Until very recently, theoretical mechanisms for forming planetary systems were constrained by observations of one system - our own. The inherent pitfalls in dealing with what Wetherill [W7] terms 'statistics of one' were well appreciated by planetary scientists and cosmogonists. Nonetheless, models for the formation of our Solar System came to represent the standard paradigm for planetary formation.
The main characteristics of the Solar System are: first, a significant change in the mean composition with increasing distance from the Sun, with the terrestial planets and asteroids at radii of less than 4 astronomical units (AU), gas giants at intermediate distances and icy planetismals at radii beyond 30 AU; second, nearly coplanar and low-eccentricity orbits for all nine planets and many lower mass objects; third, angular momentum vectors in both orbital motion and rotation that are well aligned with the direction of solar rotation. Taken together, these properties strongly suggest an origin within a disk formed by the collapse of the solar nebula. This concept of Solar System formation, first suggested by Kant [K3] and further elaborated by Laplace [L1], held sway during the nineteenth century, but was supplanted in the early years of the 20th century by the near-collision theory proposed originally by Buffon [B12], and revived by Chamberlin [C3] and Moultin [M7], and, later, by Jeans [J2] and Jeffreys [J3]. The latter hypothesis envisaged a close encounter with a passing star leading to a long spindle of material being drawn from the Sun by tidal forces, with the planets condensing from that spindle.
The near-collision model had (to some) the philosophical attraction of requiring a very rare, perhaps unique, event. In contrast, the nebular hypothesis renders planet formation part of the natural sequence in star formation. The latter hypothesis was revived by von Weizsacker [W5], who postulated the formation of cellular vortices due to instabilities within the protoplanetary disk, partly as a means of accounting for the numerical progression of planetary semi-major axes known as Bode's Law. The origin of modern theories, however, can be traced to Kuiper [K9], who not only suggested that the protoplanetary nebula was significantly more massive than the present-day sum of planetary masses, perhaps exceeding 0.1 M0, but also proposed that the gas giants are the result of gaseous accretion on solid protoplanetary cores. Safronov [S2] and Hayashi et al. [H2] further extended this concept of building planets through accretion of planetismals within a rotating disk of gas and dust. The identification in the 1980s of such disks associated with young T Tauri stars (see Section 3.6) provides strong support for this conceptual model.
Current Solar System formation models are well summarised by Lissauer [L12], Pollack et al. [P2] and Koerner [K6]. The original solar nebula is envisaged as having a diameter of —100 AU and a mass exceeding 0.02 M0, based on adding cosmic proportions of hydrogen and helium to the current 'metallic' planetary masses. These estimates are consistent with masses and radii inferred from millimetre observations of T Tauri disks [B2]. HST near-infrared imaging shows that dust is present in the equatorial plane (Figure 3.20, see colour section); supplying the vital building blocks for planet formation.
Classical formation scenarios envisaged the planets forming by progressive accretion within a relatively quiescent solar nebula. Refractory silicate grains are expected to form as the temperature drops below 1,700 K, and their formation is expected to follow a well-ordered radial condensation sequence as the proto-planetary nebulae cools. The grains aggregate to form 1-10-km planetismals, which accrete material within the Hill sphere:
where ap is the distance from the central star and MP and Mt are the mass of the planetismal and star, respectively. Simulations show that material within 4 Rh of the planetismal can be perturbed onto eccentric orbits and eventually accreted [L11]. The planetismals grow to form —10~4 Mj (Jovian mass) planetary 'embryos' and, finally, terrestrial-mass planets [W6]. Recent observations of circumstellar disks show that they are turbulent, and grain formation is likely to progress in a less ordered, more stochastic fashion. Processes such as collisional adhesion [W3], [C9] are likely to play a vital role in the formation of planetismals that form the seeds for future planets.
The traditional method of forming gas giants is accretion onto a 'super-embryo', formed through the merging of 10-20 rocky embryos. The ambient temperature in the disk is expected to drop to <100K at radii exceeding 4AU for solar-type stars. This allows ice to condense (mainly H20, but also C02, CO, NH3, CH4 and N2), and the proto-gas giants accrete larger cores and massive envelopes [M6]. Envelope accretion, however, is predicted to require as much as 107 years [P2], a timescale that conflicts with the observed lifetime of optically thick disks in young stars (<5Myr, see Section 3.6.2). This issue is less of a problem for terrestrial planet formation, since the constituent planetismals are expected to form more rapidly, but clearly makes it difficult to reach Jovian masses. Moreover, since accretion is only effective at distances less than 4 Rh, a planet on a circular orbit in an idealised quiescent disk will sweep out a low-density ring, and eventually run out material. Both of these difficulties led to suggestions that systems with Jovian-mass planets might be the exception, rather than the rule [W7]. The recent spate of planetary detections, however, shows that such systems are not rare and suggests that an alternative formation scenario may be required, as discussed in the following section.
