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Strategy for the Detection and Study of Other Planetary Systems and Extrasolar Planetary Materials: 1990-2000

3

Present Understanding of the Origin of Planetary Systems

INTRODUCTION

This section gives an overview of current theory regarding formation of planetary systems, with emphasis on relationships with astronomical observations. A great deal of effort has been devoted to the complicated problem of describing the formation of a planetary system. What is desired is the integration of a wide variety of observational evidence into a theoretical picture that includes a broad range of physical and chemical processes. Development of the theory requires calculations based on the three-dimensional hydrodynamics of a self-gravitating fluid, including the effects of pressure, viscosity, rotation, magnetic fields, shock waves, and tides. Coupled with the hydrodynamic problem are the thermodynamics of the gas and the energy transport through it, by either radiation or convection. Further, one must consider chemical processes, such as the formation of molecules and the formation, growth, and destruction of dust grains, along with their interaction with the gas. Collisions of the dust particles and their accretion into subplanetary objects, as well as gravitational and electromagnetic interactions in a many-body system, also must be incorporated. To understand the evolution of the central star in a planetary system requires the addition of nuclear physics to the above processes.

In the past 200 yr, numerous theories have been put forward regarding the origin of our solar system. Many of the earlier ideas, such as those involving capture of material from the interstellar gas by the Sun or ejection of matter from the Sun as a result of a close encounter with a passing star, have been rejected on physical grounds. The classical hypothesis of Emmanuel Kant and Pierre Simon de Laplace, that the planets originated in a disklike nebula surrounding the protosun, forms the basis for most current theoretical work on the problem. The nebula is a by-product of the stellar formation process; that is, the planets and the star are all about the same age. The committee concentrates here on the description of the problem based on the nebular hypothesis, which accounts for many, but by no means all, of the observed facts. Of course, it is possible that other planetary systems are quite different from ours in their orbital and physical characteristics; clearly the favored theory has been strongly influenced by the properties of our own system. As more information becomes available about other systems, substantial modifications of our theoretical ideas will undoubtedly be required, leading to new generalizations not yet envisioned.

Four types of observational data are crucial to understanding and potentially solving the general problem of planetary system formation: (1) general dynamical properties of our own planetary system, and statistics and properties of extrasolar planets; (2) properties of regions of current star formation; (3) statistics of multiple stellar systems; and (4) laboratory and spacecraft studies of available solar system materials (meteoritic, cometary, lunar, and terrestrial). The observed dynamical regularity of our system-the near coplanarity of the orbits, the small eccentricities and inclinations, the regular spacing of the planets, and the existence of satellite systems with similar regularities—is probably its most striking property. The masses and compositions of the inner planets as compared with those of the outer planets, as well as the existence of the asteroid belt and the composition and orbital configurations of comets, provide important clues to the nature of the solar nebula and the planetary formation process. The ordered variation in the properties of planets and satellites with radial distance from the Sun is consistent with the interpretation that they are spatially separated samples of an original continuous nebula, although accretion of each body probably occurred over a range of radial distances and the temporal sequence of formation of the planets may not coincide with their present spatial ordering. In this regard it is of great importance to measure orbital inclinations, masses, eccentricities, and other structural properties of extrasolar planetary systems.

The second type of observational information, that which describes molecular clouds and stars in the process of formation and in their early history, is extensive and diverse. It includes, for example, radio and infrared measurements. The problem is to identify those particular techniques and data that could provide clues to the origin of planetary systems. Observations of molecular clouds give some indication of the initial conditions for star formation; studies of young objects suggest the presence of disks, dense dust clouds, and mass outflows. The high spatial resolution needed to examine a nebula the size of our present planetary system even in the nearest star-forming regions (for example, at 100 parsecs, 10 AU subtends 0.1 arcsec) has been one of the greatest obstacles to progress in this area.

The third type of information relates to stellar multiplicity. A large fraction of all nearby stars of the solar type, perhaps as many as 70 to 90 percent, are members of multiple systems. There are, however, some single stars like the Sun. Whether this fraction changes significantly as a function of the mass of the primary star is observationally not well established. An important goal of the theory of star formation, therefore, is to understand the relationship between planetary formation and multiple star formation. In particular, can both occur in the same system?

