Host Star Metallicity of Directly Imaged Wide-orbit Planets: Implications for Planet Formation

Existing planetary search methods are constrained by severe selection effects and detection biases (e.g., Cumming 2004; Zakamska et al. 2011; Kipping & Sandford 2016). However, multiple detection techniques sample different regions of the star–planet parameter space, thus providing useful insights about the rich diversity and underlying population of the planetary systems. While the transit and radial velocity methods have been successful in unraveling planet populations spanning extremely close-in (∼0.1 au) to moderate (∼10 au) orbits, the direct imaging is most useful for probing the planetary architecture in the outermost regions (tens to thousands of astronomical units) of stars (Winn & Fabrycky 2015; Bowler 2016; Baron et al. 2019). The planet population discovered by the transit technique and radial velocity largely belongs to main-sequence and post-main-sequence stars. In contrast, the direct imaging method has been most effective in uncovering newly formed warm and massive planets in wider orbits around nearby young stars in the solar neighborhood (e.g., Lagrange 2014; Bowler 2016; Meshkat et al. 2017; Baron et al. 2019).

Following the success of the Kepler space mission, a wealth of new information has emerged about the planet population associated with main-sequence and evolved stars (Borucki et al. 2011; Batalha 2014; Fulton & Petigura 2018; Howard et al. 2012; Johnson et al. 2017; Mulders et al. 2016; Narang et al. 2018; Petigura et al. 2017; Petigura et al. 2018). The growing number of exoplanets from space discoveries and their follow-up studies from the ground are making planetary statistics more robust and significant. Because of their large number, the statistical properties of close-in planets (≤1 au) and their host stars are relatively better studied. A great deal of research effort has been devoted to understanding the diversity of planets and the characteristics of their primary hosts. Many useful insights have been gained by studying the interdependence of planetary properties and stellar parameters (Gonzalez 1997; Santos et al. 2000, 2004; Fischer & Valenti 2005; Udry & Santos 2007; Ghezzi et al. 2010; Johnson et al. 2010; Mulders et al. 2016; Mulders 2018; Narang et al. 2018; Adibekyan 2019). Stellar metallicity and planet occurrence rate, for example, make up one such important correlation for testing the veracity of various planet formation mechanisms under different conditions (e.g., Udry & Santos 2007; Santos et al. 2017; Mulders 2018; Narang et al. 2018). However, these results have been demonstrated only for stars with close-in (≤1 au) planets that have been detected primarily by radial velocity and transit methods.

Directly imaged planets (DIPs) are located at relatively large orbital distances from their host stars (2.6–3500 au), which provides a unique window to probe an entirely different planetary population. While there is a general consensus that giant planets are common around high-metallicity stars compared to their low-metallicity counterparts, a clear picture is still lacking about the role of metallicity and the exact mechanism of giant planet formation at larger distances.

The majority of the 51 planetary companions discovered so far by direct imaging techniques are massive planets at larger orbital distances from the host stars. Figure 1(a) shows the confirmed exoplanets in a mass–orbital distance plane, where the segregation of planets into different populations is evident. Treating DIPs as a separate population and studying their hosts' properties can provide vital clues about the dominant mechanism of planet formation at large orbital distances from the star. The parameter space of massive planets at long orbital periods occupied by DIPs is relatively unexplored for the correlation studies of host star–planet properties. Also, the high-mass limit of wide-orbit planets overlaps with the low-mass tail of brown dwarfs and substellar companions. Therefore, in certain cases, the limitation of low-number DIP statistics can be partly overcome by a complementary study of known brown dwarf companions sharing the same parameter space (Ma & Ge 2014; Vigan et al. 2017; Nielsen et al. 2019). Therefore, it is essential to investigate the role, if any, of the host star metallicity in influencing the process of giant planet and brown dwarf formation over a wide range of astrophysical conditions.

Zoom In Zoom Out Reset image size

We have examined the confirmed list of DIPs hosted on NASA's Exoplanet Archive (Akeson et al. 2013).⁴ The available stellar and planetary parameters are compiled from the composite planet data table for known exoplanets and published literature. Each of these systems has been studied and discussed in depth by individual discovery and follow-up papers. However, there are limited instances where the DIP distribution and stellar properties are studied as separate ensembles (Neuhäuser & Schmidt 2012; Bowler 2016).

Out of the 45 stars hosting DIPs listed in Table 1 taken from the NASA Exoplanet Archive, we could cross-match 42 of them with the Gaia DR2 catalog, in which T_eff and luminosity were available for 26 stars (for cross-matching, see Viswanath et al. 2020). The atmospheric properties of the stars hosting these wide-orbit companions are not very well studied, and, most notably, the metallicity is known for only 14 such systems.

