Formation Of The Jovian Planets And Comets

In Section 2.3 we saw how a circumstellar disk is believed to have formed about the Sun and saw how such disks have been observed forming around other stars. We further saw that these disks are estimated to exist for approximately 10Myr before dispersing. There is overwhelming evidence that the planets of the solar system formed from such a circumstellar cloud and a number of theories have been put forward to explain the process of planet formation.

Until the mid-1990s, the only known planetary system was the solar system and thus such models had only the observed characteristics of the solar system and circumstellar clouds to constrain them. However, in 1995 the first extrasolar planet was discovered orbiting the star 51-Pegasus by Mayor and Queloz (1995) and since then the number of confirmed "exoplanets" has risen to 306 (as of August 2008) with over 30 stars having more than one planet. What has been most remarkable about these newly discovered planetary systems is how little resemblance most of them have to the solar system! Most exoplanets discovered are of Jupiter mass and orbit within 1 AU of their star. This is not just an observational bias of the detection techniques (Irwin, 2008), but a real difference between these planetary systems and our own. Hence, formation models of the solar system can no longer be considered in isolation, but must be consistent with exoplanetary systems also.

The most commonly accepted planetary formation model is the core accretion theory, which is described below. However, this still has considerable problems, not least of which is the difficulty in forming Jupiter-mass planets within the lifetime of that deduced for circumstellar disks, and also the fact that planets do not appear to remain where they formed in the circumstellar disk, but instead appear to migrate (Alibert et al., 2005c). Hence, alternative theories have been advanced, which will also now be discussed.

2.4.1 Core accretion model

The core accretion theory is the most commonly accepted theory of how all planets, including the giant planets, came to form in our solar system (Mizuno, 1980; Pollack et al., 1996). In this model, planet growth starts with the concentration of solid material in a proto-solar nebula into a sheet in the disk plane about the proto-star. Concentration of the solid material into a sheet increases the chances of collision for small grains in similar orbits, which when they collide with low collision speeds can stick together via small forces such as Van der Waal's forces, in a process called coagulation. While the relative velocities between grains in nearby orbits reduce with distance from the proto-star, so does the collision probability since nebula density also decreases. Hence, the coagulation time increases with distance except at the "ice line'', where water first condenses and where there is a small step-like increase superimposed on the general decreasing trend. Hence, it is estimated that by the time bodies grow to 10 mm at 30 AU, bodies at 5 AU can have grown to 0.1 km-10 km, large enough to be called planetesimals.

Dust and small particles in a circumstellar disk will orbit the star according to Kepler's laws, but the gas in the nebula orbits at a slightly lower rate due to the radial pressure gradient (Hueso and Guillot, 2003; Weidenschilling, 1977). Hence, small particles experience a drag force that causes them to spiral in towards the proto-star unless they are massive enough (i.e., larger than —1km) for the drag force to be negligible. This drag implies that the growth of particles to the size of —1 km must have been rapid, or that most of the solid material forming the cores of the planets was originally condensed at much greater distances from the proto-Sun.

Conditions in these early nebulas are likely to be highly turbulent and evidence for this comes from our own solar system, with the detection of crystalline silicates in comets coming from the Oort Cloud (Bockelee-Morvan et al., 1998). As discussed below, these comets are thought to have originally condensed in the cooler outer nebula near the orbits of Uranus and Neptune. They were thus expected to have a very low abundance of crystalline silicates since these minerals have high condensation temperatures and should have condensed close to the Sun, not in the outer solar system. Detection of such minerals in these comets thus suggests considerable mixing between material that originally condensed close to the Sun and that which condensed farther away.

The formation of the giant planets from planetesimals and nebula gas is generally thought to occur in three phases (Mizuno, 1980; Pollack et al., 1996) as outlined below.

Phase 1

Once planetesimals start to reach a size of the order of 10 km, their gravitational attractive forces start to become significant. This increases the collision rate between planetesimals and leads to the growth of larger planetesimals at the expense of smaller ones. This is a runaway process and leads to the formation of a number of embryos in a timeframe of perhaps 500,000 years after the formation of the star. The embryos account for —90% of the original mass in the local feeding zone, which forms an annular strip covering a small range of distances from the star, centered on the embryo. The remaining 10% of the solid material in each feeding zone is modeled to be composed of a swarm of very much smaller planetesimals. Solar nebula models predict that both the embryo masses and the widths of the feeding zones increase with distance, with a sharp increase at the water ice condensation line (Jones, 2007). Typical modeled embryo masses at 1 AU are of the order of 0.1 Me, while at 5 AU they are of the order of 10 Mffi .While it is tempting to think that this is due to the presence of ice as well as refractory elements in the outer parts of the dust sheet, and hence a greater density of solid material, this is in fact not quite correct. The embryo formation process initially requires low-speed collisions between planetesimals in near-identical orbits and these conditions are more easily met in the outer, more slowly rotating part of the nebula, than the inner more rapidly rotating, turbulent part. An additional effect is that at greater distances from the Sun, tidal disruption forces are less, which also allows embryos to form more easily. Hence, the calculated widths of the feeding zones are modeled to increase with distance and thus the predicted embryo masses, and their separations, are larger.