Finally, data from primitive meteorites (and, ultimately, from comets) provide accurate abundance and isotope ratios for many of the chemical elements, as well as information regarding pressures and temperatures during the formation phase of these objects and therefore, presumably, of some types of preplanetary material. Measurements of both solid material and volatiles-inert gases and others—in the carbonaceous chondrites provide particularly relevant data. Some information on the magnetic fields in the primordial solar nebula can also be obtained from the meteorites, as can the time constants for some of the principal physical processes.

Four major astrophysical processes must be considered, in a unified manner, in the attempt to explain the origin of planetary systems: (1) collapse and star formation in gas and dust clouds; (2) formation, evolution, and dispersal of the disklike nebula; (3) the evolution of the central star; and (4) accretion of the nebular matter into protoplanets. The following sections discuss briefly the state of knowledge on these problems.

STAR FORMATION

The observational evidence indicates strongly that most if not all star formation takes place in molecular clouds (mean density 10-21 g cm-3), and probably in the cores of such clouds, where densities are approximately 10-19 g cm-3 and temperatures about 10 K. The basic condition that has to be satisfied for gravitational collapse to occur is the Jeans criterion—the requirement that the thermal energy of a volume of gas be less than the absolute value of the gravitational energy. To satisfy the Jeans criterion in molecular cloud cores at this density and temperature, about 4 M of interstellar gas are required. Compression to the required densities could, for example, be initiated by the passage of a shock wave through a cloud; the origin of such shocks could be supernova explosions, an expanding ionized region around an existing hot star, or the shocks associated with spiral density waves in the galaxy. However, the relatively high density cores of molecular clouds could also be formed by more gradual processes, such as the slow contraction of gaseous material relative to magnetic field lines, and a trigger may not be necessary for stars of about a few solar masses.

The simple Jeans condition neglects the effects of rotational, turbulent, and magnetic energy, all of which are significant in molecular clouds, all of which inhibit collapse, and all of which may indirectly affect the planetary formation process. Although molecular clouds rotate slowly, if the angular momentum of an element of cloud material were conserved as it collapsed into a star, the deduced stellar rotational velocity would be several orders of magnitude larger than those observed in the youngest stars. Furthermore, the increase in rotational energy as compared with gravitational energy during the collapse (again assuming conservation of angular momentum) would stop the collapse long before stellar densities were reached. The degree of ionization in molecular clouds is low but may still be sufficient for the magnetic field to inhibit collapse (magnetic braking) even if the thermal energy allows it. A further problem is that strict conservation of magnetic flux during collapse to the stellar state again predicts far-higher magnetic fields in stars than have been observed.

The density at which a protostar of about 1 M begins to collapse therefore depends on the local magnetic field, but probably lies in the range of 10-16 to 10-19 g cm-3. The chemical composition is similar to that of our Sun (75 percent hydrogen by mass, 23 percent helium, and 2 percent heavy elements), except that a large fraction of the heavy elements is in the form of dust grains whose size distribution and composition are assumed to be similar to those observed in the interstellar medium. The density of the material increases by a factor of 1015 and its internal temperature increases to about 106 K before it finally becomes a star. Depending on initial conditions, the collapse lasts 104 to 106 yr. Because this time is short compared with that of other stages of stellar evolution and because the protostar tends to be heavily obscured by the dusty cloud material, protostars in the collapse phase are difficult to observe. The detection of collapse velocities near the free-fall rate would provide important clues regarding the existence of protostars; instrumental capabilities are now on the verge of enabling such measurements.

