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27 Mar 2002 8:47 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD 10.1146/annurev.earth.30.091201.140357 Annu. Rev. Earth Planet. Sci. 2002. 30:113–48 DOI: 10.1146/annurev.earth.30.091201.140357 c 2002 by Annual Reviews. All rights reserved Copyright ° IMPLICATIONS OF EXTRASOLAR PLANETS FOR UNDERSTANDING PLANET FORMATION Peter Bodenheimer and D.N.C. Lin UCO/Lick Observatory, University of California, Santa Cruz, California 95064; e-mail: [email protected], [email protected] Key Words extrasolar planets, planetary systems, Solar System formation ■ Abstract The observed properties of extrasolar planets and planetary systems are reviewed, including discussion of the mass, period, and eccentricity distributions; the presence of multiple systems; and the properties of the host stars. In all cases, the data refer to systems with ages in the Ga range. Some of the properties primarily reflect the formation mechanism, while others are determined by postformation dynamical evolutionary processes. The problem addressed here is the extraction of information relevant to the identification of the formation mechanism. The presumed formation sites, namely disks around young stars, therefore, must provide clues at times much closer to the actual formation time. The properties of such disks are briefly reviewed. The amount of material and its distribution in the disks provide a framework for the development of a model for planet formation. The strengths of, as well as the problems with, the two major planet formation mechanisms—gravitational instability and core accretion–gas capture—are then described. It is concluded that most of the known planetary systems are best explained by the accretion process. The timescales for the persistence of disks and for the formation time by this process are similar, and the mass range of the observed planets, up to approximately 10 Jupiter masses, is naturally explained. The mass range of 5–15 Jupiter masses probably represents an overlapping transition region, with planetary formation processes dominating below that range and star formation processes dominating above it. INTRODUCTION Planets have low masses, <10−2 times the masses of their central stars, and luminosities that can be as high as 10−3 times the solar luminosity (L¯ ) during brief periods of the formation phase, but luminosities are generally in the range of 10−6 –10−10 L¯ . Even nearby planets are generally spatially separated by less than 1 arc second from their host stars. The combination of these effects makes detection of planets difficult. The available detection methods (Marcy & Butler 1998, Perryman 2000) include (a) periodic Doppler shift variations in the line-ofsight velocity of the central star, as determined from displacements in frequency of spectral lines or pulsar timing; (b) periodic small positional shifts of the central 0084-6597/02/0519-0113$14.00 113 20 Mar 2002 7:46 114 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN star as it orbits around the center of mass of a planetary system; (c) direct detection of the reflected or emitted light of the planet; (d ) observation of the periodic dimming of the light of the star caused by the transit of a planet; and (e) departures from symmetry in the light curve of a gravitationally lensed star (Sackett 2001; Peale 1997, 2001). Practically all of the detections made so far have resulted from the Doppler method, although there are a few candidates for direct imaging and one detected transit of a planet whose existence was previously known through the Doppler technique. The first detection of an extrasolar planetary system was made by Wolszczan & Frail (1992) from precise measurements of the arrival times of pulses from the pulsar PSR 1257 + 12. The two planets in that system whose properties are well determined have masses (3.4/sin i) M⊕ and (2.8/sin i) M⊕ and orbital distances of 0.36 and 0.47 AU, respectively, where M⊕ is the mass of the Earth and i is the angle (generally unknown) between the line of sight and the normal to the orbital plane. The mutual gravitational perturbations of the planets lead to fluctuations in the observed arrival times of the pulses (Wolszczan 1994), constraining i to be most likely >60◦ , so that the masses are indeed only a few M⊕ . Two other objects may be present in this system. The presence of planets is rare among the pulsars, with only one other pulsar, PSR B1620–26 in the globular cluster M4, having a confirmed planet whose mass is most likely to be 10 Jovian masses (MJ) or less (Thorsett et al. 1999). The orbital separation is approximately 60 AU (Ford et al. 2000), and the planet orbits an inner binary system consisting of the pulsar and a white dwarf in a one-half year orbit. The first extrasolar