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Published Online: 16 July 2019

Mineralogy, Structure, and Habitability of Carbon-Enriched Rocky Exoplanets: A Laboratory Approach

Publication: Astrobiology
Volume 19, Issue Number 7


Carbon-enriched rocky exoplanets have been proposed to occur around dwarf stars as well as binary stars, white dwarfs, and pulsars. However, the mineralogical make up of such planets is poorly constrained. We performed high-pressure high-temperature laboratory experiments (P = 1–2 GPa, T = 1523–1823 K) on chemical mixtures representative of C-enriched rocky exoplanets based on calculations of protoplanetary disk compositions. These P-T conditions correspond to the deep interiors of Pluto- to Mars-sized planets and the upper mantles of larger planets. Our results show that these exoplanets, when fully differentiated, comprise a metallic core, a silicate mantle, and a graphite layer on top of the silicate mantle. Graphite is the dominant carbon-bearing phase at the conditions of our experiments with no traces of silicon carbide or carbonates. The silicate mineralogy comprises olivine, orthopyroxene, clinopyroxene, and spinel, which is similar to the mineralogy of the mantles of carbon-poor planets such as the Earth and largely unaffected by the amount of carbon. Metals are either two immiscible iron-rich alloys (S-rich and S-poor) or a single iron-rich alloy in the Fe-C-S system with immiscibility depending on the S/Fe ratio and core pressure. We show that, for our C-enriched compositions, the minimum carbon abundance needed for C-saturation is 0.05–0.7 wt% (molar C/O ∼0.002–0.03). Fully differentiated rocky exoplanets with C/O ratios more than that needed for C-saturation would contain graphite as an additional layer on top of the silicate mantle. For a thick enough graphite layer, diamonds would form at the bottom of this layer due to high pressures. We model the interior structure of Kepler-37b and show that a mere 10 wt% graphite layer would decrease its derived mass by 7%, which suggests that future space missions that determine both radius and mass of rocky exoplanets with insignificant gaseous envelopes could provide quantitative limits on their carbon content. Future observations of rocky exoplanets with graphite-rich surfaces would show low albedos due to the low reflectance of graphite. The absence of life-bearing elements other than carbon on the surface likely makes them uninhabitable.