Spherical collapse is an idealization of the collapse process for a system that is both nonrotating and decoupled from the magnetic field. During the early phase of spherical collapse, an isolated protostar is transparent to its own radiation, and it collapses isothermally. A very nonuniform density distribution is set up with the highest densities, and correspondingly fastest collapse rate, near the center. As densities in the central regions increase above 10-13 g cm-3, those regions become optically thick because of the opacity of the dust grains; shortly thereafter, the collapse becomes nearly adiabatic and the interior heats up. At 1800 K molecular hydrogen begins to dissociate, and because the energy released by gravitational compression goes primarily into dissociation energy rather than into an increase in thermal pressure, further collapse is induced. Upon completion of the dissociation, the force due to the outward gas pressure gradient exceeds the force of gravity so that the collapse slows down and stops near the center. A hydrostatic core forms, and the final phase of the evolution involves the accretion of the remaining cloud material onto the protostellar core.

The foregoing discussion does not include the effects of angular momentum, which is of crucial importance in this phase of evolution. After the magnetic field decouples from the gas, the remaining angular momentum is still too large to be consistent with observed stellar rotation. Theoretical calculations indicate, however, that the collapsing cloud can fragment into two or more pieces in orbit around a common center, converting the angular momentum of the cloud into the orbital angular momentum of a binary or multiple protostellar system. The fragments can then collapse separately. Observed orbital angular momenta of wide binary systems are consistent with this suggestion. In fact, the angular momenta deduced from investigation of a number of interstellar clouds are consistent with the observation that multiple systems are often the outcome of star formation. Fragmentation may be the dominant process in the formation of multiple systems. Theoretical calculations indicate that close binary systems do not form from the fission of a rapidly rotating star in hydrostatic equilibrium. Thus although the wide binaries may form by several processes, including fragmentation, gravitational capture of one protostar by another, or the disintegration of small star clusters, the origin of close binaries is still an unsolved puzzle. Existence of a planetary system around one or more of the components of a multiple stellar system is not necessarily precluded, although the planetary orbital distances must either be very small or very large compared with the separation of the stars. Data concerning the prevalence of planetary systems associated with multiple-star systems would be of great value.

If the magnetic field transfers angular momentum efficiently from the central regions to the outer regions before protostellar collapse begins, an alternative outcome is possible. The cloud could collapse into a central star plus a surrounding disk, which would contain much of the angular momentum but relatively little mass. In this situation the disk would be stable against breakup by fragmentation, and a planetary system could form. Although the initial conditions required for the formation of a binary versus a single star are not understood, it is possible that clouds with relatively low residual angular momentum (after the magnetic braking) could take the latter course. The outcome probably depends on the distribution of density and angular momentum in the cloud just before protostar collapse begins, as well as on the total amount of angular momentum. Note that during the formation of the disk the whole inner structure is well shielded by the dust-rich outer layers of the cloud that are still in the process of collapse. Therefore at this stage the disk may not be directly observable except at radio wavelengths, but its presence could affect the infrared radiation emitted by the protosteller system. The observable layer gradually increases in surface temperature and luminosity as the central mass grows by accretion from the disk and the optical thickness of the collapsing envelope decreases. The central object becomes observable as a so-called T Tauri star, and the protostellar evolutionary phase is completed. The energetic stellar winds and bipolar outflows (jetlike collimated flows) observed during the ~105 to 106 yr of the ensuing contraction phase are now widely believed to occur simultaneously with infall of material from the protostellar cloud to the circumstellar disk and inflow of material to the central mass through the disk. There is growing evidence that these winds require the presence of an accretion disk, and that the mass inflow rate through the disk and the mass outflow rate in the wind are related.

It is important to realize that the sequence of events outlined above is simply a sketch and that only a few aspects of protostellar evolution have been calculated in detail, usually with restrictive assumptions. The general problem of collapse of a rotating, magnetic cloud, including the effects of heating, cooling, ionization, chemistry, and radiation transport, has not been solved.

PROPERTIES OF THE NEBULAR DISK

If a nebular disk forms as discussed above, it still does not have the proper angular momentum distribution to be in agreement with that deduced observationally for systems consisting of a young star plus a surrounding disk. Angular momentum must be transported out from the central regions. Various mechanisms for transport of angular momentum are under study, including gravitational or magnetic torques, viscous effects arising from turbulence or sound waves, or magnetic braking of the central star both before it appears as an optically visible pre-main-sequence star and after it reaches the main sequence. (Recent work suggests that stellar winds during intervening pre-main sequence stages are ineffective in removing stellar angular momentum.) The importance of these effects is usually studied by means of an idealized model in which the disk is thin, is small in mass in comparison with the star, is in hydrostatic equilibrium and in Keplerian rotation, and has a temperature that is low enough (<2000 K) that hydrogen is in the molecular form and dust grains are present.

