J. Astrophys. Astr. (June 2017) 38:19 © Indian Academy of Sciences
DOI 10.1007/s12036-017-9443-z
Metallicity of Sun-like G-stars that have Exoplanets
SHASHANKA R. GURUMATH1,∗, K. M. HIREMATH2 and V. RAMASUBRAMANIAN1
1Department of Physics, School of Advanced Sciences (SAS), VIT University, Vellore 632 014, India.
2Indian Institute of Astrophysics, Bangalore 560 034, India.
∗Corresponding author. E-mail: shashankgurumath@yahoo.in
MS received 10 June 2016; accepted 20 April 2017; published online 19 June 2017
Abstract. By considering the physical and orbital characteristics of G type stars and their exoplanets, we
examine the association between stellar mass and its metallicity that follows a power law. Similar relationship
is also obtained in case of single and multiplanetary stellar systems suggesting that, Sun′s present mass is
about 1% higher than the estimated value for its metallicity. Further, for all the stellar systems with exoplanets,
association between the planetary mass and the stellar metallicity is investigated, that suggests planetary mass
is independent of stellar metallicity. Interestingly, in case of multiplanetary systems, planetary mass is linearly
dependent on the stellar absolute metallicity, that suggests, metal rich stars produce massive (≥1 Jupiter mass)
planets compared to metal poor stars. This study also suggests that there is a solar system planetary missing
mass of ∼0.8 Jupiter mass. It is argued that probably 80% of missing mass is accreted onto the Sun and about
20% of missing mass might have been blown off to the outer solar system (beyond the present Kuiper belt)
during early history of solar system formation. We find that, in case of single planetary systems, planetary mass
is independent of stellar metallicity with an implication of their non-origin in the host star’s protoplanetary disk
and probably are captured from the space. Final investigation of dependency of the orbital distances of planets
on the host stars metallicity reveals that inward migration of planets is dominant in case of single planetary
systems supporting the result that most of the planets in single planetary systems are captured from the space.
Keywords. Sun: evolution—stars: chemical abundances—stars: metallicity—stars: planetary systems.
1. Introduction have a higher metallicity than the stars without planets
(Gonzalez et al. 2001b). However, low mass giant stars
Birth of a stellar system takes place in the nebula which (≤1.5M) with planets did not show any difference in
consists of gas and dust particles that are basic ingredi- their metallicity when compared with giant stars with-
ents for the formation of stars and planets. The amount out planets (Maldonado et al. 2013).
of gas, dust particles, chemical composition or metallic- Previous studies (Gonzalez 2000; Santos et al. 2000)
ity of the nebula play a significant role in the formation indicated that the detection of gas giants or hot Jupiters
of planetary system (Ksanfomality 2004; Moriarty et al. are more around the metal-rich stars than the metal-
2014; Reboussin et al. 2015). Hence, study of stellar poor stars. That means, formation of giant planet is low
metallicity and its relation with different physical char- around the metal-poor stars (Fischer & Valenti 2005).
acteristics of host stars and their planets may lead to Mordasini et al. (2012) showed that occurrence rate
better understanding of the planetary system formation. and mass of giant planets depend on the thickness and
Before the era of discovery of exoplanets, many plane- timescale of protoplanetary disk. On the other hand,
tary models concentrated mainly on the genesis of solar occurrence rate of terrestrial planets or low mass planets
system formation. The discovery of many exoplanetary is independent of the host star’s metallicity (Buchhave
systems (Boss et al. 2010; Lammer et al. 2010; Dressing et al. 2014). One explanation for the high mass plan-
& Charbonneau 2015) led to many new models (de Wit ets around the metal-rich stars is inward migration of
& Seager 2013; Kerr et al. 2015) that further improved planets during the early history of stellar system for-
the knowledge of physics of planetary formation. In mation (Dawson & Murray-Clay 2013). Due to inward
early studies, it was found that the stars with planets migration, high mass planets scatter the planetesimals
19 Page 2 of 17 J. Astrophys. Astr. (June 2017) 38:19
(or gas and dust particles) that are present in the pro- metallicity of host stars that have exoplanets, we try
toplanetary disk. These scattered planetesimals most to understand how the metal content of a stellar neb-
likely accrete on the host star’s convective envelope as ula might have affected the planetary formation, (ii)
a ‘pollution’ and hence, increases the stars metallicity we examine whether single and multiplanetary systems
(Vauclair & Vauclair 2014). During early evolutionary have similar mechanism of planetary formation or not,
stages, accreted mass mix deep inside a star, whereas, and the role of host stars’ metallicity in these mecha-
in later stages, accreted mass mix only in a shallow con- nisms, (iii) an attempt is made to confirm whether our
vective envelope. For example, the presence of 6Li in solar system is also governed by the same universal
the stellar system supports the accretion of planetary mechanism of planetary formation and, (iv) we inves-
mass on the host star (Reddy et al. 2002; Santos et al. tigate whether stellar metallicity [Fe/H] is affected by
2009; Mena et al. 2012). Hence, the effect of ‘pollution’ average galactic metallicity that in turn might have influ-
is one of the important factor that likely determines the enced the planetary formation. The plan of the present
final metallicity of host stars and, the massive planets study is as follows: description of the data used and the
near-by host star may be the reason for increase in the analysis are presented in section 2. The results with a
metallicity of host stars during the early history of stellar brief discussion are presented in section 3, followed by
system formation. conclusions in section 4.
Another explanation for high mass planets around
metal-rich stars is the metal-rich nebula from which
host stars and planets are formed (Gonzalez 2006). This 2. Data and analysis
implies that the metal-rich protoplanetary disk around
a host star (Gonzalez 2003; Bean et al. 2006) provides In order to examine the role of metallicity in the plane-
more gas and dust particles for the planetary formation. tary formation of Sun-like G stars, physical and orbital
Adibekyan et al. (2012) confirmed that the rate of plan- characteristics of exoplanets and their host stars of G
etary formation is high in the galactic-thick disk than type are considered from the website http://exoplanet.
in the galactic-thin disk. This study also suggests that eu/catalog/all_fields/. Many previous studies make use
when the iron metal content is less, other metals play of this catalog for understanding the physics of host
a major role in the planetary formation. The metal-rich stars, dynamics and atmospheres of their planets, etc.
disk with high concentration of Si, Ca, Mg, Al, etc. pro- For example, estimation of metallicity of host stars
vides a good platform for the planetary core formation (Lindgren et al. 2016), atmospheric (Walsh & Millar
(Bodaghee et al. 2003). In addition, formation of terres- 2011) and orbital (Antoniadou & Voyatzis 2016) studies
trial planets cannot be neglected around the metal-rich of exoplanets, etc. Hence, this data set is most reliable
stars (Wang & Fischer 2015), because, probability of to get answers for our aims.
formation of the solid core is high due to more number We consider 225 exoplanets that belong to 179 host
of dust particles in the disk, which eventually lead to stars. Out of 225 exoplanets, 139 are detected by radial
solid planets that are within the snow line. velocity method and the remaining are detected by tran-
The volatile elements like carbon compounds and sit method. Among these, majority (148) of stars are
oxygen help in the formation of gaseous envelope or single planetary hosts (only one planet for a star) and,
planetary atmospheres. Among various volatile materi- 31 (with 77 planets) are multiplanetary hosts (more
als, oxygen plays a major role in the planetary formation than one planet for a star). Although one can argue that
via ice accretion beyond the snow line and also by the single planetary hosts are due to limitations in detection
oxides of Si, Mg, Al, Ca, etc. (Brugamyer et al. 2011). techniques, at present it is not clear whether single plan-
The silicate grains provide a good platform for the plan- ets are really single planets or this is due to limitations
etary formation and these grains with accretion of icy of the detection. It is also not clear, due to limitations
mantle may grow into gas giants. Interestingly, there of observational detection, how much percentage of the
is no significant difference in the abundance of [C/Fe] data sample is due to the single planet. However, in this
and [O/Fe] in stars with planets and stars without planets study we assume that these are single planets.
