Current theories on the formation of planetary systems originate in the works of three major figures of the Eighteenth Century: the mystic Emanuel Swedenborg, the philosopher Immanuel Kant, and the mathematician-astronomer Pierre Simon de Laplace. Their speculations regarding the origin of our Solar System are collectively summarized as the nebular hypothesis. According to its central argument, the young Sun was surrounded by a spinning cloud of hot gases that coagulated over time to produce the orbiting planets.

The nebular hypothesis qualifies as a theory of evolution, insofar as it describes a rule-governed process that yields outcomes over time in a series of incremental changes. More catastrophic models have found adherents over the past few centuries – e.g., scenarios in which the Solar System formed when the Sun was sideswiped by a rogue star that stripped away constituent gases, which subsequently coalesced into the planets; or arguments that the Sun originally had a binary companion that exploded to produce the appropriate planet-forming materials. Variations on the nebular hypothesis once again became the dominant paradigm during the second half of the Twentieth Century, as astronomers reworked it with increasing physical and mathematical rigor.

The radial velocity detection in 1995 of a Hot Jupiter orbiting the Sun-like star 51 Pegasi exposed deep flaws even in the revised narrative. In response came a great wave of theorizing intended to remedy its defects. Until the 1990s, evolutionary arguments had only to explain the Solar System. The unexpected configurations of most newly-discovered exoplanetary systems hinted at key factors that had been neglected or ignored.

1. The primordial environment in which stars are born – that is, gas-rich star clusters like the Orion Nebula and the Rho Ophiuchi Complex – strongly constrains the formation of planetary systems. Interactions between a star and the parent molecular cloud, or among stellar siblings, may shape or disrupt evolutionary outcomes.
   
   
2. During their formation, many planets undergo orbital migration as they acquire mass, causing them to spiral inward to smaller orbits. Thus we observe many gas giant planets like 51 Pegasi b orbiting very close to their host stars.
   
   
3. Once an ensemble of planets has assumed its preliminary orbital configuration, a phase of planet-planet interactions ensues over a period of tens to hundreds of millions of years. Planetary orbits tend to become more elliptical, and semimajor axes may either shrink or enlarge, while a significant percentage of planets are ejected from their home systems entirely.

The evolution of planetary systems is now an extremely active field of inquiry. Here is a simplified summary of the current state of the discussion. (Follow the link for a visual summary of evolutionary processes.)

primordial clusters

Most stars are formed in clusters of 100 to 1000 inside vast clouds of molecular hydrogen. Observations suggest that the median cluster membership is about 300 protostars (Lada & Lada 2003, Adams et al. 2006). Stars formed in the same cluster will have similar ages and chemical compositions, but they will assume a wide range of masses and spectral types. As a result, their evolutionary paths will be diverse.

At the beginning of their existence, dozens or hundreds of stars may occupy a region of space only a single parsec in diameter. A substantial proportion will reside in binary or multiple systems, traveling in shared orbits. In such crowded environments, neighboring star systems may interact gravitationally. Close approaches among stars can perturb stellar orbits; multiple stars can lose their companions; single stars can acquire companions; and two different multiple systems can exchange components (Malmberg et al. 2007).

Nevertheless, such gravitational disruptions are likely to occur in relatively few newborn systems. Fred Adams and colleagues calculate that a typical star in a typical young cluster will experience only one close encounter with another star over the lifetime of the cluster, with the closest approach about 1000 AU (Adams et al. 2006). Such an encounter might result in a slight truncation of the circumstellar gas nebula, but it is unlikely to perturb any forming planets or planetesimals. Close approaches are more likely to disrupt wide binary systems, but again, they will affect fewer than 15% of young binaries (Adams et al. 2006), while tighter pairs resembling the systems of Alpha Centauri or Gamma Cephei will remain unperturbed.

