The Chemical link between stars and their rocky planets
Vardan Adibekyan, Caroline Dorn, Sérgio G. Sousa, Nuno C. Santos, Bertram Bitsch, Garik Israelian, Christoph Mordasini, Susana C. C. Barros, Elisa Delgado Mena, Olivier D. S. Demangeon, João P. Faria, Pedro Figueira, Artur A. Hakobyan, Mahmoudreza Oshagh, Masanobu Kunitomo, Yoichi Takeda, Emiliano Jofré, Romina Petrucci, Eder Martioli
TThe Chemical link between stars and their rocky planets
Vardan Adibekyan, , ∗ Caroline Dorn, Sérgio G. Sousa, Nuno C. Santos, , Bertram Bitsch, Garik Israelian, , Christoph Mordasini, Susana C. C. Barros, , Elisa Delgado Mena, Olivier D. S. Demangeon, , João P. Faria, Pedro Figueira, , Artur A. Hakobyan, Mahmoudreza Oshagh, , Masanobu Kunitomo, Yoichi Takeda, , Emiliano Jofré, , , Romina Petrucci, , Eder Martioli, , Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal Departamento de Física e Astronomia, Faculdade de Ciências,Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal University of Zurich, Institut of Computational Sciences, Winterthurerstrasse 190, CH-8057, Zurich, Switzerland Max-Planck-Institut für Astronomie, Königstuhl 17, 69117, Heidelberg, Germany Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain Departamento de Astrofìsica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012, Bern, Switzerland Center for Cosmology and Astrophysics, Alikhanian National Science Laboratory, 2Alikhanian Brothers Str., 0036 Yerevan, Armenia European Southern Observatory, Alonso de Córdova 3107, Vitacura, Región Metropolitana, Chile Department of Physics, School of Medicine, Kurume University, 67 Asahimachi, Kurume, Fukuoka 830-0011, Japan National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan SOKENDAI, The Graduate University for Advanced Studies, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Instituto de Astronomía, Universidad Nacional Autónoma de México, Ciudad Universitaria, CDMX, C.P. 04510, México Universidad Nacional de Córdoba (OAC), Laprida 854, X5000BGR, Córdoba, Argentina Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina Institut d’Astrophysique de Paris, UMR7095 CNRS,Université Pierre & Marie Curie, 98 bis Boulevard Arago, 75014 Paris, France Laboratório Nacional de Astrofísica, Rua Estados Unidos 154, Itajubá, MG 37504-364, Brazil ∗ E-mail: [email protected] a r X i v : . [ a s t r o - ph . E P ] F e b oung stars and planets both grow by accreting material from the proto-stellar disks.Planetary structure and formation models assume a common origin of the buildingblocks, yet, thus far, there is no direct conclusive observational evidence correlatingthe composition of rocky planets to their host stars. Here we present evidence of achemical link between rocky planets and their host stars. The iron-mass fraction ofthe most precisely characterized rocky planets is compared to that of their buildingblocks, as inferred from the atmospheric composition of their host stars. We finda clear and statistically significant correlation between the two. We also find thatthis correlation is not one-to-one, owing to the disk-chemistry and planet formationprocesses. Therefore rocky planet composition depends on the chemical compositionof the proto-planetary disk and contains signatures about planet formation processes. Low-mass transiting planets orbiting bright, nearby stars with radial-velocity (RV) follow-up observa-tions are ideal targets for interior characterization studies. These are enabled by the combination ofRV and transit techniques, that determine the two fundamental parameters: planetary radius via transitobservations and planetary mass via RV measurements. The derivation of these parameters, however,relies on the knowledge of the properties of the host stars. In this respect, planets orbiting solar-typestars (FGK spectral types) are of primary interest because of our ability to characterize them mostaccurately, and their accuracy depends on the accuracy of the same parameter as measured for thestar (
1, 2 ).Thanks to very high-precision spectroscopic and photometric (transit) measurements, 32 well-characterized (with an uncertainty both in mass and radius below 30%) low-mass exoplanets (
M < M ⊕ ) orbiting 27 solar-type stars are currently known (see Materials and Methods). The distributionof these planets on the mass-radius diagram is shown in Fig.1. A clear gap in radius can be seen (seetop panel of Fig. 2) for planets with masses greater than about 4 M ⊕ . This gap is suggested to separate2ocky planets from the water- and gas-rich mini-Neptunes ( ).In this work we explore the link between the properties of rocky planets and the chemical compo-sition of their host stars. For this reason, here we focus only on 22 planets located on the bottom partof the Radius Valley i.e. planets without significant water or gas-rich envelopes.It is generally believed that the atmospheric elemental abundances (except the lightest elements)of sun-like stars are preserved during the stellar main sequence phase within a few percent ( ). Formost of the nonvolatile elements the solar photospheric and meteoritic abundances were shown to bein good agreement ( ). In addition, it has been shown that the Fe/Si and Mg/Si abundance ratios instars and planetary bulk remain very similar during the planet formation processes ( ). As such,the atmospheric abundances of refractory elements (e.g. Mg, Si, and Fe) of solar-type stars are usuallyconsidered as a proxy of the composition of the initial proto-planetary disk and their building blocks(