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Anderson D.E., Bergin E.A., Blake G.A., Ciesla F.J., Visser R., and Lee J.-E. (2017) Destruction of refractory carbon in protoplanetary disks. Astrophys J 845:13.
Armstrong J.T. (1995) CITZAF: a package of correction programs for the quantitative electron microbeam X-ray analysis of thick polished materials, thin films, and particles. Microbeam Anal 4:177–200.
Batalha N.M. (2014) Exploring exoplanet populations with NASA's Kepler Mission. Proc Natl Acad Sci U S A 111:12647–12654.
Birch F. (1947) Finite elastic strain of cubic crystals. Phys Rev 71:809–824.
Bizzarro M., Baker J.A., Haack H., and Lundgaard K.L. (2005) Rapid timescales for accretion and melting of differentiated planetesimals inferred from 26Al-26Mg chronometry. Astrophys J Lett 632:L41–L44.
Bond J.C., O'Brien D.P., and Lauretta D.S. (2010) The compositional diversity of extrasolar terrestrial planets. I. In situ simulations. Astrophys J 715:1050–1070.
Boujibar A., Andrault D., Bouhifd M.A., Bolfan-Casanova N., Devidal J.-L., and Trcera N. (2014) Metal–silicate partitioning of sulphur, new experimental and thermodynamic constraints on planetary accretion. Earth Planet Sci Lett 391:42–54.
Brewer J.M., Fischer D.A., Valenti J.A., and Piskunov N. (2016) Spectral properties of cool stars: extended abundance analysis of 1,617 planet-search stars. Astrophys J Suppl Ser 225:32.
Carter-Bond J.C., O'Brien D.P., Delgado Mena E., Israelian G., Santos N.C., and González Hernández J.I. (2012a) Low Mg/Si planetary host stars and their Mg-depleted terrestrial planets. Astrophys J Lett 747, L2.
Carter-Bond J.C., O'Brien D.P., and Raymond S.N. (2012b) The compositional diversity of extrasolar terrestrial planets. II. Migration simulations. Astrophys J 760, 44.
Chi H., Dasgupta R., Duncan M.S., and Shimizu N. (2014) Partitioning of carbon between Fe-rich alloy melt and silicate melt in a magma ocean—implications for the abundance and origin of volatiles in Earth, Mars, and the Moon. Geochim Cosmochim Acta 139:447–471.
Colonna F., Fasolino A., and Meijer E. (2011) High-pressure high-temperature equation of state of graphite from Monte Carlo simulations. Carbon 49:364–368.
Corgne A., Wood B.J., and Fei Y. (2008) C- and S-rich molten alloy immiscibility and core formation of planetesimals. Geochim Cosmochim Acta 72:2409–2416.
Dasgupta R. (2013) Ingassing, storage, and outgassing of terrestrial carbon through geologic time. Rev Mineral Geochem 75:183–229.
Dasgupta R. and Walker D. (2008) Carbon solubility in core melts in a shallow magma ocean environment and distribution of carbon between the Earth's core and the mantle. Geochim Cosmochim Acta 72:4627–4641.
Dasgupta R., Buono A., Whelan G., and Walker D. (2009) High-pressure melting relations in Fe-C-S systems: implications for formation, evolution, and structure of metallic cores in planetary bodies. Geochim Cosmochim Acta 73:6678–6691.
Dasgupta R., Chi H., Shimizu N., Buono A.S., and Walker D. (2013) Carbon solution and partitioning between metallic and silicate melts in a shallow magma ocean: implications for the origin and distribution of terrestrial carbon. Geochim Cosmochim Acta 102:191–212.
Delgado Mena E., Israelian G., González Hernández J.I., Bond J.C., Santos N.C., Udry S., and Mayor M. (2010) Chemical clues on the formation of planetary systems: C/O versus Mg/Si for HARPS GTO sample. Astrophys J 725:2349–2358.
Deng L., Fei Y., Liu X., Gong Z., and Shahar A. (2013) Effect of carbon, sulfur and silicon on iron melting at high pressure: implications for composition and evolution of the planetary terrestrial cores. Geochim Cosmochim Acta 114:220–233.
Dorn C., Khan A., Heng K., Connolly J.A.D., Alibert Y., Benz W., and Tackley P. (2015) Can we constrain the interior structure of rocky exoplanets from mass and radius measurements? Astron Astrophys 577:A83.