The gases that comprise a star-forming nebula are dispersed on time scales of 1 to 10 million years by stellar winds, photoevaporation, and supernova shockwaves (Lada & Lada 2003, Throop & Bally 2008). Meanwhile, many individual stars maintain their own envelopes of hydrogen, which rapidly flatten into spinning disks known as proplyds or protoplanetary disks. These disks also have relatively short lifetimes, such that more massive stars lose their disks within about 3 million years, while only the least massive stars of spectral class M retain gaseous envelopes for more than 10 million years (Lada et al. 2006, Carpenter et al. 2006).

The presence within a star-forming nebula of one or more high-mass stars of spectral type O will result in rapid dispersal of the adjacent molecular clouds, either through photoevaporation or through the intense shock waves generated when these enormous stars explode as supernovae. Such events ensue within 1 or 2 million years of an O star’s formation, and either outcome will strip protoplanetary disks away from smaller stars nearby (Preibisch et al. 2002, Lada & Lada 2003). Nevertheless, large numbers of young stars in these environments manage to sustain gaseous disks that continue to evolve as the enveloping nebula dissipates.

Because individual stars form much more rapidly than their parent cloud disperses, the firstborn stars in such a nursery may give rise to nascent planetary systems while substantial quantities of molecular hydrogen remain. As Throop and Bally conclude, “For at least a few million years, as these young stellar objects move through the cluster, they have a chance to accrete additional material from reservoirs of dense gas remaining in the region” (Throop & Bally 2008). This material is accreted by the protoplanetary disk rather than by the star, replenishing gas lost to dissipative processes. It remains uncertain how this “tail-end Bondi-Hoyle accretion” affects forming planetary systems. Possibilities include a kind of “second wind” in gas accretion, with forming gas giant planets adding significant quantities of hydrogen to their atmospheres, or perhaps an encouragement of inward migration, driving these young giants into smaller orbits.

Even after the disappearance of the parent cloud, most young stars remain closely associated, so their gravitational interactions continue. One of the best-known remnants of such an association is the Ursa Major Group, whose members include many of the brightest stars in the constellation of the Big Dipper (Ursa Major). These stars (e.g., Merak, Megrez, Alioth, Mizar) have remained in proximity for at least 400 million years (King et al. 2003).

protoplanetary disks

The fraction of newborn stars that maintain active protoplanetary disks may be as high as 80% (Haisch et al. 2001). In these star systems, the process of planetary formation typically begins. Two different evolutionary models have been proposed. One is gravitational collapse, in which giant planets form much like stars out of the rapid contraction of hydrogen clouds. However, this model has so far provided a poor fit to available data, and it cannot explain the genesis of terrestrial-mass planets. Much more successful has been the planetesimal accretion model, in which all planets, giant or otherwise, assemble out of collisions between small rocky and icy objects known as planetesimals. With ongoing refinements, this model is widely accepted. (See, e.g., Ida & Lin 2004; Marcy et al. 2005; Alibert et al. 2005a; Chambers 2006; Papaloizou & Terquem 2006.)

A young protoplanetary disk is dominated by gases, mostly hydrogen, with a much smaller proportion of dust grains. The mass ratio of gas to dust is typically estimated at 100:1 (Andrews & Williams 2005). This dusty nebula is hot near the central star, cooling with distance and decreasing density. The star’s magnetosphere creates a central cavity in the nebula within a radius of about 0.05 AU, providing an inner edge for the evolving disk (Lin et al. 1996, Papaloizou & Terquem 2006, Laine et al. 2008).

Among the dust grains suspended in the gases, only rocky or “refractory” particles occur at small distances, while icy particles prevail in wider orbits. The boundary between the two regimes of ice and rock is known as the system’s ice line – the distance from the central star where free-floating molecules of water and other volatiles condense into ice (Ida & Lin 2004, Mandell et al. 2007, Kennedy & Kenyon 2008a). Just beyond this point, the presence of ice increases the density of planet-forming materials by a factor of 3 or 4, enabling large protoplanets to assemble far more rapidly than they could at larger or smaller radii (Ida & Lin 2004, Kennedy & Kenyon 2008a).

