Giant Planet Formation, Evolution, and Internal Structure Ravit Helled Tel-Aviv University Peter Bodenheimer University of California, Santa Cruz Morris Podolak Tel-Aviv University Aaron Boley University of Florida & The University of British Columbia Farzana Meru ETH Zurich¨ Sergei Nayakshin University of Leicester Jonathan J. Fortney University of California, Santa Cruz Lucio Mayer University of Zurich¨ Yann Alibert University of Bern Alan P. Boss Carnegie Institution The large number of detected giant exoplanets offers the opportunity to improve our un- derstanding of the formation mechanism, evolution, and interior structure of gas giant planets. The two main models for giant planet formation are core accretion and disk instability. There are substantial differences between these formation models, including formation timescale, favorable formation location, ideal disk properties for planetary formation, early evolution, planetary composition, etc. First, we summarize the two models including their substantial differences, advantages, and disadvantages, and suggest how theoretical models should be connected to available (and future) data. We next summarize current knowledge of the internal structures of solar- and extrasolar- giant planets. Finally, we suggest the next steps to be taken in giant planet exploration. 1. INTRODUCTION conditions of protoplanetary disks in which planets form. Furthermore, the diversity in properties (e.g. mass, radius, Giant planets play a critical role in shaping the architec- semi-major axis, density) of exoplanets calls for multiple tures of planetary systems. Their large masses, orbital an- formation and evolution mechanisms to be explored. As a gular momentum, and fast formation make them prime can- result, detailed investigations of the formation mechanism, didates for driving rich dynamics among nascent planets, evolution, and interior structure of giant planets have been including exciting the orbits of small bodies and possibly conducted for decades, although for most of that time, our delivering volatiles to terrestrial planets. Their bulk prop- understanding of giant planets was limited to the four outer erties are also key for exploring the physical and chemical 1 planets in the Solar System. Naturally, theory was driven of Johansen et al. Here we focus on the later stages, start- to explain the properties of those planets and their particu- ing at the point where runaway growth of the planetesimals lar characteristics. The detections of giant planets outside has produced a planetary embryo having a fraction of an the Solar System have led to the discovery of a rich and di- Earth mass (M ), still surrounded by a swarm of planetes- verse population of giant exoplanets, many of which have imals. The planetesimals⊕ accrete onto the embryo to form measured radii and masses. the heavy-element core of the giant planet. Once the core Clues on the nature of giant planet formation might be reaches a fraction of M and its escape velocity exceeds revealed from the two giant planet correlations with stel- the local thermal speed of⊕ the gas in the disk, the core can lar metallicity [Fe/H] of main sequence stars. The first is begin to capture gas from the surrounding disk. Solids and the correlation of the frequency of giant planets with stel- gas then accrete concurrently. When the mass of gas (Menv) lar metallicity (Gonzalez, 1997; Santos et al., 2004; Fischer approaches that of the core (Mcore), gas accretion can be- and Valenti, 2005; Mortier et al., 2013) which has now been come very rapid and can build the planet up to the Jupiter determined for stellar masses from 0.3 to 2 M and metal- mass range. Gas accretion is cut off at some point, either licities [Fe/H] between -1.0 and 0.5∼ (Johnson et al., 2010). because of the dissipation of the disk and/or by the gravita- Nevertheless, the robustness and generality of the correla- tional interaction of the planet with the disk, which tends to tion between giant planet occurrence and stellar metallicity open up a gap in the planet’s vicinity as described below. is still under investigation (Maldonado et al., 2013). The second correlation suggests that the heavy element mass in giant planets is a function of stellar metallicity. Metal- 2.1.1. Physics of the core-accretion model rich stars tend to have metal-rich planets. There is a large Core accretion rate scatter, however, and planetary mass is a better predictor of CA calculations generally start with an embryo of metal enrichment than stellar metallicity (see section 5.2). 