Table 1.  Stellar Parameters of DIP Host Stars

		Literature Values							This Paper
Serial	Star	Age	MP	Teff	log g	[Fe/H]	v · sin i	References	Teff	log g	[Fe/H]	v · sin i
Number		(Myr)	(MJ)	(K)	(cm s−2)	(dex)	(km s−1)		(K)	(cm s−2)	(dex)	(km s−1)
	DIP Host Stars Analyzed in This Paper
1	HD 106906	13	11 ± 2	${6516}_{-165}^{+165}$	⋯	⋯	${55}_{-4.0}^{+4.0}$	1, 2, A	${6798}_{-40}^{+20}$	${4.23}_{-0.05}^{+0.02}$	${0.04}_{-0.02}^{+0.01}$	${49.12}_{-0.17}^{+0.22}$
2	AB Pic	17.5	13.5 ± 0.5	${5378}_{-55}^{+55}$	4.44 ± 0.21	−0.05 ± 0.04	${11.5}_{-0.1}^{+0.1}$	3, 4, 5, 6, A	${5285}_{-9}^{+10}$	${4.53}_{-0.01}^{+0.01}$	0.04 ± 0.02	${10.35}_{-0.04}^{+0.06}$
3	GJ 504	160	${4.0}_{-1.0}^{+4.5}$	${6234}_{-25}^{+25}$	4.33 ± 0.10	0.28 ± 0.03	${7.4}_{-0.5}^{+0.5}$	7, 8, B	${6291}_{-16}^{+14}$	${4.34}_{-0.02}^{+0.01}$	${0.27}_{-0.03}^{+0.02}$	${5.47}_{-0.17}^{+0.12}$
4	HN Peg	237	21.99 ± 9.43	6034	4.48	−0.02 ± 0.02	${10.6}_{-0.5}^{+0.5}$	9, 10, 11, A	${6186}_{-7}^{+14}$	${4.48}_{-0.02}^{+0.03}$	${0.00}_{-0.02}^{+0.01}$	${8.73}_{-0.05}^{+0.06}$
5	51 Eri	20	2.0	7146	3.99 ± 0.24	${0.24}_{-0.35}^{+0.35}$	${71.8}_{-3.6}^{+3.6}$	12, 13, A	${7276}_{-9}^{+11}$	${4.08}_{-0.02}^{+0.03}$	${0.13}_{-0.02}^{+0.03}$	${65.19}_{-0.17}^{+0.14}$
6	HR 2562	600	30 ± 15	6534	${4.18}_{-0.05}^{+0.04}$	0.08	⋯	14, 15, 16, C	${6785}_{-27}^{+29}$	${4.40}_{-0.05}^{+0.04}$	${0.21}_{-0.03}^{+0.02}$	${43.51}_{-0.17}^{+0.15}$
7	Fomalhaut	440	2.6 ± 0.9	8689	${4.11}_{-0.85}^{+0.85}$	${0.27}_{-0.19}^{+0.19}$	${91.06}_{-0.5}^{+0.5}$	17, 18A	${8508}_{-12}^{+43}$	${4.02}_{-0.02}^{+0.01}$	${0.13}_{-0.03}^{+0.05}$	${75.31}_{-0.14}^{+0.57}$
8	HR 8799	30	${7}_{-2}^{+4}$	${7376}_{-217}^{+218}$	4.22	−0.5	⋯	19, 20, 21, 22, A	${7339}_{-5}^{+4}$	${4.19}_{-0.02}^{+0.01}$	$-{0.65}_{-0.01}^{+0.02}$	${34.79}_{-0.13}^{+0.24}$
			${10}_{-3}^{+3}$
			${10}_{-4}^{+7}$
9	HD 203030	220	${24.09}_{-11.52}^{+8.38}$	${5472}_{-61}^{+84}$	${4.50}_{-0.05}^{+0.05}$	${0.06}_{-0.07}^{+0.07}$	${6.3}_{-0.3}^{+0.3}$	13, 21, 23, 24, D	${5603}_{-8}^{+10}$	${4.64}_{-0.01}^{+0.03}$	${0.30}_{-0.01}^{+0.02}$	${5.62}_{-0.14}^{+0.13}$
10	HD 95086	17	5 ± 2	7750 ± 250	4.0 ± 0.5	−0.25 ± 0.5	20 ± 10	25, 26, 27, A	${7883}_{-65}^{+43}$	${4.58}_{-0.06}^{+0.02}$	${0.14}_{-0.04}^{+0.05}$	${17.14}_{-0.52}^{+1.31}$
11	β Pic	12.5	11 ± 2	8052	4.15	−0.1 ± 0.2	122.0	3, 16, 28, 29, A	${7890}_{-17}^{+13}$	${3.83}_{-0.02}^{+0.03}$	$-{0.21}_{-0.02}^{+0.03}$	${116.41}_{-2.05}^{+2.32}$
12	HIP 78530	11	23 ± 1	10,500	⋯	⋯	⋯	30, 31, A	${10,690}_{-10}^{+24}$	${4.68}_{-0.01}^{+0.02}$	$-{0.50}_{-0.01}^{+0.03}$	${144.74}_{-3.14}^{+0.55}$
13	LkCa 15	1	⋯	${4210}_{-199}^{+185}$	⋯	⋯	${13.90}_{-1.20}^{+1.20}$	21, 32, 33, D	${4589}_{-7}^{+7}$	${3.65}_{-0.01}^{+0.01}$	${0.26}_{-0.01}^{+0.01}$	${16.82}_{-0.2}^{+0.1}$
14	PDS 70	5	8 ± 6	${4225}_{-71}^{+242}$	⋯	⋯	⋯	21, 34, 35, 36, A	${4152}_{-9}^{+5}$	${3.68}_{-0.01}^{+0.01}$	$-{0.11}_{-0.01}^{+0.01}$	${17.27}_{-0.1}^{+0.1}$
			8 ± 4
15	CT Cha	2	17 ± 6	${4200}_{-115}^{+211}$	⋯	⋯	${12.80}_{-1.7}^{+1.7}$	6, 21, 37, 38, B	${4403}_{-10}^{+6}$	${3.66}_{-0.01}^{+0.01}$	$-{0.56}_{-0.01}^{+0.01}$	${13.97}_{-0.15}^{+0.10}$
16	GQ Lup	1	20	${4092}_{-165}^{+211}$	⋯	⋯	⋯	21, 39, A	${4416}_{-5}^{+3}$	${3.65}_{-0.04}^{+0.01}$	$-{0.35}_{-0.01}^{+0.01}$	${6.33}_{-0.07}^{+0.03}$
17	ROXs 12	6	16 ± 4	${3850}_{-70}^{+100}$	⋯	⋯	⋯	40, 41, D	${4059}_{-4}^{+3}$	${3.71}_{-0.01}^{+0.01}$	${0.14}_{-0.01}^{+0.01}$	${7.20}_{-0.04}^{+0.03}$
18	GSC 06214–00210	11	16 ± 1	${4200}_{-150}^{+150}$	⋯	⋯	⋯	30, 31, D	${4119}_{-13}^{+6}$	${3.70}_{-0.04}^{+0.01}$	$-{0.06}_{-0.01}^{+0.01}$	${4.24}_{-0.05}^{+0.04}$
	DIP Host Stars with Metallicity from Literature
19	HIP 65426	14	9.0 ± 3.0	${8840}_{-200}^{+200}$	${5.00}_{-0.18}^{+0.13}$	$-{0.03}_{-0.10}^{+0.10}$	299 ± 9	42, 43, 44	⋯	⋯	⋯	⋯
20	Kap And	220	${13.616}_{-1.05}^{+23.04}$	${10,900}_{-300}^{+300}$	${3.78}_{-0.08}^{+0.08}$	$-{0.36}_{-0.09}^{+0.09}$	176	45, 46, 47	⋯	⋯	⋯	-
21	GU Psc	100	11.3 ± 1.7	3250 ± 32	${4.75}_{-0.07}^{+0.07}$	${0.10}_{-0.13}^{+0.13}$	${23.0}_{-0.14}^{+0.14}$	48, 49	⋯	⋯	⋯	⋯
22	Ross 458	475	6.28536	3600 ± 73	${4.71}_{-0.05}^{+0.08}$	${0.25}_{-0.08}^{+0.08}$	9.75	50, 51, 52, 53	–	⋯	–	–
	DIP Host Stars that Are Not Analyzed in This Paper
23	ROXs 42B	2	9 ± 3	${3850}_{-394}^{+199}$	⋯	⋯	⋯	21, 54, 55
24	2MASS J02192210–3925225	20	13.9 ± 1.1	${3064}_{-76}^{+76}$	${4.59}_{-0.06}^{+0.06}$	⋯	${6.5}_{-0.04}^{+0.04}$	56	⋯	⋯	⋯	⋯
25	NAME Oph 11	2	${14}_{-5}^{+6}$	${2375}_{-175}^{+175}$	${4.25}_{-0.5}^{+0.50}$	⋯	⋯	55, 57	⋯	⋯	⋯	⋯
26	VHS J125601.92–125723.9	225	${11.2}_{-1.8}^{+9.7}$	${2620}_{-140}^{+140}$	${5.05}_{-0.10}^{+0.10}$	⋯	⋯	58	⋯	⋯	⋯	⋯
27	WISEP J121756.91+162640.2A	6000	22 ± 2	575 ± 25	5.0 ± 0.1	⋯	⋯	59	⋯	⋯	⋯	⋯
28	CFBDSIR J145829+101343	⋯	${10.5}_{-4.5}^{+4.5}$	${581}_{-24.5}^{+24.5}$	${4.73}_{-0.28}^{+0.28}$	⋯	⋯	60	⋯	⋯	⋯	⋯
29	1RXS J160929.1–210524	11	8 ± 1	${4060}_{-200}^{+300}$	${4.19}_{-0.06}^{+0.09}*$	⋯	⋯	21,30, 31	⋯	⋯	⋯	⋯
30	2MASS J21402931+1625183 A	⋯	${20.95}_{-20.95}^{+83.79}$	${2300}_{-80}^{+80}$	${5.17}_{-0.61}^{+0.24}*$	⋯	⋯	21, 61	⋯	⋯	⋯	⋯
31	2MASS J22362452+4751425	30	${12.5}_{-1.5}^{+1.5}$	${4045}_{-35}^{+35}$	${4.60}_{-0.04}^{+0.04}*$	⋯	⋯	3, 21, 62	⋯	⋯	⋯	⋯
32	DH Tau	1	${11}_{-3}^{+10}$	${3751}_{-148}^{+501}$	${5.06}_{-0.20}^{+0.25}*$	⋯	⋯	21, 33, 63	⋯	⋯	⋯	⋯
33	TYC 8998-760-1	17	${14}_{-3}^{+3}$	${4753}_{-10}^{+10}$	${4.44}_{-0.01}^{+0.01}*$	⋯	⋯	21, 64	⋯	⋯	⋯	⋯
			${6}_{-1}^{+1}$
34	USco1556 A	7.5	${15}_{-2}^{+2}$	${3400}_{-100}^{+100}$	${4.49}_{-0.10}^{+0.08}*$	⋯	⋯	21, 65, 66	⋯	⋯	⋯	⋯
35	USco1621 A	7.5	${16}_{-2}^{+2}$	${3460}_{-100}^{+100}$	${4.25}_{-0.11}^{+0.09}*$	⋯	⋯	21, 65, 66	⋯	⋯	⋯	⋯
36	HIP 79098 AB	10	20.5 ± 4.5	${9193}_{-93}^{+61}$	⋯	⋯	⋯	21, 67	⋯	⋯	⋯
37	2MASS J01225093–2439505	120	${24.5}_{-2.5}^{+2.5}$	${3530}_{-50}^{+50}$	⋯	⋯	${14.2}_{-3.2}^{+3.2}$	68	⋯	⋯	–	⋯
38	NAME SR 12 AB	2.1	${13}_{-7}^{+7}$	${3828}_{-379}^{+516}$	⋯	⋯	⋯	23, 69	⋯	⋯	⋯	⋯
39	USco CTIO 108	11	${14}_{-8}^{+2}$	${2700}_{-100}^{+100}$	⋯	⋯	⋯	31, 70	⋯	⋯	⋯	⋯
40	WD 0806–661	1500	${7.5}_{-1.5}^{+1.5}$	${9552}_{-1931}^{+54}$	⋯	⋯	⋯	21, 71, 72	⋯	⋯	⋯	⋯
41	FU Tau	1	16	2838	⋯	⋯	⋯	33, 73	⋯	⋯	⋯	⋯
42	2MASS J04414489+2301513	1	${7.5}_{-2.5}^{+2.5}$	⋯	⋯	⋯	⋯	74	⋯	⋯	⋯	⋯
43	2MASS J12073346–3932539	8	${4}_{-1}^{+1}$	⋯	⋯	⋯	⋯	75, 76	⋯	⋯	⋯	⋯
44	CHXR 73	2	${12.57}_{-5.24}^{+8.38}$	⋯	⋯	⋯	⋯	38, 77	⋯	⋯	⋯	⋯
45	2MASS J01033563–5515561	30	13 ± 1	⋯	⋯	⋯	⋯	38, 78	⋯	⋯	⋯⋯