12, 13 ). We have collected spectra from different instruments for the host stars of the planets selectedwith the aim of determining their atmospheric chemical composition (see Materials and Methods). Inparticular we determined the abundances of C, O, Mg, Si, and Fe, which together with H are the mostrelevant elements controlling the species expected from equilibrium condensation models ( ). On asecond step, we have inserted these abundances in a simple stoichiometric model (
15, 16 ) to estimatethe iron-to-silicate mass fraction ( f iron , star ) of planetary building blocks. For the solar system planetbuilding blocks, this model predicts a f iron , star of 33.2 ± ∼ ).As can be seen from the top panel of Fig. 2, for a given mass the rocky planets of our sampleshow some dispersion in radius around the Earth-like composition curve. To understand whether thedensities of the planets are linked to the primordial composition of the planet building blocks, in thebottom panel of Fig. 2 we show the normalized planet density, ρ/ρ Earth − like , as a function of f iron , star .The normalization parameter ρ Earth − like , is the density of a planet with Earth-like composition ( )for a given mass. The normalization is important because planets with the same composition havedifferent densities depending on their mass due to compression. The figure reveals a clear correlation3see Materials and Methods for details about the performed statistical tests and their results) betweenthese two quantities indicating that the final planetary density is a function of the composition of theplanet building blocks.Since one of these quantities is linked exclusively to the observed properties of the planets whilethe other one is linked to the host star composition, this trend provides the first observational evidencefor the chemical link between stars and their rocky planets. This result suggests that rocky planetspreserve information about the overall chemical composition of the proto-planetary disk in which theyare formed.Despite the general trend observed on the bottom panel of Fig. 2, it is evident that for a given f iron , star (i.e. stellar and pebble/planetesimal composition) rocky planets can have a range of densities.Although the observed scatter is compatible with the average uncertanity of ρ/ρ Earth − like , we testedwhether part of this dispersion can have an astrophysical origin. One of the parameters that mightinfluence the size and thus density of planets is the flux (high-energy photons) that planets receivefrom their host stars (
6, 19 ). We found, however, no correlation between the normalized density of theplanets and their equilibrium temperature, T eq (see the absence of a color gradient in the bottom panelof Fig. 2), suggesting that for rocky planets T eq does not have a major impact on their radius ( ).The next logical step was to study how different the final iron mass fraction of the planets canbe when compared with the iron-mass fraction of the primordial planet-building blocks as estimatedfrom the host star composition. Based on planet interior models ( ), we determined the possibleiron mass fraction of the planets ( f iron , planet ) using only their mass and radius. We considered twoscenarios i) assuming iron is present only in the core and ii) assuming iron is present both in the coreand mantle of the planets. In Fig. 3 we show the dependence of f iron , planet on f iron , star . Two interestingconclusions can be drawn from this figure. First, the iron mass fraction of planets is a function ofthe iron-mass fraction of the primordial planet building-blocks, i.e., the the two quantities show astatistically significant correlation for a monotonic dependence. Second, the planets span wider rangeof iron-mass fraction than their primordial building-blocks. It is interesting to note that the overall4istribution of core-mass fraction (which can be related to the iron mass fraction) of rocky planets wasshown to be wider than the overall distribution of exoplanet host stars ( ).It was recently suggested that the iron fraction in planets can be significantly increased due to therecondensation of evaporated pebbles ( ). In this model, planets formed close to rocklines (regionswhere refractory material condensates/sublimates) can have an increased proportion of iron when com-pared with the proto-stellar value. This effect may explain the overall larger values of f iron , planet whencompared with the f iron , star . Interestingly, the trend observed in Fig. 3 suggests that the aforemen-tioned effect should depend on the stellar iron-mass fraction, meaning that stars with naturally higheriron fraction will see a larger increase of this effect ( ).In Fig. 3 one can potentially identify a group of five planets with relatively high content of ironwhen compared to the rest of the planets - the super-Earths. Several mechanisms of planet formationand evolution are proposed in the literature to explain the high-density and high f iron , planet of theseplanets ( ), sometimes called super-Mercuries. Although the number of these planets is not largepreventing to make firm conclusion, one can still notice that they are orbiting stars with high f iron , star i.e. stars with overabundance of Fe relative to Mg and Si. This may suggest that whatever is themechanism responsible for the overabundance of iron in these planets, it should be related to thecomposition of the proto-planetary disk.Appreciating the possibility that the super-Mercuries may had a specific origin and/or evolutionarypath, we checked whether our findings hold for the rest of the planets. We found that the f iron , planet – f iron , star correlation remains significant for the sample of super-Earths. In addition, we found thatthe Fe/(Mg+Si) abundance ratio estimated for these planets shows a strong dependence on Fe/(Mg+Si)ratio of their host stars. The data reveals a non 1-to-1 relationship (see Materials and Methods) that,perhaps, should replace previously used 1-to-1 relationship.Several attempts have been made in the past trying to link the composition of low-mass planets andtheir host stars. However, these attempts were either based on single planetary systems (