Phase 2

Once the embryos reach a mass of the order of 10 Me, they start being able to trap the nebula gas itself, as well as the remaining planetesimals. This second, possibly very slow stage of accretion is predicted to last between 1 Myr and 10 Myr and leads to the accumulation of a considerable envelope of gas and ice about the initial primary ice core. Eventually the mass of some of the planets reaches a critical mass, which is so high that the remaining nebula gas becomes unstable to hydrodynamical collapse, leading to the final phase of formation. Estimates of the critical mass required range from 5 Mffi (Hubickyj et al., 2005) to 20 Mffi or more (Pollack et al, 1996).

Phase 3

Once the critical mass is reached, any remaining nebula gas in the region of the planet hydrodynamically collapses onto it. This is believed to be the most rapid phase of formation and is modeled to have lasted 30,000 yr for Jupiter and 20,000 yr for Saturn. Since the time for accretion of the critical mass is predicted to increase with distance from the star, due to the decrease in nebula density, it would appear that Uranus and Neptune in our own solar system never accreted enough mass to leave Phase 2. The energy released by the accretion of giant planets would raise the internal temperatures of the planets, including their new gaseous envelopes, significantly. Hence, most of the icy planetesimals would dissolve into the envelope, with only the more rocky materials accreting onto the core itself. The heat released by this accretion would also initiate substantial convection in the envelope, further inhibiting accretion on to the core.

Evidence in favor of the core accretion model

The timing of these phases is critical in explaining the nature of the giant planets of our solar system. Jupiter is predicted to have reached Phase 3 about 1.5 Myr after the formation of the Sun, and Saturn after something like 11 Myr (Hersant et al., 2001). These times are very much model-dependent, but what is generally accepted with these models is that before Uranus and Neptune could reach their critical mass, the remnants of the circumsolar disk were finally dissipated when the Sun entered its T-Tauri phase, about 16 Myr after the formation of the proto-Sun (Drouart et al., 1999). The high solar wind associated with this phase effectively swept all remaining gas out of the solar nebula and shut off the gas capture process.

The bulk differences between the giant outer planets, and indeed the inner terrestrial planets, are very elegantly explained with this model and an observation that supports this timescale of giant planet formation is that of the proto-planetary disk around a nearby pre-main sequence star (Brittain and Rettig, 2002). The abundance of CO (and presumably other gases) in the inner part of this disk, which is estimated to be 5 Myr to 10 Myr old, appears to be very low out to a distance of approximately 17 AU, but is substantial at larger distances. This suggests that the inner stellar system has already been substantially cleared of gas. However, H^ emission is also detected from the star system. While it is theoretically possible that such emission comes from the inner edge of the circumstellar disk near 17 AU this seems unlikely since the inferred abundance of CO at this distance should very efficiently destroy all H^ molecules there. Instead, it is suggested that the H^ emission comes from the auroral regions of one or more giant planets that have already formed at distances less than 17 AU from the star. This suggestion is consistent with the observation that the only H^ emission observed anywhere in our own solar system comes from the auroral regions of our own giant planets.

Although some of the planetesimals remaining in the nebula would have continued to be captured (as indeed they are today with Jupiter capturing Comet Shoemaker-Levy 9 in 1994), most remaining planetesimals would have been ejected from the solar system by the gravitational perturbations to their orbits exerted by the giant planets. All planetesimals in the Jupiter-Saturn region are predicted to have been accumulated or ejected completely. Planetesimals in the Uranus-Neptune region, however, would have been less violently ejected and are thought to have formed the Oort Cloud, which is believed to exist as a spherical shell of small, irregularly shaped bodies orbiting the Sun well beyond the main planets. The existence of this cloud was postulated in 1950 by the Dutch astronomer Jan Hendrick Oort (1900-1992) who noticed that no comet had ever been observed with an orbit indicating that it came from interstellar space, and that the orbits of most long-period comets had aphelia (greatest distance from the Sun) of about 50,000 AU, and no preferred direction. Hence, Oort proposed that long-period comets come from objects uniformly spread around the Sun at about this aphelia distance, which are perturbed by tiny effects such as gravitational tides exerted by stars in the galactic disk and in the galactic core. Estimates for the mass of material in the Oort Cloud vary from about 40 Mffi to perhaps the mass of Jupiter, and most Oort Cloud objects

The OorE Comet Cloud

Figure 2.5. The Oort Comet Cloud. Courtesy of Donald Yeomans, Jet Propulsion Laboratory.

are thought to orbit at a distance of between 10,000 AU and 20,000 AU from the Sun, although the cloud extends outwards as far as perhaps 50,000 AU to 70,000 AU (Figure 2.5).