Duncan M.S., Dasgupta R., and Tsuno K. (2017) Experimental determination of CO2 content at graphite saturation along a natural basalt-peridotite melt join: implications for the fate of carbon in terrestrial magma oceans. Earth Planet Sci Lett 466:115–128.
Elkins-Tanton L.T. (2012) Magma oceans in the inner solar system. Ann Rev Earth Planet Sci 40:113–139.
Fei Y., Murphy C., Shibazaki Y., Shahar A., and Huang H. (2016) Thermal equation of state of hcp-iron: constraint on the density deficit of earth's solid inner core. Geophys Res Lett 43:6837–6843. 2016GL069456.
Fortier A., Beck T., Benz W., Broeg C., Cessa V., Ehrenreich D., and Thomas N. (2014) CHEOPS: a space telescope for ultra-high precision photometry of exoplanet transits. In Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, Proc SPIE 91432J (28 August 2014).
Ghiringhelli L.M., Los J.H., Meijer E.J., Fasolino A., and Frenkel D. (2005) Modeling the phase diagram of carbon. Phys Rev Lett 94:145701.
Giordano D., Russell J.K., and Dingwell D.B. (2008) Viscosity of magmatic liquids: a model. Earth Planet Sci Lett 271:123–134.
Hakim K., Rivoldini A., Van Hoolst T., Cottenier S., Jaeken J., Chust T., and Steinle-Neumann G. (2018a) A new ab initio equation of state of hcp-Fe and its implication on the interior structure and mass-radius relations of rocky super-Earths. Icarus 313:61–78.
Hakim K., van Westrenen W., and Dominik C. (2018b) Capturing the oxidation of silicon carbide in rocky exoplanetary interiors. Astron Astrophys 618:L6.
Hashizume K. and Sugiura N. (1998) Transportation of gaseous elements and isotopes in a thermally evolving chondritic planetesimal. Meteorit Planet Sci 33:1181–1195.
Hevey P.J. and Sanders I.S. (2006) A model for planetesimal meltdown by 26Al and its implications for meteorite parent bodies. Meteorit Planet Sci 41:95–106.
Hirose K. and Fei Y. (2002) Subsolidus and melting phase relations of basaltic composition in the uppermost lower mantle. Geochim Cosmochim Acta 66:2099–2108.
Holzheid A., Palme H., and Chakraborty S. (1997) The activities of NiO, CoO and FeO in silicate melts. Chem Geol 139:21–38.
Javoy M., Kaminski E., Guyot F., Andrault D., Sanloup C., Moreira M., Labrosse S., Jambon A., Agrinier P., Davaille A., and Jaupart C. (2010) The chemical composition of the Earth: enstatite chondrite models. Earth Planet Sci Lett 293:259–268.
Johansen A., Oishi J.S., Mac Low M.-M., Klahr H., Henning T., and Youdin A. (2007) Rapid planetesimal formation in turbulent circumstellar disks. Nature 448:1022–1025.
Jugo P.J., Luth R.W., and Richards J.P. (2005) Experimental data on the speciation of sulfur as a function of oxygen fugacity in basaltic melts. Geochim Cosmochim Acta 69:497–503.
Jugo P.J., Wilke M., and Botcharnikov R.E. (2010) Sulfur K-edge XANES analysis of natural and synthetic basaltic glasses: implications for S speciation and S content as function of oxygen fugacity. Geochim Cosmochim Acta 74:5926–5938.
Klarmann L., Ormel C.W., and Dominik C. (2018) Radial and vertical dust transport inhibit refractory carbon depletion in protoplanetary disks. Astron Astrophys 618, L1.
Kruijer T.S., Fischer-Godde M., Kleine T., Sprung P., Leya I., and Wieler R. (2013) Neutron capture on Pt isotopes in iron meteorites and the Hf-W chronology of core formation in planetesimals. Earth Planet Sci Lett 361:162–172.
Kuchner M.J. and Seager S. (2005) Extrasolar carbon planets. ArXiv Astrophysics e-prints.
Kushiro I. and Walter M.J. (1998) Mg-Fe partitioning between olivine and mafic-ultramafic melts. Geophys Res Lett 25:2337–2340.
Lazar C., Zhang C., Manning C.E., and Mysen B.O. (2014) Redox effects on calcite-portlandite-fluid equilibria at forearc conditions: carbon mobility, methanogenesis, and reduction melting of calcite. Am Mineral 99:1604–1615.
Lee J. and Morita K. (2002) Evaluation of surface tension and adsorption for liquid Fe-S alloys. ISIJ Int 42:588–594.