23, 24 ), on asmall sample of planets (
15, 20, 22 ), or on a comparison of the overall properties of planets and overall5roperties of planet host stars in a population sense ( ). As a result, it was not possible to reach a firmand general conclusion either because of low-number statistics, because of the adopted non-optimalapproach, or because the results were not as informative (especially if the composition of the stars arenot derived in a homogeneous way) as they would be if a direct star-planet comparison was performed(see Materials and Methods). Our results clearly demonstrate the importance of performing a detailedchemical analysis of exoplanet hosts and making a direct star-planet comparison.The observational results obtained in this work are important for two different reasons. First, asnoted earlier, the information on the stellar relative abundance of major rock-forming elements suchas Fe, Mg, Si is commonly used to improve interior estimates for rocky planets (
12, 13 ) and has evenbeen used to estimate planet composition in different galactic populations (
16, 25, 26 ). In this context,the chemical link we observed validates the assumptions made in the aforementioned works. Second,the fact that the observed correlation between the f iron , planet and f iron , star is not one-to-one ( f iron , planet is larger than f iron , star ) suggests that the proto-planetary disk chemistry (depending on the locationof planets at the time of their formation) and specific processes acting during the formation of theseplanets play an important role for planetary composition. Moreover, our brief and only qualitativediscussion on the possible origin of the overabundance of iron in planets when comparing to theirprimordial building blocks shows the potential of using these correlations for studying the specifics ofrocky planet formation.The detection and detailed characterization of rocky planets orbiting Sun-like stars is currently oneof the main drivers for the development of large space-borne missions and ground-based instrumentsby the major international agencies (ESO, ESA, NASA). The number of well characterized rockyplanets will continually increase in the near future thanks to projects such as TESS (NASA, 2018) ( ),ESPRESSO (ESO, 2018) ( ), CHEOPS (ESA, 2019) ( ), and PLATO (ESA, 2026) ( ). Performingan analysis similar to ours, but with significantly larger number and better characterized low-massplanets will without doubt help in constraining further the chemical link between stars and their rockyplanets established in this manuscript. 6 eferences
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This work was supported by FCT - Fundação para a Ciência e Tecnologia (FCT) through national fundsand by FEDER through COMPETE2020 - Programa Operacional Competitividade e Internacional-ização by these grants: UID/FIS/04434/2019; UIDB/04434/2020; UIDP/04434/2020; PTDC/FIS-AST/32113/2017 & POCI-01-0145-FEDER-032113; PTDC/FIS-AST/28953/2017 & POCI-01-0145-FEDER-028953. V.A., E.D.M, N.C.S., and S.G.S. also acknowledge the support from FCT through In-vestigador FCT contracts nr. IF/00650/2015/CP1273/CT0001, IF/00849/2015/CP1273/CT0003, IF/00169/2012/CP0150/CT0002,and IF/00028/2014/CP1215/CT0002, respectively, and POPH/FSE (EC) by FEDER funding throughthe program “Programa Operacional de Factores de Competitividade - COMPETE”. C.D. acknowl-edges support from the Swiss National Science Foundation under grant PZ00P2_174028, this workhas been carried out within the frame of the National Center for Competence in Research Plan-etS supported by the SNSF. O.D.S.D. and J.P.F. are supported in the form of work contracts (DL57/2016/CP1364/CT0004 and DL57/2016/CP1364/CT0005, respectively) funded by FCT. E.M. ac-knowledge funding from the French National Research Agency (ANR) under contract number ANR-18-CE31-0019 (SPlaSH). B.B., thanks the European Research Council (ERC Starting Grant 757448-PAMDORA) for their financial support. Based on observations (program ID GN-217A-FT-20; PI:E. Jofré) obtained at the international Gemini Observatory, a program of NSF’s NOIRLab, which ismanaged by the Association of Universities for Research in Astronomy (AURA) under a cooperativeagreement with the National Science Foundation on behalf of the Gemini Observatory partnership: theNational Science Foundation (United States), National Research Council (Canada), Agencia Nacionalde Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina),Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy andSpace Science Institute (Republic of Korea). This work has made use of data from the EuropeanSpace Agency (ESA) mission (Gaia), processed by the Gaia Data Processing and Analysis Consortium(dpac). Funding for the dpac has been provided by national institutions, in particular the institutions15articipating in the Gaia Multilateral Agreement. In this work we used the Python language and sev-eral scientific packages.