Wetherill has pointed out that the existence of Jovian-mass planets at distances of several AU from the primary star may have a strong influence on the evolution of a solar system. Jupiter, and to a lesser extent Saturn, acts as a guardian of the inner solar system, ejecting cometary-mass objects to large radii, and therefore reducing the potential for catastrophic Shoemaker-Levy-like collisions with the terrestial planets. Uranus and Neptune perform similar tasks in the outer solar system, marshalling comets into the Kuiper and Oort belts. Thus, the development of complex life might be inhibited in a system lacking a Jovian-like planet at the requisite distance from the central star, since the higher rate of cometary and asteroid impacts could disrupt an ecosystem on relatively short (— 104 year) timescales.
Boss [B8] has advocated an alternative process to the standard core accretion scenario, reviving the gravitational instability hypothesis proposed originally by Kuiper [K9] and later championed by Cameron [C10]. Under this mechanism, gravitationally unstable condensations form within the gaseous circumstellar disk, assuming the Toomre gravitational stability parameter:
where Cs is the sound speed, k the epicyclic frequency at some point on the disk, G the gravitational constant, and X the surface density. Once the condensations form, they collapse and grow in size as they accrete further material from the disk. Boss' calculations suggest that Jovian-mass (and larger) objects can form in a matter of only a few thousand years, well within the projected lifetime of circumstellar disks.
Planet formation via gravitational instability has also been explored by Mayer and collaborators, who have completed a sophisticated series of smooth particle hydrodynamical (SPH) simulations of protoplanetary disks [M8]. The simulations show that spiral instabilities tend to appear rapidly, and the disk fragments form dense clumps. These clumps merge to give a small number of protoplanets, which continue to accrete material from the disk and can acquire masses from 0.1 to —7 Jupiter masses over a period of —1,000 years. The disks themselves are disrupted on timescales of a few x 104 years in some of the models, which is broadly consistent with observations of T Tauri stars, but may present challenges in supplying the 'hot Jupiters' in the current roster of extrasolar planets. However, the protoplanets often have orbits with significant eccentricities, leading to subsequent interactions and orbital evolution (see Section 11.4.2).
There are two main difficulties faced by this mechanism: first, forming the 0.020.03 Mj ice and rock cores that are required by models of the internal structure of Jupiter and Saturn; and, second, forming bodies that are smaller than 5-10 Mj. The first problem has been ameliorated to some extent by recent theoretical calculations, which suggest that gas giants may have core masses lower than standard values by a factor of three or more [G13]. However, the fractional metal content of the Solar System planets increases from —4 times solar in Jupiter, to —10 times in Saturn and —40 times in Uranus and Neptune [W11]. While the gaseous fragmentation models can probably accommodate the lower mass cores, it is not clear that they can account for the total metal content of the outer planets. The second difficulty arises because the gravitational instability mechanism is so efficient: again, forming gas giants as small as Uranus and Neptune is particularly problematic. Nonetheless, gravitational fragmentation offers a potential alternative to standard core accretion, and merits more extensive investigation.
11.2.3 Definitions: brown dwarfs vs. planets
As discussed in Chapter 6, it is likely that the brown dwarf mass spectrum extends to masses below ~0.01 M0 (11 Mj), reaching what might be considered the planetary regime. How, then, does one distinguish between a low-mass brown dwarf and a high-mass planetary companion? The pivotal distinction between the two (despite the pronouncements of the IAU) rests with the mode of formation: brown dwarfs form by accretion within a giant molecular cloud in the same manner as hydrogen-burning stars; planets, by definition, form within the circumstellar disk of the pro-tostellar nebula. That difference leads to a clear expectation of differences in chemical composition: as noted above, observations of Jupiter and Saturn suggest abundances of Z ~ 0.02-0.06 and ~ 0.04-0.12 respectively in the outer envelope, as compared with Z ~ 0.02 for the Sun. Unfortunately, even though there are plans for satellite missions that will provide images of the nearest systems (see Section 11.6), there are only very limited prospects of obtaining observations capable of measuring detailed chemical abundances.
In most cases, available observations of extrasolar planets allow only determination of a limited subset of orbital parameters, with the orbital inclination usually indeterminate. Kumar [in C8], Black [B6] and Boss [B9] have suggested that one can distinguish between the two types of companion on the basis of the orbital eccentricity, limiting 'planets' to objects in near-circular orbits. That definition, however, may well be biased by the 'statistics of one' argument - our Solar System may be atypical, and interactions between massive embryos have reasonable probability of scattering objects onto eccentric orbits [L11]. Both planets and brown dwarfs in close binary systems with stellar primaries are subject to similar dynamical interactions; the similarity in the distribution of orbital eccentricities therefore reflects a similar history of orbital evolution, rather than identical origins.
Given current observational limitations, it may be many years before we are able to do more than differentiate statistically between the two possible classifications.1 Clearly, if one only has a measurement of M sin(z), any individual low-mass companion might be a brown dwarf (or even a low-mass star) in a low-inclination orbit. However, barring a cosmic conspiracy, the distribution of orbital inclination should be random, allowing a statistical estimate of the mass distribution. If the companions are predominantly brown dwarfs, one might expect a distribution that shows some continuity from the mass-function of companions above the hydrogen-burning limit; a distribution confined to near-Jovian masses, on the other hand, suggests a distinct, planetary origin. Current results (see Section 11.5) favour the latter alternative.
1 The authors note that such predictions tend to be invalidated. We will happily accept the error if that proves to be the case for this prediction.
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