planet (ESP) around a solar-type star was discovered by Mayor & Queloz (1995), who measured the periodic Doppler shift in the spectral lines of the star 51 Pegasi. This star displayed an amplitude in the line-of-sight velocity of 59 m s−1, compared with a measurement accuracy of 13 m s−1, leading to a mass of (0.47/sin i ) MJ and an orbital period of 4.23 days. This discovery was confirmed by Marcy & Butler (1995), and further discoveries were soon announced of planets around the stars 47 Ursae Majoris (Butler & Marcy 1996), 70 Virginis (Marcy & Butler 1996), 61 Cygni B (Cochran et al. 1997), ρ Coronae Borealis (Noyes et al. 1997), τ Boötis (Butler et al. 1997), υ Andromedae (Butler et al. 1997), and 55 Cancri (Butler et al. 1997). The minimum masses of these objects are in the range of 0.47 to 6.6 MJ. Previous to these discoveries, a companion to the star HD 114762 with a minimum mass of 11 MJ had been reported by Latham et al. (1989); this object apparently lies near the borderline between planets and brown dwarfs. At present, the list of planetary companions around main-sequence stars with masses similar to that of the Sun includes more than 60 members. Some of these systems contain multiple planets, including υ Andromedae with three planets and at least five systems with two planets each. Detailed updated information on all ESPs is available from the Extrasolar Planets Encyclopedia (http://www.obspm.fr/planets). The detection rate in the range of parameters in which current Doppler searches can find planets—namely, masses down to 0.1–0.4 MJ and separations less than 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 115 3 AU, corresponding to a velocity semiamplitude of >20 m s−1—is approximately 6–8 systems per 100 solar-type stars studied (D. Fischer, private communication). The velocity limit is expected to go lower in the future. The transit method is most likely to detect close-in planets (<1 AU) but could, in principle, reach down to the range of 1 M⊕ . In contrast, searches for direct detections are likely to yield relatively high-mass planets far (>100 AU) from the star, and gravitational lensing is sensitive to planets in the Neptune-Jupiter mass range at separations of 1–10 AU. No firm lensing detections have been reported so far, implying that less than one third of stars in the 0.3 M¯ mass range have Jovian mass companions in the separation range of 1.5 to 4 AU (Sackett 2001). In the following sections, we review the general properties of the ESPs around main-sequence stars, discuss the observed and theoretical properties of disks that provide the environment for planet formation, describe the two main formation models for planetary systems, and conclude with an analysis of the clues that the ESPs provide for an identification of the actual mode of planet formation. OBSERVATIONAL PROPERTIES OF EXTRASOLAR PLANETS The general properties of ESPs around main-sequence stars are summarized in reviews by Marcy & Butler (1998, 1999) and Marcy et al. (2000). Figure 1 shows the discovery space surveyed to date. The semimajor axis of the planet’s orbit is plotted as a function of Mp sin i, where Mp is the actual mass of the planet. Orbits fall within 3 AU, although with a longer time baseline, Jupiter-mass planets will be detectable at greater separations. A considerable number fall inside 0.1 AU (note that the orbit of Mercury about the Sun is at 0.39 AU), with the smallest separation of only 0.038 AU (8.8 solar radii). The apparent cutoff at this separation still remains to be explained. The detection of so many Jupiter-mass planets with small separations was a major surprise, in view of the fact that the giant planets in our Solar System reside outside 5 AU. The anomaly can be explained by the hypothesis that these giant planets actually formed at 5 to 10 AU away from the star and then migrated inward, losing orbital angular momentum as a result of the torque exerted on the planet by the disk (Goldreich & Tremaine 1980, Ward 1997, Lin et al. 1996). Timescales for this process can be quite short; for example, a planetary core of 10 M⊕ at 5 AU has a characteristic migration timescale of only a few times 104 years. This rapid migration is one of the major unsolved problems of planet formation. The migration may be stopped at small distances from the star as a result of (a) dispersal of the disk, (b) tidal interactions between planet and star, or (c) truncation of the inner part of the disk by the stellar magnetic field. More details on this general topic of migration will be found in a companion paper (Lin & Bodenheimer, manuscript in preparation). The lowest Mp sin i detected so far is 0.16 MJ, in a two-planet system whose companion has Mp sin i = 0.35Mj , whereas the highest is 17 MJ, in a twocompanion system whose second component