Beyond the orbit of Neptune, the probability of embryo formation appears to have been too small to form a giant planet, perhaps due to the lack of turbulent mixing at this distance. Instead, the remaining planetesimals in this region, which form the Kuiper-Edgeworth Belt, are probably relatively unevolved examples of the planetesimals that originally existed in this region. The Kuiper-Edgeworth Belt is named after Gerard Peter Kuiper (1905-1973) and Kenneth Essex Edgeworth (18801972) who independently suggested the presence of small planetary bodies beyond the orbit of Pluto and Neptune, respectively. The Kuiper-Edgeworth Belt (often just called the Kuiper Belt) extends from the orbit of Neptune at 30 AU out to approximately 50 AU and is thought to contain at least 70,000 "trans-Neptunians" or Kuiper Belt Objects (KBOs) with diameters exceeding 100 km, concentrated near the ecliptic plane (Figure 2.6, see color section). New KBOs are continually being discovered and the total now stands at over 1,000. It is thought that the Kuiper Belt may extend farther and merge with the Oort Cloud at a distance of roughly 1,000 AU. The high eccentricity of Pluto's orbit, and the high inclination of Triton's orbit about Neptune (indicating that it is probably a captured satellite, rather than forming from the circumplanetary disk as discussed in Section 2.5) suggest that both these bodies may in fact themselves be KBOs. This conclusion is supported by the recent discovery of several KBOs with diameters of the order of 1,000 km.

Finally, the core accretion model of formation is consistent with almost all of the planets spinning in the same direction as their orbital motion (prograde). The obliquities of the planets probably arose from off-center collisions between planetesimals and perhaps embryos towards the end of formation although they may also have arisen due to spin-orbit resonances (Ward and Hamilton, 2002). One particularly extreme case is Uranus which has an obliquity of 98° and thus spins almost on its side. Such a large obliquity could have arisen from several cumulative off-center impacts, or conceivably a single massive impact towards the end of formation.

2.4.2 Gravitational instability model

Although the core accretion model fits the observed characteristics of our solar system very well, there are two main problems with it. First of all, the model as outlined above appears to be too slow when compared with the lifetimes of circum-stellar disks observed around other stars. Haisch et al. (2001) have estimated the ages of circumstellar disks about stars in nearby clusters by analyzing the mean color of the stars in these clusters. They find that circumstellar disks appear to evaporate long before the T-Tauri phase is reached and that half of the stars in these clusters lose their disks within 3 Myr, with a mean overall lifetime of 6 Myr. Similarly, Briceno et al. (2001) find that stars older than 10 Myr do not have massive, optically thick disks. A second problem with the core accretion model is that it takes no account of the fact that once planets start to form, they appear to migrate, as can be seen by the "Hot Jupiters'' of other stars, where very large gas giants are seen orbiting within 1 AU of their star.

An alternate view of giant planet formation that tackles the time of formation problem is that if protostellar disks are dense enough they may become gravitation-ally unstable. In such an unstable disk, giant planets may collapse directly from the disk in the early period of circumstellar disk evolution (Boss, 1997, 2002,2004; Mayer et al., 2002). The most widely used criterion for assessing the gravitational stability of a circumstellar disk is the Toomre stability parameter Q (Pickett and Lim, 2004; Toomre, 1964), which depends on a number of factors such as disk surface density. If the Toomre Q parameter is less than approximately unity, a disk can become unstable to the rapid growth of a spiral structure, which can then clump together to form giant planets. However, although this process is fast and can also account for the "Hot Jupiters'', the models have considerable difficulty in actually condensing a planet because the disk does not appear to cool rapidly enough (Pickett and Lim, 2004; Rice et al., 2003), although Boss (2004) suggests that convective overturning may assist this. Another drawback of the model is that condensed planets would all have a composition similar to that of the central star, which does not fit at all well with observations of the solar system giant planets, where as we shall see the abundance of heavy elements increases with distance from the Sun. The final drawback to these models is that they are not sensitive to the abundance of dust in the nebula, and thus the process should be equally likely around metal-poor stars as metal-rich ones. This goes against the observation that the exoplanets found so far are preferentially around metal-rich stars (Irwin, 2008).