References. 1. Chen et al. (2011); 2. Bailey et al. (2014); 3. Ujjwal et al. (2020); 4. Chauvin et al. (2005); 5. Ghezzi et al. (2010); 6. Torres et al. (2006); 7. Kuzuhara et al. (2013); 8. Maldonado et al. (2015); 9. Luhman et al. (2007); 10. Ramírez et al. (2009); 11. Boro Saikia et al. (2015); 12. Macintosh et al. (2015); 13. Luck (2017); 14. Konopacky et al. (2016); 15. Maldonado et al. (2012); 16. Lépine et al. (2003); 17. Kalas et al. (2008); 18. Mamajek (2012); 19. Marois et al. (2008); 20. Gravity Collaboration et al. (2019); 21. Gaia Collaboration et al. (2018); 22. Marois et al. (2010); 23. Metchev & Hillenbrand (2006); 24. Faherty et al. (2009); 25. Rameau et al. (2013); 26. Moór et al. (2013); 27. Meshkat et al. (2013); 28. Snellen & Brown (2018); 29. Heap et al. (1994); 30. Lachapelle et al. (2015); 31. Pecaut et al. (2012); 32. Nguyen et al. (2012); 33. Kenyon & Hartmann (1995); 34. Keppler et al. (2018); 35. Haffert et al. (2019); 36. Müller et al. (2018); 37. Schmidt et al. (2008); 38. Manoj et al. (2011); 39. Neuhäuser et al. (2008); 40. Kraus et al. (2014); 41. Bowler et al. (2017a); 42. Chauvin et al. (2017); 43. Bochanski et al. (2018); 44. Chauvin et al. (2017); 45. Royer et al. (2007); 46. Bonnefoy et al. (2014); 47. Hinkley et al. (2013); 48. Naud et al. (2014); 49. Malo et al. (2014a, 2014b); 50. Rodriguez et al. (2011); 51. Gaidos & Mann (2014); 52. Burgasser et al. (2010); 53. Houdebine (2010); 54. Currie et al. (2014); 55. Wilking et al. (2005); 56. Artigau et al. (2015); 57. Close et al. (2007); 58. Gauza et al. (2015); 59. Leggett et al. (2014); 60. Liu et al. (2011); 61. Konopacky et al. (2010); 62. Bowler et al. (2017b); 63. Patience et al. (2012); 64. Bohn et al. (2020); 65. Chinchilla et al. (2020); 66. Stassun et al. (2019); 67. Janson et al. (2019); 68. Bowler et al. (2013); 69. Kuzuhara et al. (2011); 70. Béjar et al. (2008); 71. Luhman et al. (2012); 72. Luhman et al. (2011); 73. Luhman et al. (2009); 74. Todorov et al. (2010); 75. Ducourant et al. (2008); 76. Mohanty et al. (2007); 77. Luhman et al. (2006); 78. Delorme et al. (2013).

