell et al. (2013), (33) Ortiz et al. (2016), (34) Hatzes et al. (2006), (35) Lee et al. (2012b), (36) Lee et al. (2014), (37) Döllinger et al. (2007), (38) Wittenmyer et al. (2017a), (39) Wittenmyer et al. (2017b), (40) Wittenmyer et al. (2016a), (41) Jones et al. (2015b), (42) Jones et al. (2017), (43) Soto et al. (2015), (44) Setiawan et al. (2004), (45) Frink et al. (2002), (46) Döllinger et al. (2009a), (47) Lee et al. (2012a), (48) Sato et al. (2010), (49) Feng et al. (2015); (50) Bang et al. (2018), (51) Hatzes et al. (2018), (52) Hrudková et al. (2017); (53) Jones et al. (2015a), (54) Jones et al. (2014), (55) Ramm et al. (2016), (56) Yılmaz et al. (2017); (57) Adamów et al. (2018); (58) Niedzielski et al. (2009b), (59) Rozenkiewicz et al. (2011), (60) Brucalassi et al. (2014), (61) Brucalassi et al. (2017), (62) Niedzielski et al. (2016b), (63) González-Álvarez et al. (2017); (64) Takarada et al. (2018), (65) Trifonov et al. (2014), (66) Wittenmyer et al. (2016b), (67) Sato et al. (2016), (68) Marshall et al. (2019), (69) Setiawan et al. (2003a), (70) Han et al. (2010), (71) Niedzielski et al. (2009a), (72) de Medeiros et al. (2009); (73) Quirrenbach et al. (2019); (74) Niedzielski et al. (2015a).

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Checking the orbital periods of the purported planets around K giants in the literature shows a conspicuous accumulation of identical or at least very similar values, especially beyond a certain stellar radius.

This impression intensifies considering the orbital period as a function of the stellar radius, as shown in Figure 1. Obviously, planetary companions around giant stars with radii smaller than 21 R_⊙ (vertical long-dashed line) demonstrate a large selection of orbital periods. In contrast, apart from four outliers (SAND 364 b, HD 47536c, HD 89484c, and HD 158996b), there are no relatively short-period (≤300 days) and long-period (≥800 days) planets orbiting larger stars. Particularly, the second planets in the HD 47536 and HD 89484 systems are rather questionable. For the former, Soto et al. (2015) did not find any evidence for its existence and for the latter, Han et al. (2010) stated that "it is still premature to firmly establish the reality and cause" of this signal. They also noted that it may be due to stellar rotation. The other two outliers lie very close to the boundaries: HD 158996b with an orbital period of 820.2 days marginally outside the range of 300–800 days and SAND 364 with a stellar radius of 21.8 R_⊙ slightly above our radius dividing line. Thus, exoplanets around K giants have similar orbital periods above a certain stellar radius. This preliminary result and the detection of RV amplitude variations of more extended K-giant host stars could be a first hint for a new phenomenon which preferably takes place in stars with radii larger than ∼21 R_⊙.

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In order to get a first impression of how many of our 62 TLS sample stars could experience this concerned phenomenon, we show a histogram of the stellar radii in Figure 2. The median is 15 R_⊙ and 18 stars have a radius of ≳21 R_⊙. Thus, about 30% of the TLS targets are within a region of the stellar radius where things become interesting due to the possible presence of an unknown phenomenon which is able to mimic robust planet detections. Furthermore, 13 stars of our survey are included as TLS planet candidates in Figure 1 (green open squares). Six out of these 13 stars show RV variations of ∼500 days and their host stars have radii of ≥21 R_⊙. This suggests that their RV variability is possibly caused by a new phenomenon identical or maybe similar to that of 42 Dra and γ Dra.

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Our long-term RV data, especially for host stars with larger radii, reveal hints for an unidentified phenomenon indicated by amplitude variations, which is able to mimic a robust planet signal over several years. Due to this fact, we guess that not all of the published planets of K giants are truly planets. If that is true, than the occurrence rate of extrasolar planets around K giants would be reduced and would be more similar to the occurrence rate of planets around their progenitor MS F-type stars and around solar-like stars.