Author contributions:
V.A. led the data analysis and wrote the paper withcontribution of C.D.. C.D. led the planetary interior analysis and S.G.S. performed the stellar param-eter analysis. V.A. determined the chemical composition of the stars with contribution of E.D.M..N.C.S., B.B., C.M., and G.I. contributed to the discussion of the implications of the data. S.C.C.B.,O.D.S.D., A.A.H, M.O. contributed to the general discussion of the results. C.D, S.G.S, N.C.S., G.I.,C.M., E.D.M., M.K., Y.T., E.J., R.P., and E.M. worked on gathering the spectroscopic observations.J.P.F. and P.F. contributed to the statistical analysis. All authors discussed the results and commentedon the manuscript.
Competing interests:
The authors declared no competing interests.
Data and ma-terials availability:
The data supporting the findings of this study are available within the paper andits supplementary tables. The combined spectra of the planet host stars are available upon reasonablerequest from the corresponding author. The main analysis routines have been written by the authorsand are available upon reasonable request from the corresponding author. The latest version of AREScode (ARES v2) is available at . BayesCorrcode is freely available for download or cloning in the git repository https://bitbucket.org/pedrofigueira/bayesiancorrelation/
Radius-mass diagram.
Distribution of low-mass planets (masses below 10 M ⊕ ) withprecise mass and radius measurements or estimates (uncertainties below 30%) in the R-M diagram(http://exoplanet.eu, on 11th May 2020). Mass determination methods are indicated by different col-ors. Grey points indicate the planets with imprecise (uncertainties above 30%) mass or radius estimates.All error bars show one standard deviation. 17igure 2: Densities of rocky planets.
Top panel. Mass-radius diagram for RV-detected planets withmasses below 10 M ⊕ for which the uncertainty both in mass and radius is below 30%. The greydashed curves, drawn by eye, indicate the location of the ’radius gap’ which separates the planets intoplanets with (red circles) and without (black circles) envelopes. The blue curve shows the mass-radiusrelationship for Earth-like composition (32% Fe + 68% MgSiO3) ( ). Bottom panel. Normalizeddensity of the planets as a function of iron mass fraction of planet building blocks estimated from thehost star chemistry. ρ Earth − like is the density of a planet with Earth-like composition for a given mass.The black dashed line represent the results of the OLS linear regression. The position of the Earth isindicated with its symbol in black. The symbols are color-coded by the equilibrium temperature of theplanets. All error bars show one standard deviation.18igure 3: Iron content in rocky planets.