(Gonzalez et al. 2001b; Da Silva et al. 2011). Although With the present precision of detection techniques,
contribution of these materials to metallicity of the host number of planets that are detected from space- and
star is insignificant, their major role in planetary forma- ground-based missions are given in Table 1. From the
tion cannot be neglected. distance measurements, we find that majority (171) of
With this brief introduction, the following are the the exoplanets are within the solar neighborhood (≤300
aims of the present study: (i) from the information of pc). Relevant data related to the physical characteristics
J. Astrophys. Astr. (June 2017) 38:19 Page 3 of 17 19
Table 1. Number of planets with dif- instruments, it is very difficult to precisely measure the
ferent exoplanetary detection missions. radial velocity or transit curves of the exoplanets that are
very far from the solar system. Hence, majority of exo-
Detection missions No. of planets planets appear to occur within the solar neighborhood
CoRoT 14 (≤ 300 pc). The Sun is situated in the galactic thin disk at
HAT-P 09 about 20 pc above the galactic mid-plane. The gradient
HIP 03 of radial variation of average metallicity in this galac-−1
HD catalog 125 tic thin disk is 0.07 dex kpc (Gonzalez et al. 2001a).
Kepler 28 It is interesting to check whether such a gradient of
TrES 02 metallicity is also true if star’s metallicity is influenced
WASP 29 by galactic metallicity that in turn might have affected
XO 01 the planetary formation. In order to check this reason-
Others 14 ing, irrespective of observed declinations (Dec.) and
right ascensions (RA), we combine different metallici-
ties and the same are plotted with respect to the observed
of planets and stars are presented in Table 2. As this exo- stellar distances from the Sun. With the present data
planetary catalog is a compilation of ground- and space- set, Fig. 1(b) illustrates the variation of stellar metal-
based observations, observers have used different sta- licity within the galactic thin disk. Since the majority
tistical techniques for estimating the error bars in the of stars are within 300 pc, from the slope of Fig. 1(b)
physical and orbital characteristics of exoplanets. For (∼0.08 dex kpc−1), one can say that variation of aver-
example, hybrid Markov chain Monte Carlo (Gregory age galactic metallicity within the thin disk is negligible
& Fischer 2010; Dumusque et al. 2014) and bootsrap in the solar neighborhood. Of course, this is also evident
(Barge et al. 2008) statistical method. However, basic from Fig. 2 wherein distribution of stars with metallic-
errors that affect different physical parameters of the ity for different galactic coordinates is illustrated. There
data are observational errors (Kovacset al. 2010; Wake- appears to be concentration of metal-deficient stars (that
ford et al. 2013). have exoplanets) near both the galactic poles. Figure 1
In Table 2, first two columns represent the name of and Fig. 2 show that observed exoplanetary systems
an exoplanet and its mass in terms of Jupiter’s mass. are within the proximity (∼2 kpc) of the Sun. Whereas,
Third and fourth columns represent the semi-major from 2–8 kpc, there is no observational evidence of
axis and eccentricity respectively. The fifth and sixth detection of exoplanets. Unless we have information
columns represent the stellar metallicity [Fe/H] and of observed exoplanetary systems from all parts of the
stellar mass in terms of the solar mass. Whereas, the galaxy, with the present dataset, it is difficult to con-
last column represents the stellar distance in parsec clude whether influence of galactic metallicity on the
(pc). planetary formation exists or not.
3.1 Stellar mass versus metallicity
3. Results and discussion
Previous studies (Winn & Fabrycky 2015 and references
Before examining a relationship between the stellar therein) show that metal-rich stars more likely harbor
(planetary) mass with stellar metallicity, let us examine the planets. In addition, abundance of metallicity of stars
how far the exoplanets are located in the solar neighbor- with planets are more than the abundance of metallicity
hood and, if any influence of average galactic metallicity of stars without planets (Mortier et al. 2013). In these
on the stellar metallicity irrespective of galactic latitude studies, results are obtained from an analysis of the host
and longitude. Figure 1(a) illustrates the distribution stars of all spectral types. However, it is interesting to
of planets with their distances from the Sun. The x- know whether each spectral type, such as Sun-like G
axis represents the distances of host stars from the Sun stars also follows the same trend or not. Importantly, it
and y-axis represents the number of planets. Similarly, is essential to understand the behavior of stellar metal-
Fig. 1(b) illustrates the distribution of stellar metallici- licity in both single and multiplanetary systems. In order
ties with their distances from the Sun. It is obvious and to assert these ideas, in Fig. 3(a) and 3(b) we examine
not surprising from Fig. 1(a) that exponential decrease a relationship between stellar mass and stellar metallic-
of number of planets with the distance is due to faint- ity for all the planetary systems, irrespective of whether
ness of the observed stars. That means, with the present they are single or multiplanetary systems. In Fig. 3(a),
19 Page 4 of 17 J. Astrophys. Astr. (June 2017) 38:19
Table 2. Physical and orbital characteristics of the host stars and their exoplanets.