To confirm our hypothesis derived from our radius–period plot, we further investigate the content of Table 1, which summarizes the crucial features of published extrasolar planets and their G- and K-giant host stars. In fact, about 30% of the published planets around K-giant stars have hosts with radii larger than 21 R_⊙ and can thus be affected by the new phenomenon. The planet frequency would be significantly decreased if all or at least a large fraction of these planets were false positives. This way, the large scatter of the planet frequency of evolved stars in the literature (9%–26%) and the difference compared to their progenitor MS F-type stars (4%, Hartmann 2019) as well as to the solar-like stars (4%–5%, e.g., Cumming et al. 2008) would be resolved.

The investigation of the entries of Table 1 reveals the further interesting points:

• G–K giants in single-planet systems: It is striking that the total number of substellar companions around G giants is more restricted than around K giants. This is possibly a bias effect because there are more planet-search surveys monitoring K giants than G giants. The aforementioned deficit of relatively short-period (≤300 days) and long-period (≥800 days) planets orbiting larger K-giant stars is also valid for the larger G giants, although only three of the G-giant host stars (HD 11755, HD 107383, and HD 119445) have a radius near or above the critical stellar radius of 21 R_⊙. Their orbital periods are in the critical range between 300–800 days and two of them (HD 11755 and HD 107383) additionally show high negative values for the stellar metallicity. This conspicuity might be a hint for the pretence of a real planet. HD 107383 and HD 119445 are listed as brown-dwarf candidate host stars. The low number of known planet-hosting G giants in general and the ambiguous classification of the spectral type in at least four cases is a problem for the statistics. Nevertheless, we are convinced that the host star identity itself (e.g., stellar radius), implying a different evolutionary stage, is the reason for the planet deficit in some regions of the radius–period diagram. Consequently, we suggest to discriminate between G and K giants before deducing conclusions.
• G–K giants in multiple-planet systems: The number of planets orbiting giant stars of both spectral types in multiple-planet systems is very limited, with 11 planet systems around K giants and only 1 system around a G giant, whose spectral type is even indistinguishable between G and K. Moreover, the second planet in two of these systems (HD 47536 and HD 110014) is questionable. Interestingly, ∼30% of the single- and multiple-planet systems around K giants have host stars with a stellar radius above 21 R_⊙, orbital periods between 300 and 800 days for at least one planetary companion, and in addition, show strong negative values for the metal content. These findings and the fact that a large fraction of multiple-planet systems around giants are dynamically challenging in terms of stability, can indicate the phenomenon of the active production of problematic multiple-planet systems by mimicking at least one fake planet. Consequently, an individual check of each multiple-planet system is necessary to prove whether one of the planetary signals could be caused by intrinsic stellar features.
• Metallicity of the host star: The metallicity of the host star is the second key issue when comparing planetary companions around MS stars and planets orbiting evolved stars. In other words, does the planet–metallicity correlation hold for G and especially K giants? While some studies find a strong positive correlation (e.g., Reffert et al. 2015), exoplanets around our K giants do not show any preference for metal-rich stars (Pasquini et al. 2007; Döllinger 2008). The latter is also supported when considering all published planets around giant stars (see Table 1). The missing planet–metallicity correlation of G and K giants is in contrast to planet-hosting solar-type MS stars (e.g., Santos et al. 2004; Fischer & Valenti 2005), to subgiants showing a weaker relation (e.g., Johnson et al. 2010b), and to giant stars more massive than 1.5 M_⊙ (Maldonado et al. 2013). The debate is still controversial and has almost become a question of faith. A conclusion is not yet in sight.
• Existence of brown dwarfs: Table 1 also shows that brown dwarfs are not uncommon around giant stars. Our Tautenburg planet-search survey indicates the presence of two brown-dwarf candidates. Finding two brown dwarfs in a sample of 62 K giants (3%) is considerably higher than what one would expect from surveys of solar-like MS stars (≤1%; Wittenmyer et al. 2009) and supports the statement that "brown dwarfs are not quite so rare around the more massive, evolved stars of the giant surveys ..." (Mitchell et al. 2013). However, according to a new definition of giant planets (masses between 0.3–60 M_Jup) and brown dwarfs (masses between 60–80 M_Jup) by Hatzes & Rauer (2015), one of our candidates lies exactly at the transition of both populations and might be also a giant planet. Considering the original definition of brown dwarfs (13–80 M_Jup, Burrows et al. 2001), there are 12 brown dwarfs listed in Table 1 (10 single ones and 1 double system). The brown-dwarf candidates orbiting the G-giant stars HD 107383, HD 119445, and HD 175679 would be redefined as high-mass planets using the modified definition from Hatzes & Rauer (2015), as is the case for the BDs around the K giants HD 13189, HD 54719, HD 158996, HD 180314, HD 186641, BD+202457, and the double system HD 163917. Thus, only the companion around HD 104358 would keep its brown-dwarf status.