The instruments listed in the reference column are as follows: A, HARPS; B, UVES; C, FEROS; D, HIRES.

Download table as:  ASCIITypeset images: 1 2

In general, previous studies (Buchhave et al. 2014; Santos et al. 2017; Schlaufman 2018; Narang et al. 2018) have shown that the average metallicity of the host star increases as a function of planetary mass. However, the trend reverses for most planetary masses above 4–5 M_J (Santos et al. 2017; Schlaufman 2018; Narang et al. 2018; Maldonado et al. 2019). These results suggest the possibility of two planet formation scenarios, with the Jupiter-like planets (0.3–5 M_J) likely formed by the core accretion process (e.g., Mizuno 1980; Pollack et al. 1996; Ida & Lin 2004; Mordasini et al. 2012) and the massive super-Jupiters (>5 M_J) formed via the disk instability mechanism (e.g., Boss 1997, 2002; Mayer et al. 2002; Matsuo et al. 2007; Santos et al. 2017; Narang et al. 2018; Goda & Matsuo 2019). These findings, backed by large statistics, truly reflect the underlying metallicity–mass distribution of compact planetary systems (orbital period ≤1 yr). This raises another important question: whether or not such trends hold for planets formed at vast orbital distances from the central star. Since DIPs are found at large distances from their host stars, this planet population motivates us to explore the mass–metallicity relationship for giant planet populations at large distances in light of various planet formation scenarios. This paper has used high-resolution spectra available from various public archives to determine the stellar parameters and metallicity of 18 stars hosting DIPs in a consistent and homogeneous way to study the various correlations among stellar and planetary properties.

The rest of the paper is organized as follows. In Section 2, we give a brief overview of DIP systems. We describe our sample and give the selection criteria in Section 3. Our methodology and Bayesian approach used for the estimation of various stellar parameters are discussed in Section 4. In Section 5, we discuss our results and compare them with previous findings. Finally, we give our summary and conclusions in Section 6.

Of the 4200+ confirmed planets, direct imaging techniques account for the discovery of 51 planetary mass objects around 45 stars. Among these, 40 are in a single planetary system, and four are in multiplanetary systems: LkCa 15, TYC 8998-760-1, and PDS 70 with two planets each and HR 8799 with four. The majority of them are discovered from deep imaging surveys of nearby star-forming regions. These planet search programs largely target young pre-main-sequence stars that belong to nearby stellar associations and moving groups, all within 200 pc of the Sun (Bowler 2016). The high luminosity of planets at the early formation stage makes them amenable to direct imaging. Further, the high-resolution and high-contrast imaging of planets is facilitated by adaptive optics technology and stellar coronography. With advanced differential imaging and point-spread function extraction techniques, a new generation of instruments, e.g., the Gemini Planet Imager, ScExAO on Subaru, and SPHERE on the Very Large Telescope, are capable of probing Jupiter-mass planetary companions within a few milliarcseconds of separation from the central star.

Masses of self-luminous planets are inferred from hot-star evolutionary tracks and infrared fluxes, but in some cases, they are well constrained by precise astrometric measurements (Baraffe et al. 2003; Snellen & Brown 2018; Wang et al. 2018; Nielsen et al. 2019; Wagner et al. 2019). The onset of the deuterium-burning limit (∼13 M_J) is a commonly used criterion to separate a planet from a brown dwarf (Burrows et al. 1997; Saumon & Marley 2008; Spiegel et al. 2011). However, by taking different composition and formation scenarios into account, the upper cutoff range could be as high as 25–30 M_J (Baraffe et al. 2010; Schneider et al. 2011). We acknowledge this ambiguity of overlapping mass range, but we clump all directly imaged objects up to ∼30 M_J in the DIP category for the present work.

The histogram shown in Figure 1(b) reveals that except for one case,⁵ the projected semimajor axis distances of all DIPs are larger than Jupiter's orbital distance. The distribution peaks at an orbital distance of 150–500 au and extends up to ≈3500 au. The lower limit of the distribution is set by the inner working angle of the coronagraph, while the drop beyond a few thousand astronomical units is influenced by the limited sensitivity to detect the positional change of planets in long-period orbits.

The median mass of the DIP population is about ≈12.5 M_J, with the lowest-mass object at 2 M_J and about half the number more massive than 13 M_J. Most stellar hosts of these planets are also relatively young, i.e., ≈75% below the age of ∼100 Myr and more than two-thirds of the total belonging to the late spectral types with T_eff ≤ 4500 K. From the literature, we also find evidence of circumstellar disks around 22 such systems.

The equilibrium temperature of the imaged planets ranges from 300 to 2800 K, though most of them are above 1600 K. The projected angular separation between the host star and planet varies by 4 orders of magnitude ranging from ≈10⁻² to 10² arcsec. A large angular separation from the central star and the inherent brightness due to their high temperature make this giant planet population ideal for direct detection (Traub & Oppenheimer 2010).