has Mp sin i = 7 Mj . Depending 20 Mar 2002 7:46 116 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN Figure 1 The minimum masses (Mp sin i), in units of Jupiter’s mass, of all extrasolar planets around main-sequence stars detected before June 2001, are plotted against their orbital semimajor axes. The symbols J and S refer to Jupiter and Saturn, respectively. The solid line indicates a line-of-sight velocity amplitude of the central star of 10 m/s, below which planets are not currently detectable by Doppler measurements. Courtesy Debra Fischer. on the precise definition of a planet, this latter system may be a triple consisting of a planet and a brown dwarf in orbit. Several of the planets appear in long-period binaries; for example, Tau Boo and 16 Cyg B have stellar companions with separations ≈1000 AU. All points in the figure are based on observations of radial velocity. In addition, direct imaging with NICMOS (Lowrance et al. 2001) has yielded a possible planetary companion to the K7 star TWA 6. If confirmed by proper-motion studies, this object would have a mass of approximately 2 MJ at a projected separation of 125 AU. Mass Distribution Figure 2 shows the distribution of Mp sin i. Two features are clearly apparent. First, the distribution has a peak at low masses, less than a Jupiter mass, even though the lower masses are more difficult to detect. The mass distribution can be approximated by a power law: d N /d M ∝ M −1 (Marcy & Butler 2000). Second, 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 117 Figure 2 Histogram of the minimum masses (M p sin i), in units of Jupiter’s mass, of all extrasolar planets around main-sequence stars detected before June 2001. Courtesy Debra Fischer. there are very few detected companions in the mass range 10–20 MJ at separations less than 3 AU. This deficiency is real, as the Doppler method should have no difficulty in picking up companions in this mass range. Speculations (e.g., Marcy & Butler 1999) indicate that the apparent minimum in the mass distribution around 10 MJ could separate two different populations with different formation mechanisms: planets below 10 MJ and brown dwarfs above. Theoretical considerations (Lin & Papaloizou 1993) suggest that the mass ratio of planet to central star is a critical factor in determining the maximum mass of a planet. If we take into account the small range in stellar masses (about 0.4 to 1.25 M¯ ) that harbor planets, clearly a minimum in the mass ratio distribution exists at about 0.01–0.02. Actual masses can be determined under special conditions: (a) if the planet transits the star so that sin i is determined; (b) if the planet is observed during a microlensing event; (c) if the star has a circumstellar disk whose inclination can 20 Mar 2002 7:46 118 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN be determined by direct imaging and if the planet is assumed to be in the same plane as the disk; (d ) if the planet is in a multiple system and planet-planet gravitational interactions are significant; (e) if astrometric measurements of the stellar position, for example, from the Hipparcos satellite, are available, they can, in conjunction with the spectroscopic measurements, be used to put limits on the mass. In the case of radial velocity observations, there is an observational selection bias toward finding planets with larger sin i, so the most likely true mass hMi is certainly less than the value one would expect with a random distribution of orbital planes, which would give hMi = (π/2)Mp sin i. Orbital Properties The orbital properties of ESPs around main-sequence stars are summarized in Figure 3, a period-eccentricity plot. Periods range from a minimum of 3 days (with a surprising clustering of planets around that period) to a maximum of 2300 days. Clearly, as observational programs progress, more planets will be discovered Figure 3 The orbital eccentricity as a function of orbital period (in days) is plotted for all extrasolar planets around main-sequence stars detected before June 2001. Courtesy Debra Fischer. 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 119 Figure 4 Histogram of the periods, in days, of all extrasolar planets around main-sequence stars detected before June 2001. Courtesy Debra Fischer. in the period range of several years; at present the median period is about 70 days. In the short-period range, approximately 1% of solar-type stars surveyed have a planetary-mass companion with a period of less than 10 days. The period and eccentricity histograms are shown in Figures 4 and 5, respectively. Most of the ESPs have anomalous orbital eccentricities, compared with those of Jupiter and Saturn (0.048 and 0.055, respectively). The close-in planets generally have small eccentricities, but the orbital circularization