The results of Table 1 and Figure 1 show that the confirmation of extrasolar planets around K giants, especially with stellar radii larger than ∼21 R_⊙, is very tricky. In addition, a low stellar metallicity might be a further hint for a suspicious planet hypothesis, as the host stars of the doubtful planets around 42 Dra, γ Dra, Aldebaran, and HD 122430 feature subsolar metallicities. In our opinion, the aforementioned differences in the planet occurrence rate and the planet–metallicity correlation between evolved and MS stars are two discrepancies, representing two sides of the same coin, namely that highly evolved K giants might mimic real planets over a long time span. Thus, it is essential to think about the concurrent intrinsic changes in K-giant stars, happening in enlarged stars (e.g., larger convective envelope), as well as their consequences for the validity of the standard tools of planet confirmation and necessity to adjust them (e.g., development of more stringent planet detection criteria).

Our first hypothesis is that the different occurrence rates observed in K giants compared to MS G- and F-type stars are most likely caused by fake planets. Host stars showing both a large radius and a subsolar metallicity possibly indicate a fake planet system. The identity of the host star (stellar characteristic) is thus maybe even more effective for the confirmation of a planetary companion than the standard planet criteria (i.e., the absence of the RV period in the Hipparcos photometry, Hα, and bisector data, etc.).

Our second guess deals with the partial lack of the planet–metallicity relation noticed for K-giant stars, depending on the stellar mass. The difference is possibly caused by the following reasons:

• 1.  
  the selection of more metal-rich stars with smaller radii because RV surveys searching for planets around giants apply mostly target selection criteria to minimize intrinsic stellar jitter (B − V < 1.2, see Figure 3 from Hekker et al. 2006) because these stars show smaller RV variations in contrast to redder K-giant stars, which demonstrate larger RV dispersions;
• 2.  
  the nonuniform calculation of the stellar abundances due to different methods and line lists;
• 3.  
  the inclusion of fake planets.

Most of the planet-search surveys have tried to optimize their observing strategy by cutting off the color index as well as by choosing targets with higher brightness. These restrictions should both reduce the intrinsic stellar jitter and make the observations efficient (short exposure times). However, excluding metal-poor targets with larger radii can easily lead to biased star samples and results. On the other hand, favoring metal-rich stars with smaller radii guarantees that the Fischer–Valenti correlation is valid and that more evolved stars with larger radii are not included. The consequence is a very restricted star sample, which is located in the "comfort zone." Thus, we are convinced that the different sample selection criteria possibly deliver an explanation for the contrary results (i.e., different planet occurrence rates, (in)valid planet–metallicity correlation). This consideration became obvious to us when investigating the stellar and orbital parameters of the published and unpublished evolved planet-hosting stars to find reasons for the different percentages of the planet frequency. It is also supported by the statement that "since the sample selection criteria might have a significant influence on the correlation between companion frequency and metallicity in addition to the not having enough giants known so far, it would be too premature to reach a conclusion" (Lee et al. 2012a).