0.01-0.1 M surrounded by solid planetesimals, which∼ This explosion of new information demonstrates the need ⊕ would be expected to have a range of sizes. Safronov’s to understand planet formation in general, and presents an equation (Safronov, 1969) is a useful approximation for the opportunity to test planet formation theories. While the ba- planetesimal accretion rate onto an embryo: sic ideas of how giant planets are formed have not changed much, substantial progress has been made recently in high- dMsolid 2 = M_ = πR σsΩFg; (1) lighting the complexity of the models, in which effects that dt core capt were perceived as second-order may actually be fundamen- 2 tal in shaping the distribution of giant planets. where πRcapt is the geometrical capture cross section, Ω Accurate measurements of the giant planets in the So- is the orbital frequency, σs is the disk’s solid surface den- lar System can provide valuable information on the internal sity, and Fg is the gravitational enhancement factor. If no structures of the planets, which are extremely important to gas is present, then Rcapt = Rcore. In the presence of an test formation models. We anticipate major progress in that envelope, gas drag and ablation can result in planetesimal direction when data from Juno and Cassini Solstice mis- deposition outside the core, with Rcapt > Rcore. sions are available. In addition, the available information In the two-body approximation in which the tidal effects on the mean densities of giant exoplanets teaches us about of the central star are not included, Fg is given by the composition of giant planets in general. This chapter summarizes the recent progress in giant planet studies. ve 2 Fg = 1 + ; (2) v 2. GIANT PLANET FORMATION MODELS where ve is the escape velocity from the embryo, and v is In the following section we summarize the two forma- the relative velocity of the embryo and the accreting plan- tion models: core accretion (CA), the standard model, and etesimal. This approximation is valid only when the effect disk instability (DI). In the CA model the formation of a of the star is negligible, otherwise three-body effects must giant planet begins with planetesimal coagulation and core be taken into account, and the determination of Fg is much formation, similar to terrestrial planets, which is then fol- more complicated (Greenzweig and Lissauer, 1992). lowed by accretion of a gaseous envelope. In the DI model, gas giant planets form as a result of gravitational fragmen- The disk of planetesimals tation in the disk surrounding the young star. The gravitational focussing factor depends strongly on the excitation state of planetesimals (eccentricity and in- 2.1. CORE ACCRETION clination), which itself is the result of excitation by the The initial step in the formation of giant planets by CA is forming planet (and other planetesimals) and damping by the same as that for terrestrial planets, namely the buildup gas drag. Therefore, the value of Fg must be determined of planetesimals with sizes from a few tens of meters to (numerically) by computing the planet’s growth, the struc- a few hundred kilometers. Planetesimal formation is itself ture of the gas disk, and the characteristics of planetesimals undergoing current research and is addressed in the chapter 2 (dynamics and mass function) self-consistently. Gravita- Rp = Reff . As the envelope contracts and Reff expands, gas tional interactions among planetesimals and, more impor- is added at the outer boundary to maintain this condition. tantly, the influence of the planetary embryo tend to stir up Once the planet has entered the phase of rapid gas accre- the velocities of the planetesimals, reducing Fg. Fortier et tion, the envelope is relatively massive, and it can contract al. (2013) show that giant planet formation is suppressed rapidly. At some point the mass addition rate required by when this effect is included. the above condition exceeds the rate at which matter can The large number of planetesimals in the feeding zone be supplied by the disk. The disk-limited rates are calcu- (> 1010) requires that the evolution, growth, and accre- lated from three-dimensional simulations of the flow around tion rate of the planetesimals onto the embryo be handled a planet embedded in a disk (Lubow and D’Angelo, 2006; in a statistical manner (Inaba et al., 2003; Weidenschilling, Lissauer et al., 2009; D’Angelo et al., 2011; Bodenheimer 2008, 2011; Bromley and Kenyon, 2011; Kobayashi et et al., 2013; Uribe et al., 2013). The rates are eventually al. 2010). Planetesimals are distributed into a finite num- limited as the mass of the planet grows, exerts tidal torques ber of mass bins, with masses ranging from tens of meters on the disk, and opens up a gap. Although gas can still to tens of kilometers. The planetesimals are also distributed accrete through the gap, the rate becomes slower as the into radial distance zones. The codes calculate the evolution gap width increases. Planet-disk interactions, however, can of the size distribution and the orbital element distribution, change the eccentricities and increase M_ env substantially as well as the accretion rate of each size onto the planetary even after gap formation (Kley and Dirksen, 2006). embryo. The size distribution evolves through collisions, and, if relative velocities between planetesimals become Structure and evolution of the envelope large enough, through fragmentation.