Name Mp a [Fe/H] M Distance
(MJ) (AU) (dex) (M) (pc)
47 Uma b 2.530(±0.065) 2.100 0(±0.07) 1.03(±0.050) 13.97
47 Uma c 0.540(±0.069) 3.600 0(±0.07) 1.03(±0.05) 13.97
47 Uma d 1.640(±0.385) 11.60 0(±0.07) 1.03(±0.050) 13.97
51 Peg b 0.468(±0.007) 0.052 0.2(±0.07) 1.11(±0.060) 14.70
61 Vir b 0.016(±0.001) 0.050 −0.01(±−) 0.95(±0.030) 8.52
61 Vir c 0.057(±0.003) 0.217 −0.01(±−) 0.95(±0.030) 8.52
61 Vir d 0.072(±0.008) 0.476 −0.01(±−) 0.95(±0.030) 8.52
70 Vir b 6.600(±0.660) 0.480 −0.11(±−) 0.92(±0.046) 22.00
CoRoT-1 b 1.030(±0.120) 0.025 0.06(±0.07) 0.95(±0.150) 460.00
CoRoT-12 b 0.917(±0.067) 0.040 0.16(±0.10) 1.07(±0.072) 1150.00
CoRoT-13 b 1.308(±0.066) 0.051 0.01(±0.07) 1.09(±0.020) 1310.00
CoRoT-16 b 0.535(±0.085) 0.061 0.19(±0.06) 1.09(±0.078) 840.00
CoRoT-17 b 2.430(±0.160) 0.046 0(±0.10) 1.04(±0.100) 920.00
CoRoT-18 b 3.470(±0.380) 0.029 −0.10(±0.10) 0.95(±0.150) 870.00
CoRoT-2 b 3.310(±0.160) 0.028 −0.04(±0.08) 0.97(±0.060) 300.00
CoRoT-20 b 4.240(±0.230) 0.090 0.14(±0.12) 1.14(±0.080) 1230.00
CoRoT-22 b 0.038(±0.035) 0.092 0.17(±0.09) 1.09(±0.049) 592.00
CoRoT-23 b 2.800(±0.250) 0.047 0.05(±0.10) 1.14(±0.080) 600.00
CoRoT-25 b 0.270(±0.040) 0.057 −0.01(±0.13) 1.09(±0.080) 1000
CoRoT-26 b 0.520(±0.050) 0.052 0.01(±0.13) 1.09(±0.060) 1670.00
CoRoT-27 b 10.390(±0.550) 0.047 0.10(±0.10) 1.05(±0.110) –
CoRoT-9 b 0.840(±0.070) 0.407 −0.01(±0.006) 0.99(±0.040) 460.00
GJ 3021 b 3.370(±0.090) 0.490 0.10(±0.08) 0.90(±0.045) 17.62
HAT-P-1 b 0.525(±0.019) 0.055 0.13(±0.008) 1.15(±0.052) 139.00
HAT-P-15 b 1.946(±0.066) 0.096 0.22(±0.08) 1.01(±0.043) 190.00
HAT-P-21 b 4.063(±0.161) 0.049 0.01(±0.08) 0.94(±0.042) 254.00
HAT-P-22 b 2.147(±0.061) 0.041 0.24(±0.08) 0.91(±0.035) 82.00
HAT-P-23 b 2.090(±0.110) 0.023 0.16(±0.03) 1.13(±0.050) 393.00
HAT-P-25 b 0.567(±0.056) 0.046 0.31(±0.08) 1.01(±0.032) 297.00
HAT-P-27 b 0.660(±0.033) 0.040 0.29(±0.10) 0.94(±0.035) 204.00
HAT-P-28 b 0.626(±0.037) 0.043 0.12(±0.08) 1.02(±0.047) 395.00
HAT-P-38 b 0.267(±0.020) 0.052 0.06(±0.10) 0.88(±0.044) 249.00
HD 102117 b 0.172(±0.018) 0.153 0.30(±0.03) 1.03(±0.050) 42.00
HD 106252 b 7.560(±0.756) 2.700 −0.07 0.96(±0.048) 37.44
HD 106270 b 11.000(±0.800) 4.300 0.08(±0.03) 1.32(±0.092) 84.90
HD 10697 b 6.380(±0.530) 2.160 0.10(±0.06) 1.15(±0.030) 32.56
HD 108874 b 1.360(±0.130) 1.051 0.14 1.00(±0.050) 68.50
HD 108874 c 1.018(±0.300) 2.680 0.14 1.00(±0.050) 68.50
HD 109246 b 0.770(±0.090) 0.330 0.10 1.01(±0.110) 65.60
HD 114729 b 0.840(±0.084) 2.080 −0.22 0.93(±0.046) 35.00
HD 11506 b 3.440(±0.685) 2.430 0.31(±0.03) 1.19(±0.020) 53.82
HD 11506 c 0.820(±0.405) 0.639 0.31(±0.03) 1.19(±0.020) 53.82
HD 117207 b 2.060(±0.206) 3.780 0.27 1.07(±0.053) 33.00
HD 117618 b 0.178(±0.020) 0.176 0.04 1.05(±0.052) 38.00
HD 117618 c 0.200(±0.100) 0.930 0.04 1.05(±0.052) 38.00
HD 11964 b 0.622(±0.056) 3.160 0.17 1.12(±0.056) 33.98
HD 11964 c 0.079(±0.010) 0.229 0.17 1.12(±0.056) 33.98
HD 125612 b 3.000(±0.300) 1.370 0.24(±0.03) 1.10(±0.070) 52.82
HD 125612 c 0.058(±0.005) 0.050 0.24(±0.03) 1.10(±0.070) 52.82
HD 125612 d 7.200(±0.720) 4.200 0.24(±0.03) 1.10(±0.070) 52.82
J. Astrophys. Astr. (June 2017) 38:19 Page 5 of 17 19
Table 2. Continued.
Name Mp a [Fe/H] M Distance
(MJ) (AU) (dex) (M) (pc)
HD 12661 b 2.300(±0.230) 0.830 0.29(±0.05) 1.07(±0.053) 37.16
HD 12661 c 1.570(±0.157) 2.560 0.29(±0.05) 1.07(±0.053) 37.16
HD 134987 b 1.590(±0.020) 0.810 0.25(±0.02) 1.07(±0.080) 22.20
HD 134987 c 0.820(±0.030) 5.800 0.25(±0.02) 1.07(±0.080) 22.20
HD 136418 b 2.000(±0.100) 1.320 −0.07(±0.03) 1.33(±0.090) 98.20
HD 13931 b 1.880(±0.150) 5.150 0.03(±0.04) 1.02(±0.020) 44.20
HD 141937 b 9.700(±0.970) 1.520 0.11 1.10(±0.055) 33.46
HD 142 b 1.250(±0.150) 1.020 0.04(±0.05) 1.10(±0.220) 20.60
HD 142 c 5.300(±0.700) 6.800 0.04(±0.05) 1.10(±0.220) 20.60
HD 142415 b 1.620(±0.162) 1.050 0.21(±0.05) 1.09(±0.054) 34.20
HD 145377 b 5.760(±0.100) 0.450 0.12(±0.01) 1.12(±0.030) 57.70
HD 1461 b 0.023(±0.003) 0.063 0.19(±0.01) 1.08(±0.040) 23.40
HD 1461 c 0.018(±0.002) 0.111 0.19(±0.01) 1.08(±0.040) 23.40
HD 147513 b 1.210(±0.121) 1.320 −0.03 0.92(±0.046) 12.90
HD 149026 b 0.356(±0.012) 0.042 0.36(±0.05) 1.30(±0.100) 78.90
HD 150706 b 2.710(±0.900) 6.700 −0.13 0.94(±0.800) 27.20
HD 154672 b 5.020(±0.170) 0.600 0.26(±0.04) 1.06(±0.090) 65.80
HD 16141 b 0.215(±0.030) 0.350 0.02 1.01(±0.050) 35.90
HD 16175 b 4.400(±0.440) 2.100 0.23(±0.07) 1.35(±0.090) 59.80
HD 163607 b 0.770(±0.040) 0.360 0.21(±0.03) 1.09(±0.020) 69.00
HD 163607 c 2.290(±0.160) 2.420 0.21(±0.03) 1.09(±0.020) 69.00
HD 164509 b 0.480(±0.090) 0.875 0.21(±0.03) 1.13(±0.020) 52.00
HD 168443 b 7.659(±0.097) 0.293 0.04(±0.03) 0.99(±0.019) 37.38
HD 168746 b 0.230(±0.023) 0.065 −0.06(±0.05) 0.88(±0.010) 43.12
HD 170469 b 0.670(±0.067) 2.240 0.30(±0.03) 1.14(±0.020) 64.97
HD 171028 b 1.980(±0.198) 1.320 −0.49(±0.02) 0.99(±0.080) 90.00
HD 17156 b 3.191(±0.033) 0.162 0.24(±0.05) 1.27(±0.018) 78.24
HD 179079 b 0.080(±0.008) 0.110 0.29(±0.04) 1.08(±0.100) 63.69
HD 183263 b 3.670(±0.300) 1.510 0.30 1.17(±0.058) 53.00
HD 183263 c 3.820(±0.590) 4.250 0.30 1.17(±0.058) 53.00
HD 185269 b 0.940(±0.094) 0.077 0.11(±0.05) 1.28(±0.100) 47.00
HD 187123 b 0.520(±0.040) 0.042 0.16 1.06(±0.053) 50.00
HD 187123 c 1.990(±0.250) 4.890 0.16 1.06(±0.053) 50.00
HD 188015 b 1.260(±0.126) 1.190 0.29 1.09(±0.054) 52.60
HD 190360 b 1.502(±0.130) 3.920 0.24(±0.08) 1.04(±0.052) 15.89
HD 190360 c 0.057(±0.015) 0.128 0.24(±0.08) 1.04(±0.052) 15.89
HD 195019 b 3.700(±0.300) 0.138 0.08(±0.04) 1.06(±0.053) 18.77
HD 196050 b 2.830(±0.283) 2.470 0.23 1.17(±0.058) 46.90
HD 202206 c 2.440(±0.244) 2.550 0.37(±0.07) 1.13(±0.056) 46.34
HD 20367 b 1.070(±0.107) 1.250 0.10 1.04(±0.060) 27.00
HD 2039 b 4.900(±1.000) 2.200 0.10(±0.16) 0.98(±0.050) 89.80
HD 207832 b 0.560(±0.045) 0.570 0.06 0.94(±0.100) 54.40
HD 207832 c 0.730(±0.115) 2.112 0.06 0.94(±0.100) 54.40
HD 20794 b 0.008(±0.0009) 0.120 −0.38(±0.06) 0.85(±0.040) 6.06
HD 20794 c 0.007(±0.0013) 0.203 −0.38(±0.06) 0.85(±0.040) 6.06
HD 20794 d 0.015(±0.0019) 0.349 −0.38(±0.06) 0.85(±0.040) 6.06
HD 208487 b 0.413(±0.050) 0.510 −0.06(±0.05) 1.30(±0.065) 45.00
HD 209458 b 0.690(±0.017) 0.047 0.02(±0.05) 1.14(±0.022) 47.00
HD 210277 b 1.230(±0.030) 1.100 0.19(±0.04) 1.09(±0.054) 21.29
HD 212771 b 2.300(±0.400) 1.220 −0.21(±0.03) 1.15(±0.080) 131.00
HD 213240 b 4.500(±0.450) 2.030 0.16 1.22(±0.061) 40.75
19 Page 6 of 17 J. Astrophys. Astr. (June 2017) 38:19
Table 2. Continued.