To verify our statement about biased samples through target selection criteria, we summarize the conditions, look at them in detail and explain their consequences for the properties of the selected stars (e.g., stellar mass, radius, and metal content).

The reference are the target stars of our Tautenburg planet-search survey and its selection criteria. This sample consists of 62 K giants that were selected to be well distributed in the sky in R.A. and with decl. ≳+45°. This ensured that the targets were accessible throughout the year from Tautenburg which resulted in a good temporal sampling.

The location of our planet-hosting stars in a color–magnitude diagram (CMD) is shown in Figure 3 (green symbols in panel (a)). These stars sample the red clump and early asymptotic giant branch regions of the CMD well, as well as a significant fraction of the first-ascent red-giant branch.

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Our Tautenburg sample does not suffer from a cutoff in the B − V color, resulting in an unbiased sample. This is essential to deduce general conclusions. However, a systematic literature search identified only two further RV surveys without or with a less-restricted cutoff in the upper B − V color: the southern FEROS program (Setiawan et al. 2003a, 2003b) containing G and K giants and the SENS (Search for Exoplanet around Northern circumpolar Stars; 0.6 < B − V < 1.6) survey monitoring dwarfs, giants, and unclassified stars (Lee et al. 2015) since 2010, respectively. In contrast, the majority of the surveys searching for exoplanets around giants (e.g., Sato et al. 2005) and subgiants (e.g., Johnson et al. 2006) are biased because of a B − V cutoff which is a double-edged sword. On the one hand, minimizing the intrinsic stellar jitter (e.g., B − V ≤ 1.2) is a common effective measure to exclude problematical cases (e.g., M giants) to make planet detections easier; on the other hand, this restriction has a profound impact on the properties of the selected stars and results. The conclusions derived from this will likely be wrong (biased) because there is only a limited view available and it is not possible to see the whole picture.

To investigate how the B − V cutoff as a target selection criterion influences the properties of the target stars and ultimately those of the planet-hosting stars and their planetary companions, we show how several stellar properties of planet-hosting stars depend on the B − V color (Figure 3). In all panels, an accumulation of K giants at B − V ∼ 1.0 is visible that is most likely due to target selection (B − V cutoff, biased samples). The stars of the unbiased samples are more or less evenly distributed over the whole range (0.8 ≤ B − V ≤ 1.7). Moreover, panels (b)–(f) show the following features:

• (b)  
  General trend: T_eff drops with B − V color. In detail, the stars of the biased samples have T_eff ≥ 4700 K, while the stars of the unbiased samples show decreasing T_eff values from 5000 to 4000 K. The TLS planet host stars and host candidates follow this trend. The doubtful planet host stars are restricted to B − V ≥ 1.2 and T_eff ≤ 4300 K. Moreover, the G giants are well separated in a small area at B − V ≤ 1.05 and T_eff ≥ 4700 K (with one exception).
• (c)  
  General trend: log g drops with B − V color. In detail, the stars of the biased samples have log g between 2.2 and 3.6, while the stars of the unbiased samples show decreasing log g values from 3.6 to 1.2. Again, the TLS planet host stars and host candidates follow this trend. The doubtful planet host stars are restricted to B − V ≥ 1.2 and $1.2\leqslant \mathrm{log}g\leqslant 2.0$. The G giants are well separated in a small area at B − V ≤ 1.05 and $2.0\leqslant \mathrm{log}g\leqslant 3.0$ (with one exception).
• (d)  
  General trend: [Fe/H] shows no clear trend with B − V color. In detail, the stars of the biased samples have [Fe/H] values between −0.4 and +0.3 (with the most densely populated area at −0.1 ≤ [Fe/H] ≤ +0.3), while the stars of the unbiased samples show a wider range of [Fe/H] values (−1.0 ≤ [Fe/H] ≤ +0.4). For B − V ≥ 1.3, there are almost no stars with [Fe/H] ≥ 0.0. The host stars of our TLS planets and planet candidates, as members of an unbiased sample, lie in the central part of this range, almost all have [Fe/H] ≤ 0.0 and their median metallicity is [Fe/H] = −0.16. On the other hand, all other K-giant host stars have a median metallicity of [Fe/H] = −0.07. When taking into account only the K-giant host stars with 0.9 ≤ B − V ≤ 1.2, as is the case in the biased samples, then the median metallicity is even higher ([Fe/H] = 0.00). Thus, there is a preference of higher metallicities in the biased samples compared to the unbiased samples. The doubtful planet host stars have [Fe/H] ≤ 0.0 as well. The G giants at B − V ≤ 1.05 are preferentially more metal poor with values of −0.6 ≤ [Fe/H] ≤ +0.2 than K giants in this B − V region.
• (e)  
  General trend: stellar mass shows no clear trend with B − V color. In detail, the stars of the biased samples have M_⋆ between 1.4–2.8 M_⊙. Toward higher B − V colors, the stars of the unbiased samples are slightly less massive (0.8–2.4 M_⊙). The TLS planet host stars and host candidates are concentrated between 1.0–1.8 M_⊙. Two of the four doubtful planet host stars (γ Dra and HD 122430) have masses M_⋆ > 1.6 M_⊙. The G giants at B − V ≤ 1.05 cover stellar masses from 1.2–4.0 M_⊙.
• (f)  
  General trend: stellar radius is rising steadily with B − V color. In detail, the stars of the biased samples have R_⋆ between 4–14 R_⊙, while the stars of the unbiased samples show increasing R_⋆ up to ∼50 R_⊙. The TLS planet host stars and host candidates follow this trend as well. The doubtful planet host stars have radii of more than 21 R_⊙. The G giants at B − V ≤ 1.05 cover stellar radii from 8–21 M_⊙.

The investigation of the dependencies of the aforementioned stellar parameters of planet-hosting giant stars on the B − V color points point directly to a particularly important dependency in the radius–metallicity diagram (Figure 4). There are several structural features in the plot which will be interpreted in the following. The most obvious is a well-populated area at 4 R_⊙ ≤ R_⋆ ≤ 14 R_⊙ and −0.4 ≤ [Fe/H] ≤ +0.4, containing the majority of the published G and K giant host stars (corresponding to the biased samples). For R_⋆ > 14 R_⊙, the points are less densely distributed because they arise from the very few unbiased surveys. Furthermore, the metallicity decreases linearly with increasing stellar radius. This effect can only be seen when avoiding a B − V cutoff at 1.2 or less, i.e., when considering a large B − V range (0.8 ≤ B − V ≤ 1.7), hence a large radius range (4 R_⊙ ≤ R_⋆ ≤ 50 R_⊙).

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In summary, the doubtful planet host stars have radii larger than ∼21 R_⊙, metallicities ≤0.0, and B − V colors ≥1.2. These problematic cases will be missed in all planet surveys applying such a B − V cutoff.

Considering the stellar radius together with the orbital periods of the planetary companions reveals a puzzle for planet hunting around evolved stars larger than ∼21 R_⊙.

• 1.  
  Where are the long-period planets (P ≥ 800 days)?
• 2.  
  Where are the short-period planets (P ≤ 300 days)?
• 3.  
  Are the planets in between real?

In finding a solution for this issue, the stellar radius seems to play a key role. Stars larger than ∼21 R_⊙ have reached a late evolutionary stage. Consequently, they possess extended atmospheres and deep convection zones that can cause intrinsic stellar variability. Because very little is known about such activity in giant stars and their consequences for RV measurements, planet hunters might be fooled when attributing RV variations to planetary companions. So far, it has been enough to confirm purported planets excluding known stellar variability (e.g., rotational modulation, pulsations, etc.) by analyzing common activity indicators (e.g., Hα) and verifying a long-lived and coherent RV signal. This procedure was sufficient until the investigations of the RV variations in 42 Dra, γ Dra, and Aldebaran showed that the standard tools of planet confirmation have failed. At this point, one should question the validity of any activity indicator.