Iron mass fraction of planet building blocks estimated fromthe host star chemistry ( f iron , star ) versus iron mass fraction from the planets ( f iron , planet ) as estimatedby mass and radius and using a detailed interior model ( ). Estimates of f iron , planet are based on theassumption that all iron resides in the core only (left panel) or iron is assumed to be present in bothmantle and core (right panel). The symbols are color-coded by the equilibrium temperature of theplanets. The black dashed and solid lines represent the results of the OLS linear regression for the fullsample and for the sample of planets without considering the five planets wiht the highest f iron , planet ,respectively. The positions of the Earth are indicated with its symbol in black. The error bars of f iron , star show one standard deviation. The error bars of f iron , planet cover the interval between the 16thand the 84th percentiles. 19 aterials and Methods The sample
We started our sample selection from exoplanet.eu ( ). Out of 4330 confirmed planets (as of 11/05/2020)364 turned out to have masses below 10 M ⊕ and to orbit around FGK-type stars (4500 < T eff < ). The distribution of these planets on the mass-radius diagramalong with the method of the mass determination is shown in the top panels of Fig.1.From this sample we then excluded all planets with mass estimations based on mass-radius empir-ical relation (indicated as “Theory” in Fig.1) and planets with mass determination based on the TTVmethod. As already discussed in the literature ( ) and also can be seen in Fig.1 the planets with TTV-and RV-based masses determinations (hereinafter referred to as TTV-planets and RV-planets) showdifferent distributions in the diagram. Because of this still to-be-understood difference we limit oursample to 33 RV-planets (in 27 planetary systems) only. Stellar parameters and chemical abundances
Paramount to the analysis of star-planet relations is our ability to derive precise stellar parameters andchemical abundances for planet host stars. Many groups all over the world are working intensively topush down the precision limits in deriving fundamental properties and chemical abundances of planethost stars (
2, 34–36 ). The general conclusion is that in most cases exoplanet host stars can be veryprecisely characterized if their spectral analysis is done homogeneously ( ).For the sample of 26 planet host stars we collected high-resolution optical spectra from publicarchives (ESO, HARPS-N@TNG, SOPHIE@OHP, ESPaDOnS@CFHT, HIRES@Keck) and throughdedicated observing programs carried out by the authors (GRACES@Gemini-N, ESPRESSO@VLT,and HDS@Subaru). Unfortunately, for one of the stars (HD 80653) we were not able to get a high-20esolution spectrum and we had to exclude this star from our sample. It is important to note thatwith the spectroscopic analysis adopted in this work the impact of using different instruments is verysmall (
40, 41 ).We determined the stellar atmospheric parameters ( T eff , log g , microturbulence (Vmic), and [Fe/H])of the sample stars following the methodology described in (
39, 42 ). We make use of the equivalentwidths (EW) of iron lines, as measured in the combined spectra using the ARES v2 code ( ), andwe assume ionization and excitation equilibrium. The process makes use of a grid of Kurucz modelatmospheres ( ) and the 2014 version of the radiative transfer code MOOG ( ).For K2-216, with a T eff of ∼ ).Stellar abundances of the elements were also derived using the same tools and models as for stellarparameter determination, as well as using the classical curve-of-growth analysis method assuming localthermodynamic equilibrium. Although the EWs of the spectral lines were automatically measured withARES, for the elements with only two-three lines available we performed careful visual inspection ofthe EWs measurements. For the derivation of chemical abundances of refractory elements we closelyfollowed the methods described in (
47, 48 ). Abundances of the volatile elements, O and C, werederived following the method of ( ). The EWs of the spectral lines of C, O, and Mg were manuallymeasured with the task splot in IRAF.C and O abundances are very difficult to determine for stars cooler than about 5200 K (
49, 50 ). Wecould not determine C abundance for 4 of the stars and O abundance for 6 stars. For the aforementionedstars we estimated the abundances of C and O empirically by using a machine learning algorithm(we used the estimator "RandomForestRegressor") from the Python Scikit-learn package ( ). Theestimation of C and O was based on the abundance of Mg and Fe ( ). Our initial sample was based onthe HARPS sample ( ). We derived O abundance for 535 stars and C abundance of 758 stars followingthe methodology of our previous works (
49, 50 ). These samples were used as training and test datasets.21he average error for the estimated C and O abundances are 0.08 and 0.09 dex respectively. We testedthe estimated C and O abundances for our sample of planet host stars for which we determined theabundances of these elements. The mean difference and standard deviation for C and O are -0.01 ± ± f iron , star (