Angular momentum transport by turbulence has been studied extensively, and at least two mechanisms have been suggested for inducing it. First, while matter from the cloud is still collapsing onto the disk, the difference in angular momentum between the existing disk material and the newly accreted material leads to shearing motions that could induce turbulence. Second, after the gravitational infall has stopped, convective instability can be induced by the increase in the opacity of the grains as a function of increasing temperature. The evolution of the system is therefore likely to be that of a viscous disk, often known as an accretion disk.

The turbulence has two effects: it results in an efficient transfer of heat from the midplane to the surface of the disk, and the Keplerian shear combined with the viscosity due to turbulence induces transfer of mass as well as angular momentum in the disk. The dissipation of energy by viscosity provides heat, which is radiated from the surface of the disk. The ultimate energy source for the turbulence and the heat is the gravitational energy of the disk and star interaction. Most of the disk mass eventually sinks slowly toward the central star. At the same time, the angular momentum, along with a small fraction of the mass, is slowly transferred outward. Given an infinite time for evolution, almost all of the nebula would spiral into the central star. However, time scales for circumstellar disk evolution of only a few million years are inferred from theoretical calculations, as well as from recent observations of excess infrared radiation arising from dust embedded in the disks with large infrared excesses at stellar ages of <3 million yr, but fewer than 10 percent of such stars still display this signature by the time they reach ages of 10 million yr. Such short time scales provide a strong constraint on theories of the planetary formation process, particularly for the gas-rich outer planets.

There has been considerable progress during the past few years in our understanding of the evolution of such disks. Yet major uncertainties remain in the theory of convection and turbulence that could affect the deduced evolutionary time scale. It is probable that the other mechanisms for angular momentum transport listed above could have a significant effect during the various phases of disk evolution.

The material in the nebular disk that does not condense into planetesimals or protoplanets is cleared away, arguably only a few million years or less after the formation of the star. A number of mechanisms have been proposed for accomplishing this clearing. (1) Strong stellar winds probably have sufficient energy to sweep out a moderate-mass nebula. But since massive T Tauri winds appear to be present only if the star is surrounded by a thick circumstellar disk, and are not seen in stars with low-mass, optically thin disks, it is not obvious what role, if any, is played by such winds in directly sweeping a disk away. (2) Particles in the nebula could be photoionized by ultraviolet radiation from the central star. The extra kinetic energy given to the particles, above the ionization energy, could induce pressure gradients and thereby mass loss. It is necessary, however, that nebular matter actually be exposed to such radiation, and here dust and gas opacity considerations are a major problem, particularly in the nebular midplane. One possibility is off-disk irradiation leading to evaporation of material from lower opacity disk boundaries at high altitudes. Radiation pressure on dust grains can also remove circumstellar material, but only for relatively massive stars is this process likely to be important in ejecting significant amounts of disk mass. (3) In turbulent viscosity models of the accretion disk, viscous evolution results in the spiraling of nebular material inward toward the central star, leading to stellar accretion during the protostellar evolutionary stage when inward mass flux is approximately balanced by infall of matter from the collapsing cloud and the disk is roughly in steady state. As noted above, however, there is evidence during later evolutionary phases for a relationship between mass inflow rate through the disk and mass outflow rate in massive winds. This suggests a wind-related mechanism for disk dissipation after termination of infall to the disk-ejection of most of the inwardly spiraling disk material in winds originating in the energetic boundary layer between disk and star, at rates that decrease, ultimately below current detectability, as the disk thins and inward mass flow declines. (Note that later-stage winds of this nature would not properly be called stellar since they are intercepting and ejecting mostly inflowing disk matter rather than stellar matter).