Moreover, ∼30% of the planetary systems around K giants have hosts with a stellar radius above 21 R_⊙ (orbital periods between 300 and 800 days) and many of them show negative metallicity values. Could these similar orbital periods, low metallicities, and variations of the RV amplitudes be the result of a new phenomenon, preferably taking place in stars above ∼21 R_⊙, masquerading false planets? Then, the puzzle seems to be much more complex than previously thought, including unknown stellar variability as well as stellar (e.g., radius and metallicity) and orbital (e.g., period) parameters. The origin of this new phenomenon is unknown, and we do not know how the common planet earmarks are influenced. As a consequence, there is not only a need for a stringent set of criteria for exoplanets but also for more understanding of the theory of giant stars, especially for highly evolved ones.

In summary, we can classify possible phenomena mimicking exoplanets as follows:

• 1.  
  Known knowns:

  • (a)  
    Surface structure (e.g., spots, plages).
  • (b)  
    Convection pattern.
  • (c)  
    Radial oscillations.
• 2.  
  Known unknowns:

  • (a)  
    Nonradial oscillations.
• 3.  
  Unknown unknowns:

  • (a)  
    Velocity spots?
  • (b)  
    New form of oscillations?
  • (c)  
    Other new phenomena?

One explanation for the unknown phenomena introducing RV variations in K giants might be the relation to oscillatory convection modes, i.e., nonadiabatic g-modes in luminous red giants. It has been suggested by Saio et al. (2015) that these modes are linked to the long secondary periods that occur in so-called long-period variables, a class of stars pulsating with periods of several hundred days (M giants, Mira variables, etc.). Another striking fact is that typical rotation periods of K giants fall exactly in this range of orbital periods. Therefore, any RV period that can be connected to the rotation period of the star should be taken with extreme caution.

The favored lower metallicities, which occur only in unbiased samples without B − V cutoff, might also be a hint of false planets. Maldonado et al. (2015) analyzed the stellar metallicity as a function of the stellar radius. Our study supports their indication of a "very mild trend of decreasing metallicities with increasing stellar radius for GWPs (giants with planets) with M ≤ 1.5 M_⊙," although they are not quite convinced about this trend. Considering giants above 1.5 M_⊙, Maldonado et al. (2015) do not find any correlation between metallicity and radius at all.

The reasoning above vividly shows the Gordian Knot of exoplanets around K giants: first, the validity of the planet–metallicity correlation, and second, the different planet occurrence rates of MS and evolved giant stars. For solar-like stars, the planet–metallicity correlation is well known, i.e., the higher the metallicity of a star, the higher the probability of hosting a giant planet (Fischer–Valenti relation, Santos et al. 2004; Fischer & Valenti 2005). However, for subgiants and giants, this effect is either weaker (e.g., Johnson et al. 2010b) or only seen for stars more massive than 1.5 M_⊙ (Reffert et al. 2015), but not for stars below 1.5 M_⊙ (Maldonado et al. 2013).

The proposed underlying process is that high metallicity induces more solid material and therefore enhances planet formation (Fischer & Valenti 2005). Alternatively, in the so-called pollution hypothesis, the high metallicity could also be the result of late-stage accretion of gas-depleted material onto the star (Gonzalez 1997; Laughlin & Adams 1997). In the first case, the planet-hosting stars should be metal rich throughout; in the latter case, only the stellar convective zone should be enriched in metals, but not the subjacent layers. In fully convective giants, however, this enhancement will be diluted due to mixing with deeper layers. The fact that a decreasing trend with increasing stellar radius is visible in the metallicity, i.e., a decreasing strength of the planet–metallicity correlation with increasing stellar radius, argues for the second case.

Assuming that most of the planets with periods of 300–800 days and host stars with lower metallicities are indeed not real, the planet fraction of giants with subsolar metallicity might be overestimated and the Fischer–Valenti relation could become valid for giant stars below 1.5 M_⊙.

Concerning the lack of planets below ∼300 days and above ∼800 days for giant stars exceeding a radius of ∼21 R_⊙, several explanations are possible.