15, 16 ).To do so, we needed to transform the relative abundances into absolute abundances considering solarreference values. The solar absolute abundances were taken as log (cid:15) C = 8.5 ( ), log (cid:15) O = 8.65 ( ), log (cid:15) Mg = 7.6 ( ), log (cid:15) Si = 7.51 ( ), and log (cid:15) Fe = 7.5 ( ). It is important to note that the f iron , star ispractically insensitive to the abundances of C and O. For example varying the C and O abundances by0.2 dex introduces an average variation of only 0.02% in f iron , star , which is by a factor of 25 smallerthan the average relative uncertainty of f iron , star .The luminosity of the planet host stars was calculated by using spectroscopic effective temperature,V magnitude, Gaia DR2 parallax ( ), and bolometric correction ( ). Physical properties of the rocky planets
The main source for the planetary parameters was exoplanet.eu. We computed the bulk density, ρ , ofthe planets based on their mass and radius. Since planets with the same composition but with differentmasses would have different bulk densities, we scaled the densities to the density of a planet withEarth-like composition ( ) for a given mass - ρ Earth − like .Given the planet’s mass and radius, we estimated their possible iron fraction f iron , planet , which isdefined as ( M Fe , mantle + M core ) /M pl , where M Fe , mantle and M core are the masses of iron in mantleand core, respectively. In addition, we also estimated the possible Fe/(Mg+Si) abundance ratio of theplanets. We used an interior model as in ( ) and a characterization scheme as in ( ) that employs aMarkov chain Monte Carlo (McMC) method. For the planet interiors, we assume a pure iron core and a22ilicate mantle, and neglect any volatile layers. The interior model uses self-consistent thermodynamicsin the core and mantle. For the core, we use the equations of state for hexagonal close packed iron ( )and for the silicate mantle we use the model from ( ). We assume an adiabatic temperature profilewithin core and mantle.When estimating f iron , planet , we test two scenarios: First, we only allow the core to vary in size andfix the iron content of the mantle at zero (Fig. 3, left panel). In a second scenario, we also allow themantle composition to vary in iron content (Fig. 3, right panel). This results in ∼
10% higher f iron , planet ,since high amounts of iron can be in part compensated by high amounts of oxygen to fit the same massand radius data. Average estimated Mg-numbers of the mantles (Mg/(Mg+Fe)) range from 0.45 to0.9 with large uncertainties of up to 60%. And this may bolster the long-range migration scenario inwhich the planets formed in a highly oxidizing environment which enabled the iron to remain in themantle ( ). These models have average oxygen fugacities -3 to -1.7 ∆IW which is comparable to theoxidation state of Earth, small bodies, both in our solar system and accreted by white dwarfs ( ).In our analysis we neglected light elements in the core, since their addition has only tiny effects onthe total radius. For example, we find that for a fixed Fe/Si bulk ratio, the addition of light alloys likeFe . O in the core only affects the radius by 0.2%, when using the recent light alloy equations of statedata ( ).The T eq of the exoplanets were computed using the stellar luminosity and orbital distances of theplanets assuming zero bond albedo ( ). Semi-major axis for K2-141 b and Kepler-406 b, however,were not available in the exoplanet.eu and were extracted from http://exoplanets.org and http://exoplanetarchive.ipac.caltech.edu,respectively.The parameters of the rocky planets are presented in Suplimentary Table 2. Oxygen fugacity is defined relative to the Iron-Wüstite equilibrium reaction
Fe+ . O =FeO (Wüstite) such that ∆ IW = log( f O ) rock − log( f O ) IW ignificance and robustness of the results We performed several frequentist and Bayesian tests to assess the significance of the observed planetdensity – f iron , star and f iron , planet – f iron , star correlations. When performing the tests besides the mainsample we also considered a sub-sample of 18 planets with uncertainties both in mass and radius below20%. The results of our tests are summarized in Suplimentary Table 3.We first performed an ordinary least squares (OLS) and weighted least squares (WLS) regressionto quantify the ρ/ρ Earth − like vs f iron , star and f iron , planet – f iron , star correlations. The inverse of variance( σ ) of the planet density and f iron , planet were, respectively, used to calculate the weights. The p-values(at α = 0.05 significance level) come from the F-statistics that tests the null hypothesis that the datacan be modeled accurately by setting the regression coefficients to zero. The p-values vary from 0.007to 1x10 − , indicating that the observed correlations are significant. It is also evident that the p-valuesare overall smaller for the sub-sample of more precisely characterized planets.We also performed two simple Monte Carlo (MC) tests to access the significance of the observedcorrelations. In the first bootstrapped Monte Carlo test (MC I), for each correlation we estimated theSpearman’s rank (Spearman’s ρ ) correlation coefficient which are presented in the Table. Then weshuffled the data points (random re-sampling with replacement) and calculated the corresponding theSpearman’s ρ . We