Name Mp a [Fe/H] M Distance
(MJ) (AU) (dex) (M) (pc)
HD 216435 b 1.260(±0.130) 2.560 0.24 1.30 33.30
HD 216437 b 1.820(±0.182) 2.320 0.25 1.06(±0.053) 26.50
HD 217107 b 1.330(±0.050) 0.073 0.37(±0.05) 1.02(±0.051) 19.72
HD 217107 c 2.490(±0.250) 5.270 0.37(±0.05) 1.02(±0.051) 19.72
HD 219828 b 0.085(±0.008) 0.052 0.19(±0.03) 1.24(±0.062) 81.10
HD 222155 b 1.900(±0.600) 5.100 −0.11(±0.05) 1.13(±0.110) 49.10
HD 222582 b 7.750(±0.650) 1.350 −0.02 0.99(±0.049) 42.00
HD 224693 b 0.710(±0.071) 0.233 0.34(±0.03) 1.33(±0.100) 94.00
HD 28185 b 5.700(±0.570) 1.030 0.24 1.24(±0.062) 39.40
HD 28254 b 1.160(±0.080) 2.150 0.36(±0.03) 1.06(±0.053) 56.20
HD 290327 b 2.540(±0.155) 3.430 −0.11(±0.02) 0.90(±0.045) 54.90
HD 30177 b 7.700(±1.500) 2.600 0.19(±0.09) 0.95(±0.050) 55.00
HD 30669 0.470(±0.060) 2.690 0.13(±0.06) 0.92(±0.030) 57.00
HD 33283 b 0.330(±0.033) 0.168 0.36(±0.05) 1.24(±0.100) 86.00
HD 34445 b 0.790(±0.070) 2.070 0.14(±0.04) 1.07(±0.020) 46.50
HD 37124 b 0.675(±0.017) 0.533 −0.44 0.83(±0.041) 33.00
HD 37124 c 0.652(±0.052) 1.710 −0.44 0.83(±0.041) 33.00
HD 37124 d 0.696(±0.059) 2.807 −0.44 0.83(±0.041) 33.00
HD 38529 b 0.780(±0.078) 0.131 0.27(±0.05) 1.48(±0.050) 39.28
HD 39091 b 10.300(±1.030) 3.280 0.09 1.10(±0.055) 18.32
HD 4208 b 0.800(±0.080) 1.700 −0.28 0.87(±0.043) 33.90
HD 4308 b 0.040(±0.005) 0.118 −0.34 0.85(±0.042) 21.90
HD 44219 b 0.580(±0.050) 1.190 0.03(±0.01) 1.00(±0.050) 50.43
HD 45350 b 1.790(±0.140) 1.920 0.29 1.02(±0.051) 49.00
HD 49674 b 0.100(±0.010) 0.058 0.25 1.07(±0.053) 40.70
HD 50499 b 1.710(±0.200) 3.860 0.23 1.27(±0.063) 47.26
HD 52265 b 1.050(±0.030) 0.500 0.21(±0.06) 1.20(±0.060) 28.00
HD 52265 c 0.350(±0.090) 0.316 0.21(±0.06) 1.20(±0.060) 28.00
HD 564 b 0.330(±0.030) 1.200 0.13(±0.06) 0.92(±0.030) 54.00
HD 6434 b 0.390(±0.039) 0.140 −0.52 0.79(±0.039) 40.32
HD 6718 b 1.560(±0.105) 3.560 −0.06(±0.02) 0.96(±0.048) 55.90
HD 68988 b 1.900(±0.190) 0.071 0.24 1.20(±0.060) 58.00
HD 70642 b 2.000(±0.200) 3.300 0.16(±0.02) 1.00(±0.050) 28.80
HD 72659 b 3.150(±0.140) 4.740 −0.02(±0.01) 0.95(±2.000) 49.80
HD 73267 b 3.060(±0.070) 2.198 0.03(±0.02) 0.89(±0.030) 54.91
HD 73526 b 2.900(±0.200) 0.660 0.25(±0.05) 1.08(±0.050) 99.00
HD 73526 c 2.500(±0.300) 1.050 0.25(±0.05) 1.08(±0.050) 99.00
HD 73534 b 1.150(±0.115) 3.150 0.16(±0.04) 1.29(±0.100) 96.99
HD 74156 b 1.880(±0.030) 0.294 0.13 1.24(±0.040) 64.56
HD 74156 c 8.030(±0.120) 3.400 0.13 1.24(±0.040) 64.56
HD 75289 b 0.470(±0.047) 0.046 0.29 1.05(±0.052) 28.94
HD 75898 b 2.510(±0.251) 1.190 0.27(±0.05) 1.28(±0.130) 80.58
HD 76700 b 0.230(±0.023) 0.049 0.14 1(±0.050) 59.70
HD 81040 b 6.860(±0.710) 1.940 −0.16(±0.06) 0.96(±0.040) 32.56
HD 82886 b 1.300(±0.100) 1.650 −0.31(±0.03) 1.06(±0.074) 125.00
HD 82943 b 4.800(±0.480) 1.190 0.32 1.18(±0.059) 27.46
HD 82943 c 4.780(±0.478) 0.746 0.32 1.18(±0.059) 27.46
HD 82943 d 0.290(±0.031) 2.145 0.32 1.18(±0.059) 27.46
HD 8535 b 0.680(±0.055) 2.450 0.02 1.13(±0.056) 52.50
HD 88133 b 0.300(±0.030) 0.047 0.34(±0.04) 1.20(±0.200) 74.50
J. Astrophys. Astr. (June 2017) 38:19 Page 7 of 17 19
Table 2. Continued.