Lee J.-E., Bergin E.A., and Nomura H. (2010) The solar nebula on fire: a solution to the carbon deficit in the inner solar system. Astrophys J Lett 710, L21.
Léger A., Rouan D., Schneider J., Barge P., Fridlund M., Samuel B., Ollivier M., Guenther E., Deleuil M., Deeg H.J., Auvergne M., Alonso R., Aigrain S., Alapini A., Almenara J.M., Baglin A., Barbieri M., Bruntt H., Borde P., Bouchy F., Cabrera J., Catala C., Carone L., Carpano S., Csizmadia S., Dvorak R., Erikson A., Ferraz-Mello S., Foing B., Fressin F., Gandolfi D., Gillon M., Gondoin P., Grasset O., Guillot T., Hatzes A., Hebrard G., Jorda L., Lammer H., Llebaria A., Loeillet B., Mayor M., Mazeh T., Moutou C., Paetzold M., Pont F., Queloz D., Rauer H., Renner S., Samadi R., Shporer A., Sotin C., Tingley B., Wuchterl G., et al. (2009) Transiting exoplanets from the CoRoT space mission. VIII. CoRoT-7b: the first super-Earth with measured radius. Astron Astrophys 506:287–302.
Li Y., Dasgupta R., and Tsuno K. (2015) The effects of sulfur, silicon, water, and oxygen fugacity on carbon solubility and partitioning in Fe-rich alloy and silicate melt systems at 3 GPa and 1600°C: implications for core-mantle differentiation and degassing of magma oceans and reduced planetary mantles. Earth Planet Sci Lett 415:54–66.
Li Y., Dasgupta R., Tsuno K., Monteleone B., and Shimizu N. (2016) Carbon and sulfur budget of the silicate Earth explained by accretion of differentiated planetary embryos. Nat Geosci 9:781–785.
Lord O.T., Walter M.J., Dasgupta R., Walker D., and Clark S.M. (2009) Melting in the Fe-C system to 70 GPa. Earth Planet Sci Lett 284:157–167.
Madhusudhan N., Lee K.K.M., and Mousis O. (2012) A possible carbon-rich interior in super-Earth 55 Cancri e. Astrophys J Lett 759:L40.
Marty B., Alexander C.M.O., and Raymond S.N. (2013) Primordial origins of Earth's carbon. Rev Mineral Geochem 75:149–181.
McDade P., Wood B.J., van Westrenen W., Brooker R., Gudmundsson G., Soulard H., Najorka J., and Blundy J. (2002) Pressure corrections for a selection of piston-cylinder cell assemblies. Mineral Mag 66:1021–1028.
Morard G. and Katsura T. (2010) Pressure–temperature cartography of Fe–S–Si immiscible system. Geochim Cosmochim Acta 74:3659–3667.
Moriarty J., Madhusudhan N., and Fischer D. (2014) Chemistry in an evolving protoplanetary disk: effects on terrestrial planet composition. Astrophys J 787:81.
Nabiei F., Badro J., Dennenwaldt T., Oveisi E., Cantoni M., Hébert C., El Goresy A., Barrat J.-A., and Gillet P. (2018) A large planetary body inferred from diamond inclusions in a ureilite meteorite. Nat Commun 9:1327.
Nakajima T. and Sorahana S. (2016) Carbon-to-oxygen ratios in M dwarfs and solar-type stars. Astrophys J 830:159.
Nisr C., Meng Y., MacDowell A.A., Yan J., Prakapenka V., and Shim S.-H. (2017) Thermal expansion of SiC at high pressure-temperature and implications for thermal convection in the deep interiors of carbide exoplanets. J Geophys Res Planets 122:124–133.
O'Neill H.S.C. and Eggins S.M. (2002) The effect of melt composition on trace element partitioning: an experimental investigation of the activity coefficients of FeO, NiO, CoO, MoO2 and MoO3 in silicate melts. Chem Geol 186:151–181.
Peplowski P.N., Klima R.L., Lawrence D.J., Ernst C.M., Denevi B.W., Frank E.A., Goldsten J.O., Murchie S.L., Nittler L.R., and Solomon S.C. (2016) Remote sensing evidence for an ancient carbon-bearing crust on Mercury. Nat Geosci 9:273–276.
Petigura E.A. and Marcy G.W. (2011) Carbon and oxygen in nearby stars: keys to protoplanetary disk chemistry. Astrophys J 735:41.
Ragazzoni R., Magrin D., Rauer H., Pagano I., Nascimbeni V., Piotto G., Piazza D., Levacher P., Schweitzer M., Basso S., Bandy T., Benz W., Bergomi M., Biondi F., Boerner A., Borsa F., Brandeker A., Brändli M., Bruno G., Cabrera J., Chinellato S., De Roche T., Dima M., Erikson A., Farinato J., Munari M., Ghigo M., Greggio D., Gullieuszik M., Klebor M., Marafatto L., Mogulsky V., Peter G., Rieder M., Sicilia D., Spiga D., Viotto V., Wieser M., Heras A.M., Gondoin P., Bodin P., and Catala C. (2016) PLATO: a multiple telescope spacecraft for exoplanets hunting. In Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, Proc SPIE 990428 (29 July 2016).