2.4.3 Migration

The second problem with the core accretion model outlined in the previous section is that it takes no account of the fact that planets appear to migrate during formation. The giant planets of our solar system and of other stars are unlikely to be at the same distance from the central star as when they initially formed due to gravitational interactions with other growing planetesimals (leading to their ejection from the solar system) and frictional interactions with the accretion disk itself. A surprising property of the known KBOs is that almost a quarter of those discovered so far are in a 3:2 orbital resonance with Neptune, meaning that they complete three orbits for every two orbits of Neptune. Pluto also has a 3:2 resonance with Neptune, and for this reason KBOs in this orbit have become known as Plutinos. That such a large proportion of KBOs occupy this resonance is strong evidence that Neptune (and probably Uranus) has migrated outwards during the evolution of the solar system, by as much as 7 AU to 8 AU, and swept up a number of KBOs into the 3:2 resonance as it did so.

The phenomenon was first conjectured by Fernandez and Ip (1984), who modeled the scattering of comets and planetesimals in the early solar system and pointed out that the orbital motions of the giant planets are interdependent since comets scattered inwards by one planet may be scattered again by other planets. In this way Fernandez and Ip (1984) found that while Jupiter was modeled to migrate towards the Sun through the ejection of comets, the other giant planets were modeled to migrate outwards. Conditions in the early circumstellar disk were probably very turbulent, perhaps including magneto-hydrodynamic (MHD) effects (Papaloizou et al., 2004) and this turbulence would have led to a net transfer of mass outward in the outer part of the disk, and inwards toward the Sun nearer the center, with a dividing radius at around 10 AU (Ida et al., 2000).

Extrasolar planetary systems with close Jovian planets or "Hot Jupiters" offer clear evidence that in many cases giant planets forming within the critical radius of the disk migrate inwards. Such planets would gravitationally eject or capture all terrestrial planets in the so-called "habitable zone" of the inner planetary system, where surface temperatures would allow the presence of liquid water and thus, perhaps, the evolution of life. Keeping giant planets at distances greater than AU not only allows the development of an inner planetary system like that in our solar system, but also efficiently expels small planetesimals that would otherwise swarm in this region, continually bombarding the inner planets and impeding the evolution of life. Hence, the "smooth" evolution of life on Earth may actually have required the presence of Jupiter, but not too close! It is thus of great interest to determine whether or not there are other planetary systems with characteristics more like ours, and multiple planetary systems with some resemblance to the solar system are now being discovered (Mason, 2008).

Until recently, the migration of planets in these circumstellar disks was thought to be restricted to two main types. Type I migration is expected when the planet mass is small, such that its Hill radius (i.e., the distance from the planet within which the gravitational field is dominated by the planet itself) is much smaller than the disk thickness. In such cases a proto-planet will tidally interact with the disk via Lindblad resonances (Ward, 1986, 1997) and is modeled to migrate rapidly. Larger planets, however, appear to be controlled by Type II migration, where the planetary mass is large enough to open up a gap in the disk, splitting it up into an inner and outer part. The planet is then locked in with the long-term evolution of the disk (Lin and Papalaizou, 1986a, b) and slowly migrates inwards toward the star (assuming it is within the critical orbital distance described above). In this model, if the planet does not migrate all the way inwards before the disk dissipates, it is likely to have an orbital distance greater than 0.05 AU to 0.2 AU, which is consistent with the observed lack of "Hot Jupiters" with mass > 4 Mj orbiting within 0.3 AU of their stars (Irwin, 2008). However, objects that have undergone this type of migration would be expected to be heavier for smaller orbital radii, since they would have had more time to accrete the disk material, which is not observed amongst known extra-solar giant planets. Hence "Hot Jupiters" do not appear to be explained by either Type I or Type II migration. Instead, "Hot Jupiters" may be explained by an intermediate, or "runaway" mode of migration (Masset and Papalaizou, 2003) where, for certain combinations of planet and disk mass, a planet very rapidly moves either toward or away from the star, changing its orbital radius by a factor of 2 or more. The runaway process does not carry on indefinitely since eventually the planet becomes so large that it clears out its "feeding zone" and is then governed by slow Type II migration.

Finally, one solution to the apparent slowness of the core accretion model is proposed by Rice and Armitage (2003) who suggest that turbulent fluctuations in a proto-planetary disk cause migrating giant planets to perform more of a random walk, with an amplitude of a few tenths of an astronomical unit, than a steady drift towards the star, resulting in an acceleration of the accretion rate by almost an order of magnitude. This scenario is further explored by Alibert et al. (2005b) who find that the migration of the early giant planets meant that their feeding zones were never depleted during Phase 2 of their formation, which was consequently much faster than predicted by the classical core accretion model. In their model an embryo was started at 11.5AU and allowed to migrate inwards, forming a planet with 30 Mffi in the envelope and 5 Mffi in the core, which is close to the current estimates of internal structure models of Jupiter (Guillot et al., 2004; Saumon and Guillot, 2004).

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