Name Mp a [Fe/H] M Distance
(MJ) (AU) (dex) (M) (pc)
HD 89307 b 2.000(±0.400) 3.340 −0.14(±0.04) 1.02(±0.040) 30.90
HD 92788 b 3.860(±0.386) 0.970 0.32 1.13(±0.056) 32.82
HD 92788 c 0.900(±0.300) 0.600 0.32 1.13(±0.056) 32.82
HD 9446 b 0.700(±0.060) 0.189 0.09(±0.05) 1.00(±0.100) 53.00
HD 9446 c 1.820(±0.170) 0.654 0.09(±0.05) 1.00(±0.100) 53.00
HD 96167 b 0.680(±0.180) 1.300 0.09(±0.05) 1.31(±0.090) 84.00
HIP 14810 b 3.880(±0.320) 0.069 0.26(±0.03) 0.99(±0.040) 52.90
HIP 14810 c 1.280(±0.100) 0.545 0.26(±0.03) 0.99(±0.040) 52.90
HIP 14810 d 0.570(±0.052) 1.890 0.26(±0.03) 0.99(±0.040) 52.90
HR 810 b 2.260(±0.180) 0.925 0.25 1.11(±0.070) –
Kepler-10 b 0.010(±0.001) 0.016 −0.15(±0.04) 0.91(±0.021) 173.00
Kepler-10 c 0.054(±0.005) 0.241 −0.15(±0.04) 0.91(±0.021) 173.00
Kepler-11 b 0.005(±0.003) 0.091 0.0 0.95(±0.100) –
Kepler-11 c 0.009(±0.007) 0.106 0.0 0.95(±0.100) –
Kepler-11 d 0.022(±0.003) 0.159 0.0 0.95(±0.100) –
Kepler-11 e 0.030(±0.005) 0.194 0.0 0.95(±0.100) –
Kepler-11 f 0.006(±0.002) 0.250 0.0 0.95(±0.100) –
Kepler-11 g 0.950(±0.475) 0.462 0.0 0.95(±0.100) –
Kepler-12 b 0.431(±0.041) 0.055 0.07(±0.04) 1.16(±0.054) –
Kepler-17 b 2.450(±0.014) 0.025 0.26(±0.10) 1.16(±0.060) 800
Kepler-20 b 0.026(±0.006) 0.045 0.02(±0.04) 0.91(±0.035) 290.00
Kepler-20 c 0.049(±0.007) 0.093 0.02(±0.04) 0.91(±0.035) 290.00
Kepler-20 d 0.060(±0.006) 0.345 0.02(±0.04) 0.91(±0.035) 290.00
Kepler-20 e 0.009(±0.0009) 0.050 0.02(±0.04) 0.91(±0.035) 290.00
Kepler-20 f 0.045(±0.004) 0.110 0.02(±0.04) 0.91(±0.035) 290.00
Kepler-22 b 0.110(±0.011) 0.849 −0.29(±0.06) 0.97(±0.060) 190.00
Kepler-4 b 0.082(±0.0128) 0.045 0.17(±0.06) 1.22(±0.091) 550.00
Kepler-41 b 0.490(±0.090) 0.029 −0.09(±0.16) 0.94(±0.090) 730.00
Kepler-412 b 0.939(±0.085) 0.029 0.27(±0.12) 1.16(±0.091) 1056.00
Kepler-43 b 3.230(±0.190) 0.044 0.33(±0.11) 1.32(±0.090) 1950.00
Kepler-44 b 1.020(±0.070) 0.045 0.26(±0.10) 1.19(±0.100) 2250.00
Kepler-66 b 0.310(±0.070) 0.135 0.01(±0.003) 1.03(±0.051) 1107.00
Kepler-67 b 0.310(±0.060) 0.117 0.01(±0.003) 0.86(±0.043) 1107.00
Kepler-75 b 9.900(±0.500) 0.080 −0.07(±0.15) 0.88(±0.060) 1140.00
Kepler-77 b 0.430(±0.032) 0.045 0.20(±0.05) 0.95(±0.040) 570.00
Kepler-78 b 0.005(±0.001) 0.010 −0.14(±0.08) 0.81(±0.050) –
KOI-192 b 0.290(±0.090) 0.091 −0.19(±0.07) 0.96(±0.060) 1100.00
KOI-195 b 0.340(±0.080) 0.041 −0.21(±0.08) 0.91(±0.060) 880.00
mu Ara b 1.676(±0.167) 1.500 0.28(±0.04) 1.08(±0.050) 15.30
mu Ara c 0.033(±0.003) 0.090 0.28(±0.04) 1.08(±0.050) 15.30
mu Ara d 0.521(±0.052) 0.921 0.28(±0.04) 1.08(±0.050) 15.30
mu Ara e 1.814(±0.181) 5.235 0.28(±0.04) 1.08(±0.050) 15.30
TrES-2 1.253(±0.052) 0.035 −0.15(±0.10) 0.98(±0.062) 220.00
TrES-3 1.910(±0.065) 0.022 −0.19(±0.08) 0.92(±0.040) –
WASP-104 b 1.272(±0.047) 0.029 0.32(±0.09) 1.02(±0.090) 143.00
WASP-110 b 0.515(±0.064) 0.045 −0.06(±0.10) 0.89(±0.072) 320.00
WASP-112 b 0.880(±0.120) 0.038 −0.64(±0.15) 0.80(±0.073) 450.00
WASP-12 b 1.404(±0.099) 0.022 0.30(±0.10) 1.35(±0.140) 427.00
WASP-16 b 0.855(±0.059) 0.042 0.01(±0.10) 1.02(±0.101) –
WASP-19 b 1.114(±0.040) 0.016 0.02(±0.09) 0.90(±0.045) –
WASP-21 b 0.300(±0.010) 0.052 −0.40(±0.10) 1.01(±0.025) 230.00
19 Page 8 of 17 J. Astrophys. Astr. (June 2017) 38:19
Table 2. Continued.
Name Mp a [Fe/H] M Distance
(MJ) (AU) (dex) (M) (pc)
WASP-25 b 0.580(±0.040) 0.047 −0.05(±0.10) 1.00(±0.030) 169.00
WASP-26 b 1.028(±0.021) 0.039 −0.02(0.09) 1.12(±0.030) 250.00
WASP-32 b 3.600(±0.070) 0.039 −0.13(±0.10) 1.10(±0.030) –
WASP-34 b 0.590(±0.010) 0.052 −0.02(±0.10) 1.01(±0.070) 120.00
WASP-36 b 2.279(±0.068) 0.026 −0.31(±0.12) 1.02(±0.032) 450.00
WASP-37 b 1.800(±0.170) 0.043 −0.40(±0.12) 0.84(±0.040) 338.00
WASP-39 b 0.280(±0.030) 0.048 −0.12(±0.10) 0.93(±0.030) 230.00
WASP-4 b 1.237(±0.060) 0.023 −0.03(±0.09) 0.93(±0.050) 300.00
WASP-41 b 0.920(±0.070) 0.040 −0.08(±0.09) 0.95(±0.090) 180.00
WASP-44 b 0.889(±0.062) 0.034 0.06(±0.10) 0.95(±0.034) –
WASP-46 b 2.101(±0.073) 0.024 −0.37(±0.13) 0.95(±0.034) –
WASP-47 b 1.140(±0.050) 0.052 0.18(±0.07) 1.08(±0.370) 200.00
WASP-5 b 1.637(±0.082) 0.027 0.09(±0.09) 1.00(±0.060) 297.00
WASP-50 b 1.437(±0.068) 0.029 −0.12(±0.08) 0.86(±0.057) 230.00
WASP-58 b 0.890(±0.070) 0.056 −0.45(±0.09) 0.94(±0.100) 300.00
WASP-6 b 0.503(±0.028) 0.042 −0.20(±0.09) 0.88(±0.080) 307.00
WASP-63 b 0.380(±0.030) 0.057 0.08(±0.07) 1.32(±0.050) 330.00
WASP-8 b 2.244(±0.086) 0.080 0.17(±0.07) 1.03(±0.050) 87.00
WASP-95 b 1.130(±0.070) 0.034 0.14(±0.16) 1.11(±0.090) –
WASP-96 b 0.480(±0.030) 0.045 0.14(±0.19) 1.06(±0.090) –
WASP-97 b 1.320(±0.050) 0.033 0.23(±0.11) 1.12(±0.060) –
WASP-98 b 0.830(±0.070) 0.036 −0.6(±0.19) 0.69(±0.060) –
XO-5 b 1.077(±0.037) 0.048 0.18(±0.03) 0.88(±0.030) –
(a) (b)
Figure 1. (a) The distribution of planets versus their host star’s distance from the Solar system. In this figure, x-axis is
binned with a size of 50 pc. (b) The dependency of observed stellar metallicity with the host star’s distance from the Solar
system for all planetary systems.