Rai N. and van Westrenen W. (2013) Core-mantle differentiation in Mars. J Geophys Res (Planets) 118:1195–1203.
Ricker G.R., Winn J.N., Vanderspek R., Latham D.W., Bakos G.Á., Bean J.L., Berta-Thompson Z.K., Brown T.M., Buchhave L., Butler N.R., Butler R.P., Chaplin W.J., Charbonneau D., Christensen-Dalsgaard J., Clampin M., Deming D., Doty J., De Lee N., Dressing C., Dunham E.W., Endl M., Fressin F., Ge J., Henning T., Holman M.J., Howard A.W., Ida S., Jenkins J., Jernigan G., Johnson J.A., Kaltenegger L., Kawai N., Kjeldsen H., Laughlin G., Levine A.M., Lin D., Lissauer J.J., MacQueen P., Marcy G., McCullough P.R., Morton T.D., Narita N., Paegert M., Palle E., Pepe F., Pepper J., Quirrenbach A., Rinehart S.A., Sasselov D., Sato B., Seager S., Sozzetti A., Stassun K.G., Sullivan P., Szentgyorgyi A., Torres G., Udry S., and Villasenor J. (2014) The Transiting Exoplanet Survey Satellite (TESS). In Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, ProcSPIE 914320 (22–27 June 2014).
Rohrbach A., Ghosh S., Schmidt M.W., Wijbrans C.H., and Klemme S. (2014) The stability of Fe-Ni carbides in the Earth#700s mantle: evidence for a low Fe-Ni-C melt fraction in the deep mantle. Earth Planet Sci Lett 388:211–221.
Rohrbach A. and Schmidt M.W. (2011) Redox freezing and melting in the Earth's deep mantle resulting from carbon-iron redox coupling. Nature 472:209–212.
Santos N.C., Adibekyan V., Dorn C., Mordasini C., Noack L., Barros S.C.C., Delgado-Mena E., Demangeon O., Faria J.P., Israelian G., and Sousa S.G. (2017) Constraining planet structure and composition from stellar chemistry: trends in different stellar populations. Astron Astrophys 608:A94.
Sata N., Hirose K., Shen G., Nakajima Y., Ohishi Y., and Hirao N. (2010) Compression of FeSi, Fe3C, Fe0.95O, and FeS under the core pressures and implication for light element in the Earth's core. J Geophys Res Solid Earth 115, B09204.
Schäfer U., Yang C.-C., and Johansen A. (2017) Initial mass function of planetesimals formed by the streaming instability. Astron Astrophys 597, A69.
Seager S., Kuchner M., Hier-Majumder C.A., and Militzer B. (2007) Mass-radius relationships for solid exoplanets. Astrophys J 669:1279–1297.
Shabalin I.L. (2014) Carbon (graphene/graphite). In Ultra-high temperature materials I. 7–235. Springer, Dordrecht, Netherlands.
Smythe D.J., Wood B.J., and Kiseeva E.S. (2017) The S content of silicate melts at sulfide saturation: new experiments and a model incorporating the effects of sulfide composition. Am Mineral 102:795–803.
Southworth J., Mancini L., Madhusudhan N., Mollière P., Ciceri S., and Henning T. (2017) Detection of the atmosphere of the 1.6M exoplanet GJ1132 b. Astron J 153:191.
Stassun K.G., Collins K.A., and Gaudi B.S. (2017) Accurate empirical radii and masses of planets and their host stars with Gaia parallaxes. Astron J 153:136.
Steenstra E.S., Knibbe J.S., Rai N., and van Westrenen W. (2016) Constraints on core formation in Vesta from metal-silicate partitioning of siderophile elements. Geochim Cosmochim Acta 177:48–61.
Stewart A.J., Schmidt M.W., van Westrenen W., and Liebske C. (2007) Mars: a new core-crystallization regime. Science 316:1323.
Stixrude L. and Lithgow-Bertelloni C. (2005) Thermodynamics of mantle minerals—I. Physical properties. Geophys J Int 162:610–632.
Takahashi S., Ohtani E., Terasaki H., Ito Y., Shibazaki Y., Ishii M., Funakoshi K.-I., and Higo Y. (2013) Phase relations in the carbon-saturated C-Mg-Fe-Si-O system and C and Si solubility in liquid Fe at high pressure and temperature: implications for planetary interiors. Phys Chem Miner 40:647–657.