repeated the entire process 10 times and counted the number of trials in whichthe Spearman’s ρ is equal to or larger than the correlation coefficient obtained for the original dataset.The results of this test, presented in Suplimentary Table 3, clearly show that the probability that theobserved correlations have happened by a random alignment of this specific data set is always below0.2%, i.e., larger than 3- σ , if a normal distribution of alpha is assumed.The second Monte Carlo (MC II) test was designed to consider the uncertainties in the parameters.For each correlation we created 10 mock samples by varying the parameters within their uncertain-ties assuming a normal distribution. Then for each of the sample we calculated the Spearman’s rank(Spearman’s ρ ) correlation coefficient. In Suplimentary Table 3 we present the fraction of cases whenthe Spearman’s ρ has a negative value (P(Sp. ρ <
0) in the Table) i.e. opposite to what we expect if24he correlation is real. The table suggests that the probabilities that the observed positive correlationsare influenced by the uncertainties varies from 2 to 5 percent depending on the sample and correlation.Again, significance is higher when considering the sub-sample of the best characterized planets.Finally, we used the BayesCorr ( ) code based on a Bayesian approach to assess the significance ofa dependence of ρ/ρ Earth − like , f , planet , and f , planet on f iron , star by calculating the Spearman’s rankcorrelation coefficient. This method, unfortunately does not consider the impact of the uncertaintieson the measurements. In Table 3 we present the mean and standard deviation of Spearman’s ρ , aswell as the associated 95% credible intervals (highest posterior density; HPD). The results show thatthe significance of the correlations vary from about 3.4- σ to 4.8- σ . As in the previous two tests thecorrelation is of higher significance when considering the sub-sample of the best characterized planets.The four tests described in this section confirm that there is indeed a correlation between planetarydensity, iron-mass fraction of planets, and iron-mass fraction of planet building blocks. The fact that thecorrelations always become statistically more significant for the most precisely characterized planetsfurther points towards the robustness of the observed trends.Since the planetary parameters used in this work are not determined homogeneously, but takenfrom http://exoplanet.eu we performed another test to explore further how robust are ourresults to the heterogeneity in the planet data. From the NASA Exoplanet Archive ( https://exoplanetarchive.ipac.caltech.edu/ ) we selected up to three latest published planetaryparameters which satisfy the 30% relative uncertainty threshold we adopted in this work. For majorityof the planets only one or two measurements were available in the aforementioned database, whilefor a few planets (e.g. Kepler-78 b and 55 Cnc e) literature is rich in measurements. For 55 Cnc e,we ignored the old measurements that lead to radius estimates above 2R ⊕ , because in these cases theplanet would lie above the radius gap and would not be included in the sample. We then considered allthe possible combinations ( ∼ ρ/ρ Earth − like vs f iron , star correlation. In addition, we calculated the Spearman’s rank for each realization. This test25howed that the P(F-stat) values both for the OLS and WLS regressions are always smaller than 0.05with the mean values being 0.01 and 0.004 for the OLS and WLS analysis, respectively. The values ofSpearman’s ρ lied in between 0.44 and 0.71, with a mean value of 0.60 ± Super-Earths and super-Mercuries
As discussed in the manuscript and as can be seen in Fig. 3 the planets of our sample can be tentativelyseparate into super-Mercuries and super-Earths, where super-Mercuries are the planets with the highest f iron , planet . For the sample of super-Earths we performed the main statistical tests discussed in theprevious section. The results of our tests are presented in Suplimentary Table 4. Most of the testsshow that the relation between f iron , planet and f iron , star is statistically significant, although the level ofsignificance is lower than when considering the full sample. This is both because the planets with thehighest f iron , planet are excluded and because the size of the sample is reduced by about 25%.In Fig. 4 we show the dependence of Fe/(Mg+Si) abundance ratio of the planets on the same abun-dance ratio derived for the host stars. The super-Earths and super-Mercuries can be clearly identifiedin this plot. While, the sample of super-Mercuries is small and it is not possible to conclude whethera correlation exist for these planets, the sample of super-Earths clearly reveal a strong correlation.The p-values of the OLS and WLS analysis range from 0.005 to 6x10 − , indicating that the observedcorrelations are significant.We also performed an orthogonal distance regression analysis to quantify the F e/ ( M g + Si ) star – F e/ ( M g + Si ) planet relation considering uncertainties of both variables. The results are different forthe two assumptions we made about the iron content in the planet: F e/ ( M g + Si ) = − . ± .
48) + 5 . ± F e/ ( M g + Si ) star F e/ ( M g + Si ) = − . ± .