We note that the current DIP sample is not a true representative of the underlying population of planets in outer orbits. It is heavily biased toward young, hot, more massive (≥4 M_J) companions of young stars. The complexity of high-contrast instruments and the limitation of observing a single object at a time also makes the discovery rate slow. Studying DIP hosts spectroscopically is a major challenge because of their wide spectral range and the complexities (veiling, extinction, etc.) associated with young and pre-main-sequence stars. Therefore, it is also difficult to apply a strictly uniform and homogeneous methodology for the whole sample's characterization.

The NASA Exoplanet Archive has 3185 stars with confirmed planets found by various discovery methods. We found 2831 stars cross-matched with the Gaia DR2 catalog, which has the most accurate parallaxes and precise multiband photometry of all-sky stellar sources down to magnitude G ≈ 21. Figure 2 shows the location of these stars in the Hertzsprung–Russell (H-R) diagram with T_eff, and stellar luminosity is taken from the Gaia catalog.

Zoom In Zoom Out Reset image size

The archive also contains the list of 45 host stars of DIP given in Table 1. Of these, 42 are found in the Gaia DR2 catalog, and their position in the H-R diagram is also shown in Figure 2. The summary of the astrophysical parameters of the DIP host stars listed in Table 1 and our selection criteria for spectroscopic analysis is as follows.

• 1.  
  We searched various public archives for the availability of high-resolution optical spectra for individual DIP hosts and also surveyed the literature on their metallicity. Based on these findings, we separated the 45 DIP host stars in Table 1 into three distinct groups, demarcated by horizontal lines.
• 2.  
  The first 18 stars in Table 1 are a subsample of DIP host stars analyzed in this paper for which the spectra are available from public archives, but the literature metallicity is known for only 10 targets. These stars have an effective temperature range between 4059 and 10,690 K and a G-band magnitude smaller than ∼13. For this subsample, we determined the atmospheric parameters and metallicity [Fe/H] homogeneously for the first time. We obtained high-resolution, high signal-to-noise ratio (S/N) spectra for 14 targets from the ESO science archive facility⁶ and four targets from the Keck⁷ archive. The ESO's Science Portal provides access to the already reduced and wavelength-calibrated data. Details of the original spectra, e.g., telescope/instrument, resolution, wavelength coverage, and S/N, are listed in Table 2.
• 3.  
  In the second group of Table 1, there are four DIP host stars for which the metallicity is taken from the literature. The last 23 DIP hosts belonging to the third group in Table 1 are not analyzed in this paper because the majority of them are fainter (m_v > 13). For these stars, either the spectra were not available in the public domain or the quality of the data was poor (low S/N). This group also includes some of the hot and very rapidly rotating stars (v · sin i > 160 km s^–1), which do not have clear spectral features and reliable atmospheric models for parameter estimation.
• 4.  
  Most stellar parameters listed in Table 1 are taken from the NASA Exoplanet Archive. Furthermore, we cross-checked the accuracy of these parameters and replaced the missing values with those from the discovery and relevant follow-up papers. The log g values marked by asterisks are not listed in the standard archives (such as the NASA Exoplanet Archive), and we have calculated them from stellar mass and radius values available from the literature.

Spectral synthesis and the equivalent width (EW) method are two commonly used techniques to derive the stellar parameter of interest from high-resolution spectra of stars (Gray & Corbally 1994; Erspamer & North 2002; Nissen & Gustafsson 2018; Blanco-Cuaresma 2019; Jofré et al. 2019). Despite intrinsic differences, each method requires the proper prescription of a stellar atmospheric model, a well-characterized atomic line list, reference solar abundance, and radiative transfer code. Most notably, the relevant model parameters in both methods are allowed to vary, and a least-squares minimization is performed to reach the convergence. For example, in the EW case, the desired parameters are those for which the correlation between abundances and EWs (excitation equilibrium and ionization balance) is minimized to zero. In spectral synthesis, theoretical spectra are iteratively generated from the model atmosphere and compared with the observed spectra of the star until a best match is found. The parameters of the best-matched spectra are the closest that describe the properties of the real star. The spectral synthesis method, which we adopted for our Bayesian model, is also suitable for analyzing the young and fast-rotating stars present in our sample.

4.1. Generation of Model Spectra

4.2. Data Preparation

Doing Bayesian analysis on the whole spectrum is computationally prohibitive. To reduce the computational load, we considered three distinct wavelength regions of the spectrum. These regions are free from telluric lines and also serve as good proxies for different stellar parameters without any degeneracy (Petigura et al. 2018).

The first region is the Mg i triplet (5150–5200 Å), which is sensitive to log g. The second region (6000–6200 Å) includes a significant number of well-isolated and unresolved spectral lines that are sensitive to v · sin i and [Fe/H], and the third region (6540–6590 Å) covers the H_α line, whose outer wings are sensitive to T_eff. We have used all three regions for most targets except for HIP 78530, which shows severe line blending due to fast rotation. In that case, we have used only the Mg i triplet and H_α segments.

Additionally, some of the stars in our sample (stars with serial numbers 13–18 in Table 1) have emission features that indicate the presence of an accretion disk around the star. The characteristic veiling-dominated H_α emission for these stars is shown in Figure 3. This accretion-shocked region on the stellar surface generates the veiling continuum and decreases the depth of the stellar absorption lines (Calvet & Gullbring 1998). Since we do not have reliable models for emission lines (such as the H_α), we chose the less contaminated and emission-free region 5900–5965 Å for deducing the stellar parameters (Stempels & Piskunov 2002, 2003). In addition, we included the 6100–6200 Å segment for LkCa 15, Ross 12, PDS 70, and GSC 06214–00210, together with 5900–5965 Å for determining stellar parameters, since this region also lacks emission lines. In the Bayesian analysis discussed in the next section, we considered veiling as a free parameter to account for the excessive line filling due to accretion, following the procedure by Stempels & Piskunov (2002, 2003).

Zoom In Zoom Out Reset image size

The individual spectra of stars come from single-object spectroscopic observations from the different instruments. The FITS files contain a 1D spectrum with specification of wavelength, flux, and flux errors. If the flux error was not specified, we assumed the errors to be limited by the photon noise. A certain amount of preprocessing was needed to prepare the data for further analysis. We used standard packages in IRAF⁸ for continuum normalization and radial velocity correction in the spectra. The model spectrum was generated at the same wavelength grid as the observed spectrum.

