Giant planet formation models

The observation that the mass function of young objects in star-forming regions extends down through the brown dwarf mass range to below the deuterium burning limit (Zapatero Osorio et al. 2000), together with the lack of any convincing theoretical reason to believe that the collapse process that leads to stars cannot also produce substellar

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Figure 6. Our standard planetesimal disk placed around two 0.5 Mq stars with aB = 0.2 AU and eB = 0.5 (run CB_.2_.5_.5_c in Quintana & Lissauer 2006) results in the ejection of much of the material in the terrestrial planet region, leaving less mass in the terrestrial planets than in simulations of growth from an analogous disk around a single 1 Mq star. A simulation with very similar initial conditions that yields only a single terrestrial planet is shown by Lissauer et al. (2004).

objects (Wuchterl & Tscharnuter 2003), strongly implies that most isolated (or distant companion) brown dwarfs j and isolated high planetary mass objects formed via the same collapse process as do stars.

By similar reasoning, the 'brown dwarf desert,' the profound dip in the mass function of companions orbiting within several AU of Sun-like stars (Marcy et al. 2004), strongly suggests that the vast majority of extrasolar giant planets formed via a mechanism different from that of stars. Within our Solar System, bodies up to the mass of Earth consist almost entirely of condensable (under reasonable protoplanetary disk conditions) material, and the fraction of highly volatile gas increases with planet mass through Uranus/Neptune, to Saturn and finally Jupiter (which is still enriched in condensables at least threefold compared to the Sun), arguing for a unified formation scenario for all of the planets and smaller bodies. The continuum of observed extrasolar planetary properties, which stretches to systems not very dissimilar to our own, suggests that extrasolar planets formed as did the planets within our Solar System.

Models for the formation of gas giant planets were reviewed by Wuchterl, Guillot, & Lissauer (2000). Star-like direct quasi-spherical collapse is not considered viable, both because of the observed brown dwarf desert mentioned above and the theoretical arguments against the formation of Jupiter-mass objects via fragmentation (Bodenheimer et al. 2000a). The theory of giant planet formation that is favored by most researchers is the core-nucleated accretion model, in which the planet's initial phase of growth resembles that of a terrestrial planet, but the planet becomes sufficiently massive (several M®) that it is able to accumulate substantial amounts of gas from the surrounding protoplanetary disk. The only other hypothesis receiving significant attention is the gas instability model, in which a giant planet forms directly from the contraction of a clump that was produced via a gravitational instability in the protoplanetary disk.

Numerical calculations on gravitationally unstable disks by Adams & Benz (1992), recent work by Boss (2000), and Mayer et al. (2002) have revived interest in the gas instability model. However, these instabilities can only occur in disks with atypical physical properties (Ravikov 2005). Additionally, the gas instability hypothesis only accounts for massive stellar-composition planets, requiring a separate process to explain the smaller bodies in our Solar System and the heavy element enhancements in Jupiter and Saturn. It is particularly difficult to account for the existence of intermediate objects like Uranus and Neptune in such a scenario. See Durisen (this volume) for a more extensive discussion of the gas instability model.

The core nucleated accretion model relies on a combination of planetesimal accretion and gravitational accumulation of gas. In this theory, the core of the giant planet first forms by accretion of planetesimals, while only a small amount of gas is accreted. Core accretion rates depend upon the surface mass density of solids in the disk and physical assumptions regarding gas drag, planetary migration, etc. (Lissauer 1987; Pollack et al. 1996; Inaba et al. 2003; Alibert et al. 2005). The escape velocity from a planetary embryo with M > 0.1 is larger than the sound speed in the gaseous protoplanetary disk. Such a growing planetary core first attains a quasi-static atmosphere (that undergoes f Following Lissauer (2004), these definitions are used throughout this chapter: Star: self-sustaining fusion is sufficient for thermal pressure to balance gravity. Stellar remnant: dead star—'no' more fusion (i.e., thermal pressure sustained against radiative losses by energy produced from fusion is no longer sufficient to balance gravitational contraction).

Brown dwarf: substellar object with substantial deuterium fusion (more than half of the object's original inventory of deuterium is ultimately destroyed by fusion). Planet: negligible fusion (< 13MJ) + orbits star(s) or stellar remnant(s).

Kelvin-Helmholtz contraction as the energy released by the accretion of planetesimals) and gas is radiated away at the photosphere.

The contraction timescale is determined by the efficiency of radiative transfer, which is relatively low in some regions of the envelope. Spherically symmetric (1-D) models show that the minimum contraction timescale is a rapidly decreasing function of the core's mass (Pollack et al. 1996). The gas accretion rate, which is initially very slow, accelerates with time and becomes comparable to the planetesimal bombardment rate after the core has grown to ~10 M®. Once the gaseous component of the growing planet exceeds the solid component, gas accretion becomes very rapid, and leads to a runaway accumulation of gas.

The composition of the atmosphere of a giant planet is largely determined by how much heavy material was mixed with the lightweight material in the planet's envelopes. Once the core mass exceeds ~0.01 M®, the temperature becomes high enough for water to evaporate into the protoplanet's envelope. As the envelope becomes more massive, late-accreting planetesimals sublimate before they can reach the core, thereby enhancing the heavy element content of the envelope considerably.