The theory of these processes has not been accurately worked out, but theoretical and observational estimates indicate that an amount of mass comparable to the primordial nebula could in principle be partly lost by outflow from the star-disk system and partly accreted within the system on time scales of a few million years, which is also the approximate time of evolution of the star itself through its classical T Tauri phase. Further detailed numerical work, in conjunction with observational and laboratory studies, is required to establish the critical time scales for angular momentum transport in the disk and for the clearing of the disk, both of which are important for the planet-forming process.

At this time, available observational evidence suggests a disk evolutionary sequence from (1) very massive 0.1 to 1 M structures with high accretion rates (protostellar stage) and high mass loss rates from the star-disk system, through (2) intermediate 0.001 to 0.1 M disks with intermediate accretion and mass loss rates, to (3) tenuous disks containing <<0.001 M of unassembled material with very low stellar mass loss rates. Whether a planetary system forms in all or a majority of cases within this sequence is unknown. If it does, one likely epoch of planet building appears to be during transition from stage (2) to stage (3), that is from the large infrared excesses characteristic of the classical T Tauri stars to the small or undetectable infrared excesses of the so-called naked T Tauri stars.

THE EVOLUTION OF THE CENTRAL STAR

No discussion of the origin of a planetary system is complete without consideration of the central star. The star influences the planetary formation process in several ways. First, its mass as a function of time influences the properties—for example, the vertical thickness—of the nebular disk. Second, the mass outflow from the star as it settles into the stellar state may terminate the collapse of the protostellar cloud. The observed bipolar outflows near young stars may be a manifestation of such a process. Some of the infrared objects that exhibit bipolar flow also may be interpreted as having associated disks or tori, with the plane of the disk perpendicular to the flow. As noted above, outflow from the boundary layer and ionization by ultraviolet photons may control the dissipation of the disk. Third, the tidal influence of the star plays an important role in the planetary formation process by limiting the region of gravitational influence of the protoplanets. In turn, the evolution of the nebula influences the evolution of the star, as viscous processes transfer matter to the star. The transfer of angular momentum between the star and the nebula, which also affects the evolution of the star, requires further study.

Generally speaking, once the protostellar collapse phase is over, the star is an object in hydrostatic equilibrium, with a radius a few times that which it will ultimately have on the main sequence, and with internal temperatures of a few million degrees and surface temperatures around 4000 K. The star now enters the pre-main-sequence evolutionary phase. The energy it radiates is derived from gravitational contraction, and the initial luminosity is a few times that of the present Sun. The earlier phases of the contraction proceed in the Hertzsprung-Russell (H-R) diagram along the so-called Hayashi track, that is, with nearly constant surface temperature and steadily decreasing luminosity. Energy transport in the bulk of the star is by convection during this stage and, for 1 M, the time spent on this track is about 10 million yr. The observed "classical" T Tauri stars appear within the first one-third or so of this evolutionary phase. As discussed above, they are observed to be bright in the infrared, suggesting the presence of circumstellar material. This active, classical T Tauri phase is estimated and observed to terminate within a few million years, probably through evolution by accretion or loss of disk material into the naked T Tauri stars. These T Tauri systems appear to be very likely sites for accretion of subplanetary and protoplanetary objects.

After the Hayashi phase, the path followed by a contracting star changes direction in the H-R diagram, evolving with gradually increasing luminosity and increasing surface temperature until hydrogen burning ignites at the center. During this phase the energy transport within the star is primarily by radiation. When nuclear reactions contribute 100 percent of the energy output, the star is said to have arrived on the "zero age" main sequence.

Some aspects of the evolution of the star seem to be reasonably well understood. Others, such as the role of its rotational and magnetic energies in generating and collimating bipolar outflows, still require further and more detailed observational and theoretical study.