Because disk evolution begins while a star is still in its pre-main sequence phase, before it reaches long-term stability in temperature and luminosity, the location of the ice line changes with time. Its excursions have important consequences for planetary formation (Kennedy et al. 2006, Garaud & Lin 2007, Kennedy & Kenyon 2008a). Kennedy & Kenyon argue that the ice line moves inward by a few astronomical units during the early stages of disk evolution (Kennedy & Kenyon 2008a). Like other theorists, they agree that the ice lines around massive stars are located at larger radii than those of more lightweight stars, but they place the final boundaries for each spectral type closer to the central star than do, for example, Ida & Lin (2004, 2005).

The ice line of an A-type star like Fomalhaut (2 MSOL) has been estimated as 18 to 20 AU (Hernandez et al. 2006, Sato et al. 2007). However, Kennedy & Kenyon argue that, for stars of this mass, the ice line actually begins at a radius of about 8 AU and rapidly migrates inward to 3 AU. For a star of Solar mass, whose ice line is canonically defined as 2.7 AU (Marcy et al. 2005, Ida & Lin 2005), Kennedy & Kenyon argue instead that it migrates from 5 AU (just inside the present orbit of Jupiter) almost to the semimajor axis of the Earth. Finally, for a lightweight K dwarf or oversize M dwarf of 0.6 MSOL, the ice line moves inward from about 2.75 AU to less than 0.75 AU.

Because evolutionary processes are sensitive to initial conditions, the earliest location of the ice line constrains the accretion of massive planets. Kennedy & Kenyon find that the optimal region for planetary accretion around a star of one Solar mass extends from 6 to 11 AU. This region is narrower and closer for lower-mass stars and wider and more distant for higher-mass stars. Accretion is encouraged in disks of high metallicity – that is, a relatively high ratio of heavy elements to hydrogen and helium – and substantial mass (Marcy et al. 2005, Greaves et al. 2007). Given sufficiently massive disks, stars of 1.2 MSOL or more can even form giant planets inside their ice lines (Kennedy & Kenyon 2008a).

planetesimal accretion

Nevertheless, any protoplanetary disk with an appreciable mass in solids will experience accretion, as encounters among dust grains result in the coagulation of increasingly larger objects. Although this scenario seems perfectly intuitive – a Looney Toons analogy might involve a snowball rolling down a mountainside, accumulating enough ice until it is big enough to demolish a house – it has been surprisingly difficult to model analytically or numerically (Johansen et al. 2007, 2008; Ida & Lin 2008). In theory, accreting particles face at least three major obstacles:

1. As they grow, particles encounter aerodynamic drag as an effect of the ambient nebular gas, so that their orbits may decay rapidly, carrying them into the central star.
   
   
2. Colliding particles may shatter as often as they stick, so that pebbles may be ground into dust as fast as they can congeal out of the gas. Under such a regime, no net growth could occur.
   
   
3. Even if pebble- to boulder-size objects avoid this fate, and protoplanets as large as Mars or Earth manage to form, they may still fall prey to tidal interactions with the nebula (Ida & Lin 2008, Chambers 2008). This potentially catastrophic process is known as Type I migration, and it can carry young planets into star-grazing orbits much smaller than Mercury's, from which they may fall into the central star.

formation of giant planets

In other systems, the evolution of the disk will result in the formation of one or more gas giant planets. In such cases planetesimal accretion proceeds much faster than gas depletion, so that protoplanets steadily accrete smaller bodies until they reach a critical mass about 10 times that of Earth (Ida & Lin 2004). At this point the protoplanet enters a phase of runaway growth in which it rapidly accretes sufficient quantities of cool gas to reach at least 20% of the mass of Jupiter. This snowballing process is evidently efficient and fairly common.