The fact that Uranus and Neptune contain much less H2 and He than Jupiter and Saturn suggests that Uranus and Neptune never quite reached runaway gas accretion conditions, possibly due to a slower accretion of planetesimals (Pollack et al. 1996). The rate at which accretion of solids takes place depends upon the surface density of condensates and the orbital frequency, both of which decrease with heliocentric distance. Alternatively/additionally, Uranus and Neptune may have avoided gas runaway as a result of the removal of gas from the outer regions of the disk via photoevaporation (Hollenbach et al. 2000). Additional theoretical difficulties for forming planets at Uranus/Neptune distances have been addressed by Lissauer et al. (1995) and Thommes et al. (2003). New models are being proposed to address these problems by allowing rapid runaway accretion of a very small number of planetary embryos beyond 10 AU. In the model presented by Weidenschilling (2005), an embryo is scattered from the Jupiter-Saturn region into a massive disk of small planetesimals. Goldreich et al. (2004) propose that planetesimals between growing embryos are ground down to very small sizes and are forced into low inclination, nearly circular orbits by frequent mutual collisions. Planetary embryos can accrete rapidly in such dynamically cold disks as those in the models of Weidenschilling and of Goldreich et al. Alternatively, Thommes et al. (2003) suggest that Uranus and Neptune accreted much closer to the Sun than these planets are at present, and were subsequently scattered out to their current locations by gravitational perturbations of Jupiter and Saturn (see also Tsiganis et al. 2005).

During the runaway planetesimal accretion epoch, the protoplanet's mass increases rapidly. The internal temperature and thermal pressure increase as well, preventing substantial amounts of nebular gas from falling onto the protoplanet. When the planetesimal accretion rate decreases, gas falls onto the protoplanet more rapidly. The protoplanet accumulates gas at a gradually increasing rate until its gas component is comparable to its heavy element mass. The key factor limiting gas accumulation during this phase of growth is the protoplanet's ability to radiate away energy and contract (Pollack et al. 1996; Hubickyj, Bodenheimer, & Lissauer 2005). The rate of gas accretion then accelerates more rapidly, and a gas runaway occurs. The gas runaway continues as long as there is gas in the vicinity of the protoplanet's orbit. The protoplanet may cut off its own supply of gas by gravitationally clearing a gap within the disk (Lin & Papaloizou 1979). Such gaps have been observed around small moons within Saturn's rings (Showalter 1991). D'Angelo, Kley, & Henning (2003) are using a 3-D adaptive mesh refinement code to follow the flow of gas onto an accreting giant planet. Models such as this will eventually allow the determination of final planetary mass as a function of the time-varying properties (density, temperature, viscosity, longevity, etc.) of the surrounding disk. Such a self-regulated growth limit provides a possible explanation to the observed mass distribution of extrasolar giant planets. Alternatively, the planet may accumulate all of the gas that remains in its region of the protoplanetary disk.

A major uncertainty associated with the emergence of planets is their predicted orbital migration as a consequence of the gravitational torque between the disk and the planet (Goldreich & Tremaine 1980; Ward 1986; Bate et al. 2003). Planetary orbits can migrate towards (or in some circumstances away from) their star as a consequence of angular momentum exchange between the protoplanetary disk and the planet. Planets that are more massive than Mars may be able to migrate substantial distances prior to the dispersal of the gaseous disk. Thus, it is quite possible that giant planets may form several AU from their star and then migrate inwards to the locations at which most extrasolar planets have been observed. Disk-induced migration is considered to be the most likely explanation for the 'giant vulcan' planets with periods of less than a week, because in situ formation of such objects is quite unlikely (Bodenheimer et al. 2000b). Livio & Pringle (2003) find no basis to suggest that planetary migration is sensitive to disk metallicity, and conclude that higher metallicity probably results in a higher likelihood of (giant) planet formation. The difficulty with the migration models is that they predict that planets should migrate too rapidly, especially in the Earth-to-Neptune mass range that planetary cores grow through in the core-nucleated accretion scenario. Moreover, because predicted migration rates increase as a planet moves inwards, most migrating planets should be consumed by their star. However, a planet may end up in very close 51 Peg-like orbits if stellar tides can counteract the migration, or if the disk has a large inner hole (Lin et al. 2000). Resolution of this rapid migration dilemma may require the complete and nonlinear analysis of the disk response to the protoplanet in the corota-tion regions. See Ward & Hahn (2000), Masset & Papaloizou (2003), and Thommes & Lissauer (2005) for more extensive discussions of planetary migration.

Many of the known extrasolar giant planets move on quite eccentric (0.2 < e < 0.7) orbits. These orbital eccentricities may be the result of stochastic gravitational scatterings among massive planets which have subsequently merged or been ejected to interstellar space (Weidenschilling & Marzari 1996; Levison, Lissauer, & Duncan 1998; Ford, Havlickova, & Rasio 2001), by perturbations of a binary companion (Holman, Touma, & Tremaine 1997), or by past stellar companions if the now-single stars were once members of unstable multiple-star systems (Laughlin & Adams 1998). However, as neither scattering nor migration offer a simple explanation for those planets with nearly circular orbits and periods from a few weeks to a few years, the possibility of giant planet formation quite close to stars should not be dismissed (Bodenheimer et al. 2000b).

Most of the observed extrasolar giant planets orbit between a few tenths of an AU and a few AU from their star, i.e., they are located much closer to their stars than Jupiter is from our Sun. These planets may have formed farther from their star and migrated inwards, but without a stopping mechanism, which isn't known at these distances, they would have fallen into the star. Lissauer (2001) suggested that the orbits could be explained if disks cleared from the inside outwards, leaving the planets stranded once they were too far interior to the disk for strong gravitational coupling to persist. Observations of the 2:1 resonant planets orbiting GJ 876 by Marcy et al. (2001; see also Rivera et al. 2005) support such a model, as do data which imply that the star CoKu Tau/4 has a disk with an inner hole (Forrest et al. 2004).

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