FORMATION OF THE PLANETS

The theory of planetary formation rests on calculations of particle dynamics, collisional accretion theory, and gas dynamics, some aspects of which are still quite uncertain. The committee discusses briefly the concept that all planets formed by essentially the same process, that is, by gradual accretion of small dust particles into larger subplanetary bodies (commonly called planetesimals in this context), which later coalesced to form the planets. This scenario, although not the only possible planetary formation process, is one that is now undergoing intensive study. Even though models based on this picture are oversimplified because of existing limitations of computers, they contribute to the advance of general insight. In these models, the major difference between the inner and outer planets is simply that the latter grew to the point (10 to 20 M)where they were able to attract a significant amount of nebular gas to form an envelope around the solid core, which presumably consisted of both rocky and icy material. In the case of Uranus and Neptune the gaseous envelope was much smaller in mass compared to the rest of the planet, and part of the accretion of solid matter could have occurred after dissipation of the nebular gas. In the inner solar system both the heating and tidal effects of the Sun, as well as the smaller amount of condensable material, apparently prevented the buildup of cores to the critical mass where significant gas accretion was possible.

The starting point is the nebular disk, composed of gas mixed with about 1 percent by mass of dust, at temperatures in the range of 100 to 2000 K. The dust particles have essentially interstellar characteristics, with typical particle sizes of 10-5 to 10-4 cm (0.1 to 1 m). Dust would be absent close to the central star, where temperatures are expected to be high enough to vaporize it. In the inner parts of the nebula beyond this region, out to the point where the temperature falls to roughly 200 K, the particles are composed principally of compounds of oxygen, magnesium, silicon, and iron. In the outer regions, below 200 K, water ice can also exist, as well as ices of ammonia, methane, and various clathrates.

The first stages of dust accumulation into larger objects are proving to be perhaps the most difficult of all the phases of planetary formation to understand. In one long-standing scenario, dust grains gradually sink to the midplane of the nebula, growing by accretion to centimeter size on a time scale of a few thousand years. Once the dust layer at the midplane becomes dense enough, gravitational instability occurs. The layer fragments into rings, and these further fragment into gravitationally bound aggregates with characteristic sizes of a few kilometers and masses on the order of 1018 g at the Earth's distance from the Sun. This gravitational instability model of planetesimal formation is simple and appealing, but there are now serious questions concerning many of its basic assumptions and predictions. They focus in particular on the disruptive effects of turbulence in nebular gas, the role of stickiness of dust grains in grain coagulation processes, the physical morphology and settling times of resulting dust aggregates, and the short time scale of 104 yr predicted for accretion of kilometer-size objects (there are estimates that it may have taken 10 to 100 times longer). It is fair to say that at present the mechanisms of growth to this size range, and their required time scales, are poorly understood.

There is, however, a widely accepted standard model for subsequent planetary accumulation. Planetesimals, whatever their means of formation, undergo collisions and gradually accumulate into a few large bodies that eventually form the terrestrial planets and the cores of the giant planets. Monte Carlo simulations of the accumulation process suggest that it proceeds rapidly during the first few million years, forming objects up to ~25 percent of the Earth's present mass in the terrestrial planet zone; subsequent collisional growth occurs more slowly because accreting objects decline in number and become orbitally more isolated from the protoplanets. Estimates for the total time required to fully accrete the terrestrial planets range from 107 to 108 yr. Once a system of planetesimals forms, it also serves as a reservoir from which dust can be eroded over much longer time scales. As discussed further in Chapter 4, collisional processes could explain the observed maintenance of dust around main-sequence stars 109 yr or more after formation.

The properties of our own solar system strongly indicate that Jupiter must have formed more rapidly, because (1) the core must have accreted to its present size before the nebula gases disappeared and (2) the presence of the asteroid belt without a major planet in it strongly suggests that the prior presence of Jupiter and its gravitational influence prevented the final stages of accretion from occurring there. Current research is directed toward the question of how to build Jupiter's core, which probably contains about 20 M, within a few million years (if, in fact, this correctly represents the time scale for dissipation of nebular "gas." There are no observational astronomical constraints on the lengths of time required for disappearance of the gaseous component of accretion disks; they must be inferred from the dust survival times deduced from infrared excesses, and this may not necessarily be a valid extrapolation.). It is possible that improvements in the theory will show that the phase of rapid accretion of planetesimals continues to well beyond lunar mass at Jupiter's distance from the Sun. If that is true, Jupiter's core could build up quickly to the point where it could start accreting gas.