The primary region for giant planet formation is relatively small. Only the most massive protoplanetary disks can sustain runaway gas accretion inside their ice lines; in less massive disks, large planetary cores cannot form before the gases in the disk have largely dissipated (Ida & Lin 2004). Similarly, about 5 AU beyond the ice line of a Sun-like star, the rate of planetesimal accretion slows down considerably, so that cores rarely reach a critical mass within the available window of time (Ida & Lin 2004). This outer region is the place where ice giants like Uranus and Neptune are most likely to assemble – planets much smaller than Jupiter with a substantial percentage of their mass in the form of ices rather than gases.

In some systems, the rapid capture of a deep hydrogen atmosphere results in the inward migration of giant planets from larger orbits to smaller orbits, with the planets continuing to acquire mass and spiraling starward until the available gas is depleted (Trilling et al. 2002, Ida & Lin 2004, Ford 2005, Alibert 2005a). This process is known as Type II migration, and it affects only planets of approximately Saturn mass or more, especially those in high-mass or highly metallic protoplanetary disks.

The stopping mechanism for Type II migration seems to be the inner edge of the disk. Giants that find stable orbits at these small radii are known as Hot Jupiters. However, according to simulations by Ida & Lin, a large percentage of giant planets that travel as far inward as 0.05 AU may actually perish by colliding with the central star (Ida & Lin (2004).

One way or another, many theoretical studies have found that newly-formed giant planets rarely achieve stable orbits around their primaries. Ingestion by the parent star is one potential hazard. Another, unique to systems containing at least two giant planets, arises out of mutual gravitational perturbations. Such planet-planet interactions may eventually eject one of them from the system altogether (Ford 2005). Between the opposing threats of blazing coalescence with the central star or expulsion into the void, the evolution of planetary systems appears to proceed by a kind of natural selection in which only the “fittest” planets survive. Fitness seems to be defined primarily by mass and orbit.

formation of terrestrial planets

With masses ranging up to 10 times that of Earth, terrestrial planets form more slowly than gas giants or ice giants, on time scales of tens of millions of years (Chambers 2001, Raymond et al. 2006, Fogg & Nelson 2006). In our own Solar System, for example, isotopic dating of meteorites establishes that the asteroid Vesta was formed within 3 million years of the birth of the Sun, while Mars required about 10 million years. The much larger Earth-Moon system, with 10 times the mass of Mars, required at least 30 million years (Yin et al. 2002).

Current evolutionary theories agree that terrestrial planets gather their building blocks entirely inside the ice line, in a region that provides limited orbital space and primarily rocky and metallic components. The relatively slow accretion rates of terrestrial planets are explained by this deficiency in ices and gas, since it is the easy acquisition of volatiles that makes giant planet formation so rapid. Like giant planets, nevertheless, terrestrial planets begin their evolution with the accretion of dust grains into billions of planetesimals, which subsequently interact and collide in a phase of runaway growth to form planetary “embryos” or protoplanets with diameters of several hundred kilometers/miles.

Runaway growth concludes at a system age of about 10 million years with the emergence of a population of 10 to 40 large protoplanets (“oligarchs”), which are nested inside the ice line on circular orbits (Nagasawa et al. 2007). Calculations indicate that these objects have an approximate mass range of 0.1 to 0.2 MEA – making them more or less equivalent to Mars – with more massive protoplanetary disks giving rise to fewer, more massive oligarchs, and less massive disks yielding the converse (Nagasawa et al. 2007). This population will be accompanied by an extensive retinue of still smaller and more eccentric protoplanets, numbering in the hundreds and ranging from asteroid-size to Moon-size.

As an example, simulations suggest that the founding population of protoplanets needed to produce a system of four terrestrial planets analogous to the inner Solar System might range anywhere from 30-50 Mars-size bodies to several hundred Moon-size bodies (Raymond et al. 2006). Having accreted a viable starting mass, this population of rocky bodies enters an extended phase of oligarchic growth, in which a small collection of objects accretes mass through collisions with more numerous, less massive bodies. Of the scores or even hundreds of planetoids that begin the process of oligarchic growth, the vast majority will either coalesce with larger objects or be ejected from the system entirely.