Thiabaud A., Marboeuf U., Alibert Y., Leya I., and Mezger K. (2015) Elemental ratios in stars vs planets (Research Note). Astron Astrophys 580, A30.
Toplis M.J. (2005) The thermodynamics of iron and magnesium partitioning between olivine and liquid: criteria for assessing and predicting equilibrium in natural and experimental systems. Contrib Mineral Petrol 149:22–39.
Tsuno K. and Dasgupta R. (2015) Fe-Ni-Cu-C-S phase relations at high pressures and temperatures—The role of sulfur in carbon storage and diamond stability at mid-to deep-upper mantle. Earth Planet Sci Lett 412:132–142.
Tsuno K., Ohtani E., and Terasaki H. (2007) Immiscible two-liquid regions in the Fe–O–S system at high pressure: implications for planetary cores. Phys Earth Planet Inter 160:75–85.
Unterborn C.T., Kabbes J.E., Pigott J.S., Reaman D.M., and Panero W.R. (2014) The role of carbon in extrasolar planetary geodynamics and habitability. Astrophys J 793:124.
Unterborn C.T., Dismukes E.E., and Panero W.R. (2016) Scaling the Earth: a sensitivity analysis of terrestrial exoplanetary interior models. Astrophys J 819:32.
Valencia D., O'Connell R.J., and Sasselov D. (2006) Internal structure of massive terrestrial planets. Icarus 181:545–554.
Valencia D., O'Connell R.J., and Sasselov D.D. (2009) The role of high-pressure experiments on determining super-Earth properties. Astrophys Space Sci 322:135–139.
Valencia D., Sasselov D.D., and O'Connell R.J. (2007) Radius and structure models of the first super-Earth planet. Astrophys J 656:545–551.
van Kan Parker M., Mason P. R.D., and van Westrenen W. (2011) Trace element partitioning between ilmenite, armalcolite and anhydrous silicate melt: implications for the formation of lunar high-Ti mare basalts. Geochim Cosmochim Acta 75:4179–4193.
Wagner F.W., Sohl F., Hussmann H., Grott M., and Rauer H. (2011) Interior structure models of solid exoplanets using material laws in the infinite pressure limit. Icarus 214:366–376.
Wang C., Hirama J., Nagasaka T., and Ban-Ya S. (1991) Phase equilibria of liquid Fe-S-C ternary system. ISIJ Int 31:1292–1299.
Watson E.B., Wark D.A., Price J.D., and Van Orman J.A. (2002) Mapping the thermal structure of solid-media pressure assemblies. Contrib Mineral Petrol 142:640–652.
Whitehouse L.J., Farihi J., Green P.J., Wilson T.G., and Subasavage J.P. (2018) Dwarf carbon stars are likely metal-poor binaries and unlikely hosts to carbon planets. Mon Not Roy Astron Soc, 479:3873–3878.

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Published In

cover image Astrobiology
Volume 19Issue Number 7July 2019
Pages: 867 - 884
PubMed: 30994366


Published online: 16 July 2019
Published in print: July 2019
Published ahead of print: 26 April 2019
Accepted: 11 January 2019
Received: 6 July 2018


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Kaustubh Hakim* [email protected]
Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands.
Department of Earth Sciences, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.
Rob Spaargaren
Department of Earth Sciences, ETH Zürich, Zürich, Switzerland.
Damanveer S. Grewal
Department of Earth, Environmental and Planetary Sciences, Rice University, Houston, Texas.
Arno Rohrbach
Institut für Mineralogie, Westfälische Wilhelms-Universität Münster, Münster, Germany.
Jasper Berndt
Institut für Mineralogie, Westfälische Wilhelms-Universität Münster, Münster, Germany.
Carsten Dominik
Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands.
Wim van Westrenen
Department of Earth Sciences, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.


Current Affiliation: Center for Space and Habitability, University of Bern, Bern, Switzerland.
Address correspondence to: Kaustubh Hakim, Center for Space and Habitability, University of Bern, 3012 Bern, Switzerland [email protected]

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No competing financial interests exist.

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