x-axis represents the observed metallicity with a bin is a logarithmic value of ratio of star’s [Fe/H] to Sun’s
size of 0.1 dex in which stellar masses are collected and, [Fe/H]. In case, there is a linear relationship between
average and standard deviations (σ ) are computed. Error host star’s metallicity and different physical parameters
in each bin is the estimated from the ratio √σ (where of their respective host star and planets, then logarith-
n
n is the number of data points in each bin). Conven- mic values of metallicity have to be converted into
tional usage is that, observed metallicity of a host star absolute values. Now onwards this transformation from
J. Astrophys. Astr. (June 2017) 38:19 Page 9 of 17 19
Figure 2. The distribution of stars (that harbor planets) with metallicity for different galactic coordinates within the observed
distance of 2.1 kpc.
logarithmic scale to linear scale is called as absolute nebula, the rate of formation of a central star (or accre-
metallicity and is denoted as abs[Fe/H]. tion of mass on the central star) is much higher than the
In Fig. 3(b), we illustrate a relationship between the rate of formation (or accretion of mass on the central
stellar mass and absolute metallicity, where the absolute star) in a metal-poor nebula (Jones et al. 2016). The
metallicity values are binned with a size of 0.25. The accretion process helps in acquiring more mass (i.e.,
average and standard deviations σ of stellar masses in more gas and dust particles that increases the chemical
each bin are calculated as explained earlier. Errors in composition) by a central star. Hence, the metallicity of
each bin are estimated from the ratio √σ . a host star is directly proportional to the stellar mass in
n
Compared to a relationship between stellar mass and logarithmic scale.
absolute metallicity (Fig. 3(b)), we find a strong rela- As explained in the Introduction, other plausible
tionship between logarithmic stellar mass and observed interpretation is that the accretion of disk or protoplan-
metallicity [Fe/H] (Fig. 3(a)) with a best fit of the fol- etary material or inward migration of planets add dust
lowing form: materials on the central star as a ‘pollution’ that ulti-
( ) mately increases the stellar metallicity. On the other
M = ± hand, one can also argue that accretion of mass on alog (0.007 0.006)
M central star during later evolutionary stages may not
+ (0.165 ± 0.026)[Fe/H], (1) increase the central mass substantially. Therefore, the
effect of ‘pollution’ (accretion of mass) on the stellar
where M is the stellar mass in terms of Sun’s mass M. mass is negligible, yet one can observe from Fig. 3(a)
We conclude that a relationship illustrated in Fig. 3(a) that metallicity increases as the stellar mass increase.
is better than a relationship illustrated in Fig. 3(b) for Thus, one may conclude that contribution to the final
the following reasons: (i) high correlation coefficient stellar metallicity from ‘pollution’ is small and most of
(99%) and (ii) small value of chi-square 1.376. Hence, the stellar metallicity is likely to be of primordial com-
it is concluded that there exists a power law relationship position of a nebula (Santos et al. 2004).
between the stellar mass and the observed metallicity. As the majority of stars in this analysis are single
One can notice from Fig. 3(a) that, the host star’s planetary systems, it is not clear whether multiplane-
metallicity increases non-linearly with increase in stel- tary systems follow a similar power law relationship.
lar mass. One can interpret this result as the metal rich Thus, in order to delineate this combined data bias,
stars are most likely originated in metal-rich disks. Due in the following section, we investigate the stellar
to high friction of dust and gas particles in a metal-rich mass-metallicity relationship separately for single and
19 Page 10 of 17 J. Astrophys. Astr. (June 2017) 38:19
(a) (b)
Figure 3. (a) The dependency of logarithmic stellar mass with the observed metallicity. The metallicity is binned with a
size of 0.1 dex. (b) The dependency of stellar mass with the absolute metallicity for all planetary systems. The metallicity is
binned with a size of 0.25. In both the figures, continuous line is a best least square fit between both the variables.
multiplanetary systems. Another aim of classification on the Sun (Melendez et al. 2009), that might have
of this data is to examine whether single and multiplan- resulted in a slight increase in the Sun’s mass. In case we
etary systems originate in different ways or not. Hence, accept this result, one can also estimate the amount of
we investigate the relationship between stellar mass and Sun’s mass for the present metallicity, which is found to
metallicity for both single and multiplanetary systems be ∼0.995M from equation (2) and ∼0.962M from
in linear and non linear scales. equation (3). Hence, by accepting a value from a best
fit (equation (2)), present mass of the Sun is about 1%
3.1.1 Stellar mass versus metallicity: Multiplanetary higher than the original mass.
systems. In case of multiplanetary systems, Fig-
ures 4(a) and 4(b) show the variations of stellar mass
with observed and absolute metallicity respectively, 3.1.2 Stellar mass versus metallicity: Single planetary
with the best fits as follows: systems. Similar plots for single planetary systems are
M illustrated in Figures 4(c) and 4(d) respectively. In this =(0.995 ± 0.022)+(0.396 ± 0.096)[Fe/H] (2) case the best fit is obtained between the stellar mass and
M absolute metallicity, except that the stars that have same
and metallicity as those of multiplanetary systems produce
M = ± + ± massive planets. Hence, these results imply that the ori-(0.801 0.012) (0.161 0.022)abs[Fe/H].
M gin and formation of single and multiplanetary systems
(3) appear to be entirely different.
Coefficients of different linear and non linear laws
Among both the fits, if we accept χ2 as a constraint that show the dependency of stellar mass on its metal-
on goodness of fit, stellar mass versus observed metal- licity are summarized in Table 3. The first column of
licity is a best fit (equation (2)). Both these relationships Table 3 represents the different laws of fit, second and
show a clear increasing trend between stellar mass and third columns represent the intercept (C1) and ratio of
its metallicity. In Figures 4(a) and 4(b), the symbol  error in the intercept with respect to values of intercept
represents metallicity of the Sun. One can notice from (| δC1C1 |) respectively. The fourth and fifth columns rep-
both the figures that the Sun’s mass is slightly higher resent the slope (C2) and the ratio of error in the slope
than the fitted line. This slight higher mass of the Sun with respect to values of slope (| δC2C2 |) respectively, fol-
might be due to ‘pollution’ from the solar system ter- lowed by chi-square (a measure of goodness of fit) in the
restrial planets. In other words, during the early history sixth column for all planetary systems. Similar results
of the solar system formation, dust and gas materials are presented in other columns that represent the single
in the vicinity of the Sun might have been accreted and multiplanetary systems respectively.