After a concluding phase of chaotic impacts, in which planets as big as Venus, Earth, or the recently discovered Super Earths may assemble, terrestrial planet formation ceases (Nagasawa et al. 2007). Rresidual debris is swept out of unstable orbits and the surviving lineup of objects enters into a phase of long-term perturbations and other interactions. In the Solar System, a period known as the Late Heavy Bombardment ensued about 700 million years after the commencement of planetesimal accretion and some hundreds of millions of years after the end of oligarchic growth (Gomes et al. 2005). At that time a massive scattering of debris, agitated by resonant interactions with the system’s giant planets, rained comets and meteors on all of the larger orbiting bodies of the Solar System. The scars of this violent epoch are still visible as craters on the surface of the Earth's moon and other airless satellites throughout the system. With the conclusion of the bombardment, the much-denuded system assumed its mature configuration. It is uncertain whether other planetary systems follow a similar course after oligarchic growth concludes.

planet-planet interactions

Two or more gas giants may form in a given extrasolar nursery, with numbers likely to increase along with the mass and metallicity of the central star. Numerous astronomers have explored the possible secular (long-term) dynamics of planet-planet interactions such systems (Weidenschilling & Marzari 1996, Rasio & Ford 1996, Ford 2005, Ford & Rasio 2008, Chatterjee et al. 2007, Nagasawa et al. 2008). After gas accretion has resulted in an initial ensemble of planets, a kind of sorting period ensues - in effect, a grand game of musical orbits. Mutual perturbations and orbit crossings excite eccentricities and eject planets from unstable configurations. Eric Ford cites numerical simulations suggesting that, even in systems that begin with large numbers of gas giant planets, dynamic interactions over tens of millions of years result in collisions and ejections that leave a minimum of one and a likely maximum of three surviving giants (Ford 2005).

For most cases studied or theorized, the most massive planet in a system is the key determinant of its ultimate configuration. Simulations by Barnes & Quinn (2004) indicate that the most massive planet in any system is the least likely to be ejected and the most likely to eject less massive objects. In the evolution of the Solar System, Jupiter has clearly played the deciding role, in part by nudging the lesser giants (Saturn, Uranus, and Neptune) into wider orbits than they originally occupied (Tsiganis et al. 2005), and in part by preventing any additional planets from forming in the region between 2 AU and 5 AU (a zone whose primordial debris has survived to the present under the name of the Asteroid Belt).

The presence of giant planets strongly constrains the formation and orbital elements of neighboring terrestrial planets. Their effects on system architecture have been intensively studied by Sean Raymond, specifically with regard to the formation of terrestrial-mass planets in the habitable zone. As Raymond uses this term, it refers to the region lying between 0.8 AU and 1.5 AU away from a G-type star. Raymond and colleagues find that the presence of a Jupiter-mass planet with a semimajor axis between 0.5 AU and 2.5 AU will prevent the formation of any planets larger than 0.3 Earth mass in the habitable zone (Raymond 2006, Raymond et al. 2006b). The corresponding boundaries for M-type stars will be 0.06 AU and 0.32 AU, and for F-type stars 1.45 AU and 7.2 AU (Mandell et al. 2007).

Raymond further suggests that giant planets orbiting within 3.5 AU tend to eject icy bodies from the primordial disk and may thereby prevent terrestrial planets within this radius from accreting volatiles. Thus, he proposes that “water-rich habitable planets can only form in systems with giant planets beyond 3.5 AU” (Raymond 2006). He notes the additional constraint that such giants must be traveling on circular orbits, which are common in the Solar System but quite rare elsewhere. Increasing orbital eccentricities in giant planets must be offset by increasing semimajor axes, in order to permit stable terrestrial orbits and adequate delivery of volatile elements. As always, orbital parameters will vary for companions of stellar types significantly more or less massive than our Sun.

Last update August 2008