Terrestrial Planet Interiors C. Sotin fet Propulsion l-aboratory, Caffirnia Institute of Techno,loSy J. M. Jackson Caffirnia Institute of Technology S. Seager Massachus etts Institute of Tbchnology The discovery and study of exoplanets has always motivated the question of the existbnce and nature of terrestrial exoplanets, especially habitable planets. Exoplanet mass and radius measurements (yielding average density) are possible for a growing number of exoplanets, including terrestrial planets. The mass and radius provide a constraiiit for terrestrial planet interior models and, via models, enable interpretation of a planet's bulk composition. This chapter describes the fundamental equations for calculating the interior structure of terres- trial planets (including silicate-rich, iron-rich, and water-rich planets). A detailed description of interior structure models is given, with emphasis on the equation of state. High-pressure experimental measurements are needed to understand the internal structure and evolution of massive terrestrial exoplanets. Interpretation of low-mass planet interiors are fundamentally limited by degeneracies, because there a1e only two data points per planet: mass and radius. For example, large terrestrial planets having a massive primordial atrnosphere of H, and IIe cannot be distinguished from planets having dominant internal H2O layers based on the mass and radius alone. The occurrence of plate tectonics on exoplanets more massive than Earth is a controversial question, and, although unanswered, this chapter addresses the relationship between plate tectonics and thermal convection. A,s more and more low-mass exoplanets are being discovered, mass vs. radius statistics will build up. The hope for terrestrial exoplanet mass and radius measurements is that unique populations will emerge from statistics, helping us to understand planet formation and evolution. 1.. INTRODUCTION J) is related to the planet's ability to retain a large primordial atmosphere of H and He. Whether or not a planet retains The search for terrestrial exoplanets is one of the most substantial amounts of H and He depends primarily on a exciting challenges of the twenty-first century. For the first planet's mass. Wuchterl et al. (2000), for example, propose time astronomers have the chance to uncovet alarge sample that a planet less than 15 times the mass of Earth (Md will of planets that are predominantly rocky or icy and not the be terrestrial in nature, i.e., without significant H and He. easier-to-detect giant planets, which are composed mostly Beyond the terrestrial and giant planet groupitrgs, each of H and He. Terrestrial planets are of major scientific sig- category can actually be subdivided into two subsets. The nificance because they are the planets suitable for life as we terrestrial planets include both silicate-dominated planets like know it and amenable for future observational searches for Earth and Venus, as well as Mercury-like planets, which are atmospheric biosignature gases. In the conventional sense enriched in iron (i.e., depleted in silicates). The Mercury-type a habitable planet is one with some surface liquid water, exoplanet is of interest because finding many close to the because all life on Earth requfues liquid water. In contrast host star will help further understand Mercury's formation. to terrestrial planets, gtant and Neptune-sized planets en- The giant planet category includes not only the FI/He- shrouded by gas envelopes have no solid or liquid surfaces to dominated Jupiter and Saturn but also icy planets Uranus and support life as we know it, and their temperatures just below Neptune. The ice giants have a much smaller H-He envelope the deep atmosphere rapidly become too hot for life to exist. than Jupiter and Saturn (10-1 5Vo by mass). Note that how The solar system planets are conveniently divided into water-rich Uranus and Neptune are is not accurately known. two categories: the terrestrial planets (Mercury, Venus, Earth, Although their atmospheres are hydrogen-rich, there is a Mars) located in the inner solar system, and the giant planets tradeoff for their interior bulk compositions between ice + (Jupiter, Saturn, Uranus, Neptune) located in the outer solar an H/He envelope and a combination of rock/iron, much less system. The difference between teffestrial. and giant planets ice, and a more massive FI/FIe envelope. Extrapolating to icy 375 316 Exoplanets planets with insignificant H-He envelopes compared to Ura- total mass of the planet: O, Fe, Mg, and Si explain 9570 nus and Neptune are exoplanets of signiflcant astrobiological of the mass of Earth. If Ni, S, Al, and Ca are added, then interest: ocean planets or water worlds, which could also be 99.9Vo of the mass is taken into account (Thble 1).The latter called super Ganymedes or super Titans. Under the right at- three minor elements add a lot of complexities in the system. mospheric mass and interior temperature conditions, some of For example, experimental