J. Astrophys. Astr. (June 2017) 38:19 Page 11 of 17 19
(a) (b)
(c) (d)
Figure 4. For multiplanetary systems, (a) and (b) illustrate the dependency of stellar mass with the observed and absolute
metallicity respectively. For single planetary systems, (c) and (d) illustrate the dependency of stellar mass with the observed
and absolute metallicity respectively. In all the plots, continuous line is a best least square fit. In (a) and (b), metallicity of the
Sun is represented by .
Table 3. Stellar mass versus metallicity.
Different laws All systems Multiplanetary systems Single planetary systems
C1 | δC1 | C2 | δC2 | χ2 C1 | δC1 | C2 | δC2 2C1 C2 C1 C2 | χ C1 | δC1C1 | C2 | δC2 2C2 | χ
Linear–linear 0.855 0.018 0.147 0.081 10.100 0.801 0.014 0.161 0.136 1.35 0.858 0.025 0.156 0.108 1.693
Linear–log 1.021 0.005 0.377 0.066 7.831 0.995 0.022 0.396 0.242 0.50 1.036 0.007 0.370 0.083 14.878
Log–log 0.007 0.857 0.165 0.157 1.376 −0.003 7.333 0.173 0.578 0.10 0.014 0.571 0.159 0.201 2.806
3.2 Dependence of metallicity with the planetary planets are skewed Gaussian distributions with a peak
physical properties around 0.0 to 0.2 dex in case of observed metallicity
(Fig. 5(a)) and around 1.0 to 1.5 in case of absolute
3.2.1 Occurrence rates of single and multiplanetary metallicity (Fig. 5(b)). For both Figures 5(a) and 5(b),
systems. In order to examine the occurrence rate of best fits yield the lognormal and normal (Gaussian)
planets with metallicity, the number of planets in each distributions respectively. This apparent result strongly
bin is illustrated in Fig. 5 against the stellar metallicity suggests that the occurrence rate of planets with stel-
for both observed and absolute values. One can notice lar metallicity is a random phenomenon. This picture
from Figures 5(a) and 5(b) that the occurrence rates of changes when we classify the data into two parts: (i)
19 Page 12 of 17 J. Astrophys. Astr. (June 2017) 38:19
(a) (b)
(c) (d)
(e) (f)
Figure 5. Histograms representation of number of the planets versus the stellar metallicity. (a) and (b) The dependency of
the number of planets with the observed and absolute metallicity for all the planetary systems. (c) and (d) The dependency of
the number of planets with the observed and absolute metallicity for the multiplanetary systems. (e) and (f) The dependency
of the number of planets with the observed and absolute metallicity for the single planetary systems. The bin sizes are 0.1
dex and 0.2 in case of observed and absolute metallicity respectively.
multiplanetary systems and (ii) single planetary sys- variables. However, due to low statistics in the region
tems. As for multiplanetary systems, occurrence rate of of low metallicity ([Fe/H] < 0 or abs[Fe/H] < 1),
planets with metallicity is not a random phenomenon, with a caveat we conclude that more number of data-
and we get a power-law relationship between both the points are required to confirm an apparent power law
J. Astrophys. Astr. (June 2017) 38:19 Page 13 of 17 19
(a) (b)
Figure 6. (a) The linear dependency of planetary mass with absolute stellar metallicity [Fe/H]. (b) The normal distribution
of planetary mass with absolute metallicity. Both the plots are binned with a size of 0.25. In both the plots, continuous lines
represent the best least square fits.
( )
relationship between both the variables in case of mul- Mpln = (−0.341 ± 0.152)
tiplanetary systems. Whereas, single planetary systems MJ
follow lognormal and normal distributions as presented + (1.381 ± 0.330)abs[Fe/H]
in Figures 5(e) and 5(f) respectively. From these two − (0.469 ± 0.142)abs[Fe/H]2. (4)
classifications it appears that single planetary systems
probably might not have been originated from the host However, there is a data bias such that these fits are
star’s protoplanetary disk. This view will be strength- for the combined data set of single and multiplanetary
ened from the results presented in the following sections systems. The data has been separated into single and
3.2.2 and 3.3. multiplanetary systems in the following analysis.
Figure 7(a) represents the dependency of planetary
3.2.2 Planetary mass versus metallicity. As men- mass with respect to stellar absolute metallicity in the
tioned earlier, chemical composition of nebula affects case of multiplanetary systems. Whereas, in case of sin-
the planetary physical properties and metallicity of gle planetary systems, Figures 7(b) and 7(c) illustrate
the host stars. Nayakshin (2015) showed that there is the dependency of planetary mass with respect to the
no correlation between the population of planets with absolute metallicity with linear and normal distribution
metallicity except for gas giants that were present within respectively. As illustrated in Fig. 7(a), although there
few AU from the host star. In the present study we is a scatter, variation of planetary mass clearly shows an
investigate the association between planetary mass with increasing trend with the host star’s absolute metallicity
respect to stellar metallicity for single and multiplane- and best fit yields the following relationship
tary systems. Probably this investigation may give hints
M
on origin and formation of single and multiplanetary p =(0.861 ± 0.740)+ (1.363 ± 0.429)abs[Fe/H],
systems. MJ
As metal-rich stars show the tendency of increased (5)
occurrence rate of planets, it is interesting to exam- where Mp is the planetary mass in-terms of Jupiter mass
ine whether planetary mass is dependent on the stellar MJ.
metallicity. In order to confirm this conjecture, in Fig. 6, Similarly, the relation between planetary mass and
irrespective of single and multiplanetary systems, we absolute metallicity for single planetary system
illustrate the dependence of planetary mass with respect (Fig. 7(c)) is given by the best fit of normal distribu-
to star’s metallicity. The results presented in Fig. 6(a) tion as follows:
show that, for absolute metallicity (linear–linear space), ( )M
planetary mass is independent of host star’s metallicity. pln = (−0.426 ± 0.154)
Whereas in Fig. 6(b), a Gaussian or normal distribution MJ
fits very well for planetary mass–absolute metallicity + (2.240 ± 0.366)abs[Fe/H]
relationship as follows: − (0.953 ± 0.165)abs[Fe/H]2. (6)
19 Page 14 of 17 J. Astrophys. Astr. (June 2017) 38:19
(a)
(b) (c)
Figure 7. (a) For multiplanetary systems, the dependency of planetary mass with absolute metallicity, (b) for single
planetary systems, the linear fit between planetary mass and absolute metallicity, and (c) the normal distribution. In all the
plots, continuous line is a best least square fit. In (a), the total planetary mass of solar system is represented by a triangle.