One could argue that the larger stars show higher intrinsic stellar variability, which makes the detection of corresponding RV signals more difficult. While this might be the case for planets with very long orbital periods, where the RV amplitudes are smaller and comparable to the RV scatter caused by intrinsic stellar variability, this argument does not hold for the shorter-period planets. One may also think of orbital evolution during the giant phase to explain the absent long-period orbits (e.g., orbital decay). The quantitative analysis, however, is beyond the scope of this paper.

Another plausible point for the missing planets below ∼300 days could be that a significant fraction of the monitored stars has already reached the first ascent (first dredge-up) in their evolution, resulting in the engulfment of existing planets within ∼1 au.

Beside these rationale, one may simply speculate that there are no planets above a certain radius threshold (∼21 R_⊙). This implication has not been obvious to the majority of the exoplanet community because their RV surveys suffer from the B − V cutoff and so their targets lack the larger radii.

The mentioned B − V cutoff has an impact on further stellar parameters of the observed samples compared to the unbiased samples, as discussed in Section 5. Applying this cap, the target stars show preferences in higher effective temperatures (T_eff ≥ 4700 K), higher surface gravities (2.2 ≤ log g ≤ 3.6), higher metallicities (−0.1 ≤ [Fe/H] ≤ +0.3), and slightly higher masses (1.4 M_⊙ ≤ M_⋆ ≤ 2.8 M_⊙). Because of the nearly linear dependence between stellar radius and B − V color, there is the same behavior in the radius–period and color–period diagram. Thus, the B − V color cutoff also yields a bias in the observed orbital periods of the planets, introducing biases to all statistical analyses based on these parameters.

Henceforth, one should question the consequences of the commonly used selection criteria. Restricting a sample to the brightest giant stars will favor stars with larger radii, which are on average more metal poor and older considering a typical mass range (1–2 M_⊙). Applying a B − V cutoff to avoid intrinsic RV variability to make planet detections easier, one designs the sample throwing out stars with larger radii and lower metallicities, as shown in Figures 3(d) and (f). Therefore, it is not surprising that these samples contain planet host stars that are more metal rich and more massive, supporting general relations, such as the planet–metallicity correlation or the increasing planet fraction with increasing stellar mass.

In contrast, a star sample not limited in B − V leads to problematic cases, where planetlike RV signals turn out to be due to other stellar phenomena. It is troubling for planet hunters that these signals can initially be attributed to planetary companions because these stars show no variations in the common activity indicators. The periodic signals seem to be long lived, but may suddenly weaken or disappear and come back at the same phase as before or even with a phase shift (e.g., 42 Dra, γ Dra, Aldebaran). These characteristics only become apparent after many years of continuously monitoring and may be missed when observing stars only for a short period of time (e.g., one orbit).

To find these suspicious stars mimicking bona fide planets, the "host" star identity (mass, radius, metallicity, etc.) should be given more importance. Exploring these parameters for the aforementioned doubtful planet host stars, it became obvious that they have large radii (R_⋆ ≳ 21 R_⊙), low metallicities ([Fe/H] < 0.0), low effective temperatures (T_eff ≲ 4300 K), and low surface gravities (log g ≲ 2.0). On this basis, we suggest to use these parameters with their thresholds as criteria, for which the planet hypothesis to explain an RV signal should be considered with the highest caution because K giants hosting bona fide planets might turn into K giants hosting fake planets in this regard.

We thank the anonymous referee for the very careful review of the manuscript and all the valuable suggestions. We also thank William D. Cochran and Artie P. Hatzes for useful comments. We acknowledge the support of the DFG priority program SPP 1992 "Exploring the Diversity of Extrasolar Planets (DO 2106/1-1)." We are grateful to the user support group of the Alfred Jensch Telescope: M. Ball, B. Fuhrmann, C. Högner, M. Kehr, U. Kypke-Burchardi, U. Laux, T. Löwinger, F. Ludwig, R. Neubert, J. Schiller, and J. Winkler. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.