4.3. Bayesian Inference and Markov Chain Monte Carlo Sampler

We chose the Bayesian approach for probabilistic inference because it eliminates the dependence of the derived stellar parameters on the initial guess values and also places realistic constraints on the errors (Shkedy et al. 2007). We denote our minimal set of model parameters as $\theta \,\equiv \,\{{T}_{\mathrm{eff}},\mathrm{log}g,[\mathrm{Fe}/{\rm{H}}],v.\sin i\}$ and observed stellar spectrum as D ≡ {y_data, y_err, λ}, where y_data is the measured flux at wavelength λ and associated uncertainty y_err. The model-predicted normalized flux y_mod(θ, λ) is calculated from first principles using the radiative transfer code and appropriate model of the stellar atmosphere. The goal is to find the posterior p(θ∣D), which is the most likely distribution of the model parameters θ conditioned on the observed data D. We know from Bayes' theorem that

$$\begin{eqnarray}&&p(\theta | D)=\displaystyle \frac{p(\theta )p(D| \theta )}{p(D)},\end{eqnarray} \tag{ 1 }$$

where p(D∣θ) is the likelihood of observing spectra D, given the set of model parameters θ, and p(θ) is the prior function. The term p(D) in the denominator of Equation (1) is a normalization constant, also called evidence, which is hard to compute but not required when we use a sampler. Note that each term in Equation (1) is a probability density function whose analytical form is rarely known in practice. The Markov Chain Monte Carlo (MCMC) process allows us to numerically estimate the parameters by randomly drawing a sequence of samples from the posterior distribution of model parameters constrained by the data (Hogg & Foreman-Mackey 2018).

We used the emcee implementation of MCMC⁹ in Python. The flowchart of the algorithm is shown in Figure 4. First, we initialize the starting parameters θ_s of the model from our prior knowledge of the star, e.g., spectral type, luminosity class, etc. Using θ_s as seed, we generate an ensemble of {θ₁, θ₂, ... θ_k} called walkers drawn from a physically realistic range of uniform priors, i.e., ±200 K for T_eff, ±0.5 dex for log g, ±0.25 dex for [Fe/H] and ±2 to ±20 for $v\cdot \sin i$, depending on the star.

Zoom In Zoom Out Reset image size

Each walker is a random realization of θ that relies on an algorithm (e.g., Metropolis–Hastings) for sampling the parameter space. A function call to iSpec generates the model spectrum for the proposal parameter from the MCMC sampler. We define a simple log-likelihood function, $\mathrm{ln}P(D| \theta )$, to compare the observed spectrum y_data with the model spectrum y_mod as

$$\begin{eqnarray}&&\mathrm{ln}P(D| \theta )=-\displaystyle \frac{1}{2}\sum {\left(\displaystyle \frac{{y}_{\mathrm{data}}-{y}_{\mathrm{mod}}(D| \theta )}{{y}_{\mathrm{err}}}\right)}^{2}.\end{eqnarray} \tag{ 2 }$$

Every walker numerically explores the parameter space by taking a "step" to a new value, θ_j+1, that is drawn from a normal proposal distribution centered on θ_j. The new proposal, θ_j+1, is accepted if it has a higher posterior value than the current sample, θ_j. If the new proposal value has a lower posterior, then the choice to accept or reject a new proposal with a certain probability is made randomly.

The walker, thus guided by Markov's process, iteratively converges toward the target distribution by producing a chain of accepted parameters, as illustrated in Figure 4. We discard some of the early samples in each chain, as they are likely to lie outside the target distribution. This is termed "burn-in." Finally, after the burn-in, we obtain a posterior distribution of our stellar parameters.

After some experimentation, we found that by using 300 steps following a burn-in limit of 140 steps for 40 test chains, we get a reasonable posterior distribution to determine the statistics of the stellar parameters. For illustration, the final distribution of T_eff, log g, [Fe/H], and $v\cdot \sin i$ for HR 2562 is shown in Figure 5. Since our posterior distribution is multivariate, some of the model parameters are likely to correlate. The shape of the contour plots in Figure 5 reflects the degree of correlation between different stellar parameters; e.g., the expected correlation can be seen between log g and T_eff, while for others, the scatter is uniform, implying no correlation. As a representative example, we show the synthetic spectra for HR 2562 generated using Bayesian inferred model parameters in Figure 6, which matches reasonably well with the observed spectra.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

For the stars with veiling (S.No 13–18 in Table 1), the estimation of stellar parameters was done in parallel with the determination of veiling. This was possible because the line shapes and relative absorption line depths are affected by the stellar parameters and independent of the presence of veiling. We followed a similar procedure as described in Stempels & Piskunov (2002, 2003), where veiling was modeled as a free parameter V(λ) in the log-likelihood function in Equation (2). We used the modified log-likelihood function to obtain the stellar parameters with the same procedure as described above.

The final stellar parameters for our selected stars with mean values and ±1σ uncertainty are listed in Table 1. The errors associated with the stellar parameters are the Bayesian error bars that are related to the sampling of the model spectra. The intrinsic uncertainty associated with the model generating the spectrum is not taken into account. Typical standard errors associated with metallicity (±0.15) are discussed in detail by Blanco-Cuaresma et al. (2014a) and Jofré et al. (2019).

5.1. Metallicity of DIP Host Stars

We have estimated the stellar parameters for a subset of stars harboring DIPs listed in Table 1. Figure 7 shows the distribution of observed metallicity for 22 stars, 18 of which are analyzed in the present work, and the metallicity value for four stars is taken from previous studies. The metallicities of these targets do not show any trend or clustering but widely vary from +0.30 dex (HD 203030) to −0.65 dex (HR 8977) with a median centered at 0.04 dex, which is closer to the solar value. The first and third quartiles are −0.21 and 0.14 dex, respectively, with 12 of them having a metallicity higher than the solar value. The large scatter seen in [Fe/H] is not very surprising, as it likely reflects the heterogeneity of the DIP host stars associated with different star-forming regions, parent clusters, or moving groups.

Zoom In Zoom Out Reset image size

5.2. Metallicity and Planet Mass

To study the relationship between host star metallicity and planet mass, we used the planetary mass data from the NASA Exoplanet Database from the composite planet list. We divided our DIP sample into three mass bins, 1 M_J < M_p ≤ 5 M_J, 5 M_J < M_p ≤ 13 M_J, and M_p > 13 M_J, as shown in Figure 8. The average metallicity is 0.17 ± 0.07 dex for four stars in the first bin, −0.08 ± 0.29 dex for seven stars in the second bin, and −0.11 ± 0.30 dex for 10 stars in the third bin. The mean metallicity in each bin shows a declining trend with increasing planetary mass. We also note that regardless of their orbital distance, DIPs with M_p ≤ 5 M_J have mostly metal-rich hosts.