Both these results suggest that, single planetary sys- giants or massive planets is higher in case of metal rich
tems on average produce massive planets and probably stars.
their origin is different compared to multiplanetary sys-
tems. 3.2.3 Estimation of solar system planetary mass. With
As for the results presented in Fig. 7(a), following the equation (5) that relates planetary mass and stars
is the reason for low planetary mass for the metal- metallicity for multiplanetary systems, it is interesting
poor stars. Probably these metal-poor stars might have to examine whether total planetary mass of our solar sys-
originated with metal-poor disks around them. These tem (a multiplanetary system) follows such a universal
metal poor disks in turn might have less number of relationship. We find that the estimated total plane-
dust particles that eventually might have decreased tary mass of the solar system, by using equation (5),
the rate of planetary formation and hence less mas- is ∼2.224 MJ which is roughly 1.5 times higher com-
sive planets. Whereas in case of high metallicity stars pared to the present observed solar system total mass
with metal-rich disks, the scenario of planetary forma- (∼1.4 MJ) (that includes masses of asteroids, Kuiper
tion probably might be exactly opposite. Due to more belt and Oort’s cloud objects). This result suggests that
number of gas and dust particles in the protoplane- there is a missing mass of ∼0.8 MJ in the solar system
tary disk, time period of planet’s core formation is planetary bodies. Let us conjecture where this missing
less. Such a solid core rapidly acquires gas and dust mass of ∼0.8 MJ might have gone. When we closely
particles as gaseous envelope to form massive or gas examine Fig. 3(a), a decrease of about 1% mass from the
giants and grow big in size before dissipation of proto- present solar mass fits the universal law of stellar mass-
planetary disk. Hence, the chance of formation of gas metallicity relationship. One possibility is that such a
J. Astrophys. Astr. (June 2017) 38:19 Page 15 of 17 19
missing planetary mass might have accreted onto the stars. One can notice that single planetary systems are
Sun during the early history of the solar system for- majority in the present data set. However, with a power-
mation (Melendez et al. 2009). However, at present law, Figures 5(c) and 5(d) confirm that planets in the
it is not clear how much percentage of missing mass multiplanetary systems are not random events. That
(∼ 0.8MJ) is accreted onto the Sun. Moreover, due to means, these planets are not captured from the space,
high activity of the Sun during the early history of solar instead most likely they are originated in the protoplan-
system formation, some parts of planetary missing mass etary disks around the host stars.
in the vicinity of the Sun might have also been blown off
to the outer region probably through ambient magnetic 3.3 Orbital distances of exoplanets versus stellar
field lines. The leftover dust particles within the vicin- metallicity
ity of the Sun might have formed as terrestrial planets.
Hence, due to less amount of gas and dust particles, Planets prefer to form in the cooler region of protoplan-
the inner planets were unable to grow bigger in size etary disk. This is because, at high temperature, the rate
explaining why solar terrestrial planets are less massive of condensation of gas and dust particles is low due
compared to Jovian planets. In fact in the previous study to high activity of the central star, like Sun (Hiremath
(Shashanka et al. 2015), we came to a similar conclu- 2009). Hence most of the planets migrate before settling
sion. into the stable orbits around their host stars. Inspite of
migration of the planets, it is interesting to examine
3.2.4 Estimation of planetary mass beyond the solar whether orbital distances of planets depend upon the
system Kuiper belt. Coming to the picture of missing metallicity of the host stars. Figure 8(a) illustrates the
mass, if protoplanetary disk is in hydrostatic equilib-
−r variation of average orbital distances for all the plan-
rium, then density ρ varies as ρ0e H (where ρ0 is ets versus absolute metallicity with a bin size of 0.1
density at the center, r is distance from the center and, dex. Whereas, Fig. 8(b) represents the same relation-
H is density scale height), where maximum density is ship for single planetary systems. One can notice that
concentrated near the center. In case we accept this rea- among all the fits (linear–linear, log–log and lognormal
sonable density profile, then there is every possibility distribution space), for the both the figures, lognormal
that maximum missing mass (∼80%) might be accreted distribution is a best fit with the following forms:
onto the Sun. Whereas a small (∼20%) mass that is
in plasma state might have been transported along the ln(a) = (0.533 ± 0.112)
magnetic field lines to larger distances, probably beyond + (0.407 ± 0.346)[Fe/H]
the present Kuiper belt objects. That means, about 20% − (8.406 ± 0.708)[Fe/H]2, (7)
of missing mass might have been dumped into the outer
regions of the solar system. Interestingly, this 20% of and
missing mass turns out to be ∼60 Earth’s mass that is ln(a) = (0.386 ± 0.122)− (0.639 ± 0.455)[Fe/H]
probably residing in the outer edge of the solar system − (9.678 ± 0.839)[Fe/H]2. (8)
unless it is ejected from the catastrophic events. In fact,
this interesting estimation of missing mass might have These relationships suggest that, occurrence events of
formed as ninth and tenth or probably more planets in single planetary systems are random. Hence, as we dis-
the outer region (∼200 AU) of the solar system (Batygin cussed in section 3.2.5, again an inevitable conclusion
& Brown 2016). is that single planetary systems most likely are captured
planets from space.
3.2.5 Single planetary systems: Wandering and cap- For multiplanetary systems, Fig. 8(c) illustrates the
tured planets. When we examine the results emerged stable orbital distances of the planets as a function of
from the histograms (Figures 5(a), 5(b), 5(e) and 5(f)), absolute metallicity that clearly suggests a direct rela-
and planetary mass–stellar metallicity relationships tionship. Careful observation of Figures 8(b) and 8(c)
(Figures 6(b) and 7(c)), events are random and there reveals that average semi major axis of stable orbits
is no relationship between metallicity of the host stars for the multiplanetary systems (Fig. 8(c)) is higher than
and planets of the single planetary systems. That means, the average semi major axis for single planetary sys-
these planets probably are not formed in the host star’s tems (Fig. 8(b)). Hence, these results show that inward
protoplanetary disks. Rather these planets might have migration of planets and probably accretion of plane-
been originated and were formed elsewhere in the tary mass on to the host stars is dominant in case of
galaxy, wandered and probably captured by the host single planetary systems. This accretion of planetary
19 Page 16 of 17 J. Astrophys. Astr. (June 2017) 38:19
(a) (b)
(c)
Figure 8. (a) and (b) illustrate the lognormal distribution of semi major axis with the observed metallicity for all planetary
systems and single planetary systems respectively. (c) illustrates the dependency of semi-major axis of planets with the
absolute metallicity for multiplanetary systems. In case of multiplanetary systems, metallicity is binned with a size of 0.5,
whereas in case of all and single planetary system, it is 0.1 dex.
mass on the central host star acts as a ‘pollution’ and logarithmic stellar mass and its metallicity that suggests
further increases the stellar metallicity. As for multi- most of the stellar metallicity is due to primordial ori-
planetary systems, it appears that inward migration is gin. Hence, the contribution of ‘pollution’ to the final
less compared to migration in case of single planetary stellar metallicity is small.
systems. The investigation of planetary mass with respect to
their stellar absolute metallicity for all planetary sys-
tems, does not show any significant dependence on each
4. Conclusions other. However, an analysis by separating the dataset
into single and multiplanetary systems reveals that,
To conclude this study, we have considered the physical in case of multiplanetary systems, planetary mass is
characteristics of Sun-like G stars and their exoplanets linearly dependent on the stellar absolute metallicity.
with their orbital distances. Initially, an analysis has Whereas, we find a normal distribution between the
been done to examine the effect of galactic metallicity same variables in case of single planetary systems, that
on the planetary formation. However, we conclude that suggests most of the planets in single planetary systems
with the present dataset of Sun-like stars, it is difficult might be captured from space.
to infer the influence of galactic metallicity on the stel- Interestingly, the relationship between planetary mass
lar/planetary system formation. Further, the association and absolute metallicity for multiplanetary systems sug-
between stellar mass with their metallicity is examined. gests that there is a missing planetary mass (∼0.8MJ)
We find that, there is a direct relationship between the in the solar system. It is argued that majority (∼80%)
J. Astrophys. Astr. (June 2017) 38:19 Page 17 of 17 19
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