64) + 7 . ± F e/ ( M g + Si ) star F e/ ( M g + Si ) and F e/ ( M g + Si ) correspond to the cases when iron is allowedto be only in the core, and in the core and mantle of planets, respectively. In both cases, however, therelation is not 1-to-1, which was typically assumed in the literature. Relation to previous works
Detection of only a few giant planets was required to notice that presence of these planets correlateswith stellar metallicity (
65, 66 ). Since these pioneering works, different research groups tried to linkthe chemical composition of stars with the properties of planets. With the increased precision of massand radius of planets, it become possible to characterize the bulk composition of low-mass exoplanets.On a sample of five well-characterized planets with masses below 6 M ⊕ it was shown that these low-mass planets can be characterized with a fixed ratio of iron to magnesium silicate corresponding tothe value for the Earth ( ). Immediately, the hypothesis that the hosts of these planets should havesimilar compositions was tested on a sample of three stars ( ). While the later results ( ) providedsome hints that the iron mass fraction of planets is compatible with that inferred from the host starcomposition, making a general and firm conclusion was not possible because of the small samplesize. Very recently, two interesting articles have been published performing a direct comparison of thecomposition of individual planets with the composition of their host stars (
20, 22 ) and comparing theoverall distribution of planet composition with the overall composition of planet host stars ( ).The approach adopted in this work is fundamentally different from the previous approaches in sev-eral aspects. 1) Performing a direct comparison of individual star-planet compositions is anti-sensitiveto the precision of the planet and host star properties, meaning that the large uncertainties in the com-positions of planets and stars will naturally lead to a similar composition at a low σ -level. 2) Sincethe typical uncertainties in planetary compositions are significantly larger than those determined fromthe host star abundances ( ) (compare also Suplimentary Table 1 and 2), one can underestimate theimportance of the high-precision chemical characterization of planet host stars ( ). 3) Finally, com-paring compositions of individual planet-star system, makes difficult to infer general conclusions about27he relation and form of relation between compositions of stars and their planets.Opposite to this, our approach was to statistically compare the composition of planets and their hoststars. In our approach, high precision and homogeneity in compositions of both stars and planets ishighly crucial. As a result, our approach allowed us to reach to a general conclusion that the iron massfraction of planets correlates with the iron mass fraction of planet building blocks as inferred from thehost star composition, and that this relation is not 1-to-1. Suplimentary Tables and Figures
Table 1:
Table S1 | Properties of the host stars.
Star T eff [K] log g [dex] Vtur [cgs] [Fe/H] [C/H] [O/H] [Mg/H] [Si/H] f iron , star [%] Table 2:
Table S2 | Properties of the rocky planets.
Planet R [R ⊕ ] M [M ⊕ ] Semi-major axis [AU] T eq [K] ρ/ρ Earth − like f iron,planet [%] f iron,planet [%] Table 3:
Table S3 | Results of the statistical tests.
Data OLS WLS MC I MC II BayesianSlope ± σ P(F-stat) Slope ± σ P(F-stat) Sp. ρ orig P(Sp. ρ ≥ ρ orig ) P(Sp. ρ ≤
0) Sp. ρ ± σ
95% HPD ρ/ρ
Earth − like vs f iron , star (30% precision) 0.09 ± ± − ± ρ/ρ Earth − like vs f iron , star (20% precision) 0.10 ± ± − − ± f , planet vs f iron , star (30% precision) 6.97 ± ± − ± f , planet vs f iron , star (20% precision) 7.52 ± − ± − ± f , planet vs f iron , star (30% precision) 6.11 ± ± − ± f , planet vs f iron , star (20% precision) 6.45 ± ± − ± Table S4 | Results of the statistical tests for Super Earths.
Data OLS WLS MC I MC II BayesianSlope ± σ P(F-stat) Slope ± σ P(F-stat) Sp. ρ orig P(Sp. ρ ≥ ρ orig ) P(Sp. ρ ≤
0) Sp. ρ ± σ
95% HPD f , planet vs f iron , star (30% precision) 4.27 ± ± − ± f , planet vs f iron , star (20% precision) 4.84 ± ± − ± f , planet vs f iron , star (30% precision) 4.02 ± ± − ± f , planet vs f iron , star (20% precision) 4.24 ± ± ± Figure 4:
Abundance ratios in planets and their hosts.
Fe/(Mg+Si) abundance ratio of planet build-ing blocks estimated from the host star chemistry versus Fe/(Mg+Si) ratio from the planets as estimatedby mass and radius and using a detailed interior model ( ). The estimates for planets are based onthe assumption that all iron resides in the core only (left panel) or iron is assumed to be present inboth mantle and core (right panel). The symbols are color-coded by the equilibrium temperature ofthe planets. The black dashed lines represent the results of the OLS linear regression for super-Earths.The error bars of Fe/(Mg+Si) star show one standard deviation. The error bars of f iron , planetplanet