An alternative theory, in which all planets formed as large gaseous condensations, of which only the cores persist in the case of the terrestrial planets, has encountered a number of difficulties. In particular, the high interior pressure may suppress bonding differences, making the precipitation of core material unlikely. This idea does provide a natural way of forming the giant planets quickly, but a considerable amount of theoretical work is necessary to clarify the formation process of these objects.

An understanding of the early evolution of the giant planets is of particular importance because of the possibility that they can be detected near young stars. A number of observational constraints can be used to guide the theory, including the present chemical composition of the giant planets, their present masses, luminosities, radii, and gravitational moments, and the fact that all except Neptune have regular satellite systems.

Detailed numerical calculations support the following scenario for the various phases of the evolution of Jupiter. First, the solid core builds by accretion to about 1 M Second, the gravitational influence of the core attracts nebular gas, which forms a thin layer in hydrostatic equilibrium around the core. As the core continues to accrete planetesimals, its region of influence (defined by its accretion radius or tidal radius, whichever is smaller) grows, causing further gas accretion. Third, the core, having approached the critical mass, has sufficient gravitational influence to attract an envelope of comparable mass. The energy radiated by the envelope then can no longer be supplied by the accretion energy of the planetesimals, and the envelope begins to contract. Fourth, the envelope mass increases rapidly, reaching its present value in a few thousand years, with no significant change in the core mass. The radiated luminosity increases also, because of the rapid contraction and increasing mass, to values of 10-4 or 10-3 times the present solar value, far higher than the luminosities (10-9 to 10-11 L) of the present giant planets. Fifth, gas accretion terminates. The termination may result because the protoplanet has grown to a mass sufficiently large that its tidal influence on the nebula opens up gaps in its vicinity and prevents further accretion of gas onto it. Alternatively, the accretion could terminate when there is no gas left to accrete after escape of gas from the nebula.

Thereafter, the protoplanet evolves at constant mass and contracts on a time scale of 105 yr, releasing energy at a level of 10-4 L at surface temperatures of a few thousand Kelvin. This phase could possibly be observable. The later evolution involves cooling of the interior and only a very slow decrease in radius; the luminosity and surface temperature decline as a function of time. After 4.5 times 109 yr the present radius and intrinsic luminosity of Jupiter are reached.

The above theory of the evolution of the giant planets is based on numerous approximations, does not include rotation and the formation of satellite systems, and will undoubtedly require extensive revision in the future; nevertheless, it agrees with many known properties of the giant planets. For example, the theoretically deduced critical core masses are in good agreement with the core masses deduced from observations of the giant planets. The formation process for the outer planets Uranus and Neptune, however, is still not well understood. In particular, the time scale currently inferred for accretion of their cores at their present distances is longer than the lifetime of the nebula and may be longer than the age of the solar system. Perhaps resonances played some role, as suggested by such observations as the trapping of Pluto in a 3:2 resonance with Neptune, and the extraordinary circularity of Neptune's orbit. Moreover, it is not understood how these planets could have acquired their gaseous envelopes of approximately 1 M. Possibly the accretion of Uranus and Neptune may have started closer to the Sun than their present distances. Their cores may have grown sufficiently large to attract some gas from the nebula, and later the protoplanets could have migrated to the outer parts of the nebula under the gravitational influence of Jupiter and Saturn. Their buildup could have been completed simply by the accretion of planetesimals.

What is certain is that various critical aspects of planetary formation still need to be clarified. Progress depends on development and testing of improved models for the process, and thus on continuing theoretical and observational investigation of planetary systems. Many theoretical and computational initiatives will require expansion of currently available computer capacity and improved numerical techniques for solving coupled systems of differential equations. New and detailed observational data on chemical compositions, present physical states, and dynamical behavior both within and outside our own solar system, from spacecraft instruments and from ground and Earth-orbital facilities, are central to this effort.

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