Zoom In Zoom Out Reset image size

5.3. Metallicity and Other Stellar Parameters

Figure 9 shows the distribution of metallicity as a function of orbital distance, stellar mass, log g, and v · sin i . For low-mass stars, M_⋆ ≤ 1 M_⊙, we find that the average metallicity is near solar with a standard deviation of 0.21 dex. Stars with M_⋆ > 1 M_⊙ are found to be slightly metal-poor with an average metallicity of −0.10 dex and a standard deviation of 0.30 dex.

Zoom In Zoom Out Reset image size

We also find that the average metallicity of fast-rotating stars (v · sin i > 15 km s⁻¹) is −0.1 dex with a standard deviation of 0.29 dex, while for slow rotators (v · sin i < 15 km s⁻¹), it is solar, 0.02 dex with a standard deviation of 0.28 dex. The Spearman rank correlation coefficient between the stellar metallicity and projected rotational velocity of the star v · sin i is −0.42 with a p-value of 0.05, which suggests a weak negative correlation. Furthermore, there is no noticeable dependence of host star metallicity on orbital distance and log g.

5.4. Comparison with Literature

In the standard paradigm for the formation of a Jupiter-like planet via core nucleated accretion (e.g., D'Angelo & Lissauer 2018), a rocky protoplanetary core forms first, which then accretes gas and dust from the surrounding disk to become a gas giant (Bodenheimer & Pollack 1986; Pollack et al. 1996; Boss 1997; Ikoma et al. 2001). The critical (or minimum) core mass required to form a gas giant depends on various factors (e.g., location on the protoplanetary disk, accretion rate of solids, etc.) and generally decreases with increasing disk radius; the minimum core mass drops from ∼8.5 M_⊕ at 5 au to ∼3.5 M_⊕ at 100 au (Piso & Youdin 2014; Piso et al. 2015). If the protoplanetary disk is rich in solids, i.e., higher metallicity, then the rocky core can grow faster and reach the critical mass for gas accretion well before the disk is depleted of gas. Therefore, it is easier to form Jupiter-like gas giants in disks around higher-metallicity stars (e.g., Ida & Lin 2004; Kornet et al. 2005; Wyatt et al. 2007; Boss 2010; Mordasini et al. 2012). Indeed, observations have shown that the frequency of Jupiter-like planets is higher around higher-metallicity stars (e.g., Gonzalez 1997; Santos et al. 2001; Fischer & Valenti 2005; Udry & Santos 2007). While not as strong as that seen for gas giants, smaller planets also show a weaker tendency to occur more frequently around relatively higher-metallicity stars, even though their host stars appear to have a larger spread in metallicity (e.g., Buchhave et al. 2014; Wang & Fischer 2015; Mulders et al. 2016). It has now been adequately established that the host star metallicity ([Fe/H]), on average, increases with increasing planet mass or radius (e.g., Buchhave et al. 2014; Mulders 2018; Narang et al. 2018; Petigura et al. 2018). Thus, the observed strong dependence of the planet mass/radius on the host star metallicity supports the core accretion model for planet formation.

However, the observed correlation of increasing host star metallicity with increasing planet mass turns over at about 4–5 M_J. For planet masses higher than this (super-Jupiters), the correlation reverses, and the average host star metallicity decreases as the mass of the planet increases (Santos et al. 2017; Narang et al. 2018). This suggests that stars hosting super-Jupiters are not necessarily metal-rich, unlike stars hosting Jupiters. This trend appears to continue for more massive companions; the average metallicity of stars with a brown dwarf secondary is also close to solar to subsolar and not supersolar, like stars hosting Jupiters (Ma & Ge 2014; Schlaufman 2018; Narang et al. 2018).

Our sample of DIPs occupies a mass range similar to that of super-Jupiters and brown dwarfs. The fact that the average host star metallicities of brown dwarfs and super-Jupiters are similar and that they differ from that of Jupiter hosts perhaps indicates a similar formation scenario for them that is different from that of Jupiters. It has been suggested that massive planets and low-mass brown dwarfs can form via gravitational fragmentation of the disk rather than core accretion (e.g., Boss 1997; Mayer et al. 2002). This gravitational instability model of planet formation predicts no dependence between planet mass and host star metallicity (e.g., Boss 2002; Cai et al. 2006; Matsuo et al. 2007; Boss 2010), unlike the core accretion model, which predicts such a dependence.

We further compare the DIPs with the large population of giant planets and brown dwarfs around main-sequence stars discovered by techniques other than direct imaging. To this end, we found 637 stars hosting 746 giant planets and massive objects with masses in the range 1–55 M_J listed in NASA's Exoplanet Archive. We also searched the above sample in the SWEET-CATALOG (Santos et al. 2013; Sousa et al. 2018), which provides metallicity information for 459 stellar hosts having 494 companions. Additionally, a catalog of 58 brown dwarfs and their stellar companions was chosen from Ma & Ge (2014). A joint sample of 552 objects was formed by combining the giant planets and brown dwarfs. This combined sample has a mass range from 1 to 80 M_J and an orbital distance spanning 0.02–20 au. Since objects in the combined sample come from radial velocity, transit, transit-timing variation, astrometry, and microlensing observations, we have used the minimum mass (M · sin i ) wherever the true mass was not available.

We then ran a clustering analysis on the 2D data set of combined samples of giant planets and brown dwarfs with host star metallicity as one parameter and orbital distance and companion mass as another. For the clustering analysis, we considered a Gaussian mixture model and implemented it using a Python library scikit-learn package (Pedregosa et al. 2011). The Gaussian mixture model optimally segregated the combined sample into three clusters in the metallicity–planet mass plane, as shown in the top panel of Figure 10, and two clusters in the metallicity–orbital distance plane, as shown in the bottom panel of Figure 10.

Zoom In Zoom Out Reset image size

The clustering analysis in Figure 10 (top panel) clearly divides the combined sample into three mass and metallicity bins. The mass boundaries roughly located at ≈4 and ≈14 M_J are consistent with multiple populations of giant planets (i.e., Jupiters and super-Jupiters) and brown dwarfs, pointing to their different physical origins. Further on, the declining centroid metallicity of each group in Figure 10, i.e., 0.089 ± 0.02, 0.023 ± 0.002, and 0.013 ± 0.009 dex, is also consistent with previous results. The DIP population studied in this work is also shown for comparison in Figure 10. The DIP population falls between the super-Jupiter and brown dwarf populations in both mass and metallicity.