studies suggest that the oxidation these planets are likely to harbor internal liquid water oceans. state of iron and exsolution of metallic iron particles from Icy exoplanets with thin atmospheres can be considered as iron-bearing silicates is strongly affected by the presence of lnge analogs of the large icy satellites of Jupiter (Europa, Al (Frost et al., 2004) and extreme pressures and tempera- Ganymede, Callisto) and Saturn (Titan). tures (Jackson et al., 2009).If S is added to Fe, the melting The bulk interior composition of an exoplanet can be con- temperature decreases with increasing pressure and the phase strained with planet mass and radius measurements together relations become very complex (Chen et al., 2008). Although with planet interior equations. The planet mass is measured there is considerable debate sunounding the identity of the via radial velocity measurements (see chapter by Lovis and light element and crystal structure of the Fe-domin ant al- Fischer) and the planet radius via transit measurements (see loy in Earth's core, the effect on total planet mass is small. chapter by Winn). Some exoplanets are discovered with the Based on the available data, adding Ni, S, Al, and Ca to their radial velocity method and arc Iater found to transit, while closest major element results in a less than l%o error in the others are discovered by the transit technique and followed model-calculated total mass. Therefore, the composition of up for mass measurements via radial velocity. each layer can be described with four elements: O, Fe, Mg, Conceptually the equations that describe a terrestrial and Si (see Sotin et aI., 2001).In the mantle, Al is equally planet interior ate the conservation of mass, hydrostatic divided between Mg and Si for charge conservation and Ca equilibrium, energy transport, and the equation of state. The is added to Mg. In the core, Ni and S are added to Fe. most basic assumptions common to most models are that the Due to Earth's seismically active interior, the average terrestrial planet interior is formed from three basic materials structure of Earth (Fig. 1) is well known from global Earth (iron, silicate, and water) with some mixture and of various models (Dziewonski and Anderson, 1981). Earth is mainly phases, and that the planets have differentiated interiors. The composed of two layers: the iron-rich core (one-third of the new territory for terrestrial exoplanet interior models lies in mass) and the silicate mantle (two-thirds of the mass). These the equation of state, because terrestrial exoplanets more two layers differentiated very early in Earth's evolutionary massive than Earth (super Earths) can have interior pressures history because the melting temperature of iron alloys is much higher. For example, a planet ten times more massive lower than that of silicates and their density is higher. It is than Earth can have internal pressures three times higher envisaged that this differentiation processes occuffed into (e.9., Sotin et a1.,2007), which implies that new high-pressure the planetesimals by segregation and into protoplanets by mineral phases may exist. Super Earths are loosely defined Rayleigh-Thylor instabilities (Chambers, 2005). When the to be planets between 1 and 10 Mo that are predominantly protoplanets collided to form the terrestrial planets, their iron rocky or icy (see the Appendix of the chapter by Seager and cores would have merged. The change in gravitational energy Lissauer for exoplanet definitions). during the accretion processes controls the temperature differ- This chapter describes the concepts and equations needed ence between the core and the mantle (e.g. , Solomon, 1919). to understand and model terrestrial planet interiors. Applica- tion to the mass-radius relationship for a variety of terrestrial planet types and a detailed presentation of the equation of state different given. for materials is This chapter also fo- TABLE 1. Mass fraction of the major elements contained in cuses on terrestrial planet internal dynamics by providing EH enstatite chondrites (values from Javoy, 1995). the equations describing subsolidus convection in plan etary mantles and investigating the controversial question of plate Element Enstatite Model tectonics. We conclude with an outlook for the future of Mass Fraction charactenzing terrestrial exoplanet interiors based on the o 30.28 limited observational data (two data points per planet) and Fe 33.39 anticipated planet harvests. Si 19.23 Mg 12.2r 2. INTERIOR STRUCTURE Total 95.17 2.1. Bulk Composition and Structure Ni 2.02 Ca 1.01 AI 0.93 The minerals that compose the different layers of a planet S 0.85 are determined according to the elements that are present, the Total 99.92 pressure, and the temperature. Previous studies (e.g. , Sotin et al., 2007, and references therein) have shown that only This example shows that 8 elements account for more than 99.970 a limited number of elements are necessary to describe the of the total mass.