The analysis of orbital distance and stellar metallicity shows that the combined population of close-in objects separates into two distinct groups, as shown in the bottom panel of Figure 10. Again, the DIP sample analyzed in this work is added to the plot for comparison. In the metallicity–orbital distance plane, three populations again clearly separate out. On comparing the centroid values of the metallicity, which are 0.076, 0.042, and −0.097 dex (standard deviation in each case ≤10⁻⁶), we find a decreasing metallicity trend with increasing orbital distance. A similar metallicity dependence with orbital distance is also reported for the Jupiter analogs (Mulders et al. 2016; Buchhave et al. 2018; Mulders 2018).

In Figure 11, we compare the cumulative metallicity distribution of DIP host stars with stellar companions of brown dwarfs (Ma & Ge 2014) and giant planets, both Jupiter-type and super-Jupiters. We note that the cumulative distribution of DIP host stars in the lower-metallicity region clearly differs from the stellar hosts of Jupiter-type planets, whereas the distribution for super-Jupiters and brown dwarf hosts is falling between the two. However, there is no marked difference in the higher-metallicity side beyond [Fe/H] > 0.

Zoom In Zoom Out Reset image size

Although the specific factors that influence planet formation are still not fully understood, metallicity seems to be one of the major contributing factors that determine the type of planet likely to be formed around a star. Using synthetic planet population models, Mordasini et al. (2012) showed that a high-metallicity environment determines whether or not a giant planet in the mass range 1–4 M_J can form. But metallicity is not the only parameter in determining the final mass of the planet, except for the very massive planets (≥10 M_J), as the critical core must form very fast before the dissipation of the gas in the disk by accretion onto the star (Hayashi et al. 1985; Matsuo et al. 2007). The prediction of Mordasini et al. (2012) that the very massive planets (≥10 M_J) can form only at very high metallicity conditions is contrary to our findings. Our results are indicative of the possibility of two planet formation pathways: one in which the giant planets up to 4–5 M_J are formed by core accretion processes and one in which the massive super-Jupiters and brown dwarfs are formed via gravitational fragmentation of the protoplanetary disk.

Our results for wide-orbit (tens to thousands of astronomical units) planets are also consistent with the mass–metallicity trend observed for super-Jupiters and brown dwarfs in close-in (≤1 au) orbits around main-sequence stars. The formation mechanism of planets in wider orbits is still unclear. However, the mixed metallicity of our DIP host star sample and its close resemblance to the commutative metallicity distribution of brown dwarf hosts make it likely that massive and young planets in wider orbits also formed via gravitational instability. However, a larger sample is required to further validate such conclusions.

We have used high-resolution spectra to measure the atmospheric parameters of young stars that are confirmed host stars of planets detected by direct imaging techniques. Our sample consists of 22 such stars selected from NASA's Exoplanet Archive. For 18 of these targets, the stellar parameters and metallicity are determined in a uniform and consistent way. The summary of our results is as follows.

• 1.  
  We used the Bayesian analysis to estimated the atmospheric parameters and metallicity for 18 DIP host stars. The MCMC technique was used to obtain the posterior distribution of stellar parameters using model spectra generated using iSpec. The computed metallicity [Fe/H] of these stars spans a wide range, from +0.3 to −0.65 dex.
• 2.  
  We investigated the trend between the average host star metallicity and mass of the planet, which shows that DIPs with M_P ≤ 5 M_J tend to have metal-rich hosts. This is in line with the predictions of planet formation via core accretion. However, as the planet mass increases, the average metallicity of the host stars shows a declining trend, suggesting that these planets are likely formed by gravitational instability. These findings seem consistent with the results reported by Santos et al. (2017) and Narang et al. (2018). Since the metallicity of a star does not change during evolution, we do not expect these trends to change significantly for the currently undetected population of cool and massive giant planets in the outstretched regions of the main-sequence stars. Moreover, main-sequence host stars in general show a trend of decreasing metallicity with increasing orbital distance of the planet (e.g., Mulders et al. 2016; Buchhave et al. 2018; Mulders 2018; Narang et al. 2018).
• 3.  
  From clustering analysis, as discussed above in Section 6, we find that the DIP host stars separate as a different class of celestial objects in the stellar metallicity–orbital distance plane. Furthermore, we can see a decreasing trend in the centroids of the host star metallicity as the star–planet separation increases.
• 4.  
  In the planetary mass–stellar metallicity plane, it is found that Jupiter-like planets are more likely to form around a metal-rich star. It also shows a decreasing trend in average stellar metallicity as the planetary mass increases. The DIP population clusters lie in between the super-Jupiter and brown dwarf populations.

It is also important to recognize that the composition of circumstellar material from which the planets are formed need not necessarily be the same as the composition of the parent star. The degree of similarity or difference would depend on how and where planets are formed, what stage of evolution they are in, and the disk mass and planet multiplicity. A clear picture is expected to emerge from ongoing high-contrast imaging surveys and future experiments aimed at searching for planets in wider orbits.

This work has made use of (a) ESO archival data that were observed under programs 192.C-0224, 098.C-0739, 266.D-5655, 094.A-9012, 084.C-1039, 074.C-0037, and 65.I-0404; (b) the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with the National Aeronautics and Space Administration; (c) the NASA Exoplanet Database, which is run by the California Institute of Technology under an Exoplanet Exploration Program contract with the National Aeronautics and Space Administration; and (d) the European Space Agency (ESA) space mission Gaia, the data from which were processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

Some initial test observations for this work were taken with the 2 m Himalayan Chandra Telescope at Hanle. The facilities at IAO and CREST are operated by the Indian Institute of Astrophysics, Bangalore. Furthermore, this work has made use of the NASA Exoplanet Database, which is run by the California Institute of Technology under an Exoplanet Exploration Program contract with the National Aeronautics and Space Administration. C.S. would also like to thank Aritra Chakrabarty at the Indian Institute of Astrophysics for the insightful discussion on the Bayesian analysis.

Software: astropy (Astropy Collaboration et al. 2013), iSpec (Blanco-Cuaresma et al. 2014a), emcee (Foreman-Mackey et al. 2013), scikit-learn (Pedregosa et al. 2011), IRAF (Tody 1986, 1993).