time, a result of tidal dissipation in the planet (Goldreich & Soter 1966), is on the order of 109 years for a planet at 0.05 AU, a time somewhat shorter than the typical age of the primary star. At longer periods, the tidal circularization time is too long to be of importance, and there is a wide range of eccentricities at a given period. The same property applies to the low-mass stellar companions in short-period spectroscopic binary systems, with separations less than 3 AU. Black (1997) and Stepinski & Black (2000) show that the period and eccentricity distributions of the two groups are practically statistically identical, a fact that has led them to the speculation that the ESPs and the stellar companions are members of the same population, implying a common 20 Mar 2002 7:46 120 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN Figure 5 Histogram of the eccentricities of all (upper line) extrasolar planets around main-sequence stars detected before June 2001. The hatched region corresponds to only those planets with periods greater than 10 days. Courtesy Debra Fischer. origin. Actually, it would be more precise to say that the similarity between the two types of systems simply implies that the eccentricity excitation mechanism could have been the same for the two groups. A further fact is that there is apparently no correlation between eccentricity and Mp sin i among the ESPs (Figure 6) or among the low-mass stellar companions (Marcy & Butler 1999), whereas one would be expected if the eccentricity were excited by disk-companion interaction (Artymowicz et al. 1998, Lin et al. 2000). Radius and Internal Structure The radii of the ESPs are not known except for the one case of the companion to HD 209458, which has been observed in transit across the star (Charbonneau et al. 2000, Henry et al. 2000). The most precise determination of the radius of the planet, based on accurate photometric observations with the Hubble Space Telescope (Brown et al. 2001), gives Rp = 1.347 ± 0.060R J , where Jupiter’s 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 121 Figure 6 The orbital eccentricity as a function of Mp sin i, in units of Jupiter’s mass, is plotted for all extrasolar planets around main-sequence stars detected before June 2001. Filled and open circles correspond, respectively, to planets with periods greater than and less than 10 days. Crosses indicate planets in known multiple systems. Plus signs indicate planets in systems with trends in the data suggesting multiplicity. Courtesy Debra Fischer. radius RJ is generally taken to be 7.0 × 109 cm. This relatively large value for the radius, for a planet with Mp sin i of only 0.69 MJ (note that Saturn’s radius is about 0.82 RJ and its mass is 0.30 MJ), indicates that the planet is composed mostly of hydrogen and helium and that it has a mean density less than that of Saturn. The age of the star is about 5 Ga, at which age a giant planet of 0.69 MJ a few AU from the star would be expected, on the basis of detailed cooling calculations, to have a radius close to 1 RJ (Burrows et al. 1997). However, this planet is orbiting at only 0.045 AU from the star and has a probable surface temperature in the range 1300– 1400 K, a factor of 10 hotter than that of Jupiter. It has been suggested (Guillot et al. 1996, Burrows et al. 2000) that the effect of the stellar heating over the long-term evolution of the planet is to slow down its gravitational contraction and internal heat loss, therefore keeping its radius somewhat larger than if it were isolated. By calculating the contraction history of a heated planet of 0.69 MJ, they obtain theoretical radii close to the observed value, provided that the planet maintained its present orbit over most of its lifetime. Thus, if the planet migrated inward from a 20 Mar 2002 7:46 122 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN larger initial separation, it must have done so during the formation stage or shortly thereafter. The radius of an ESP is dependent on its internal structure and chemical composition, properties for which there are no data at present. In the case of the Solar System, all giant planets have envelopes made predominantly of hydrogen and helium, but overall they are metal rich with respect to the Sun, with the metal fraction by mass being enhanced over the solar value by roughly factors of 4 ± 2, 14 ± 3, 42 ± 3, and 44 ± 3 for Jupiter, Saturn, Uranus, and Neptune, respectively (Wuchterl et al. 2000). The structure of these planets is thought to consist of a solid core composed of ice and rock, surrounded by an envelope of metallic and/or molecular hydrogen, helium, and heavy elements with abundances relative to hydrogen above the solar value. However, the division of the heavy elements between core and envelope is not clear (Wuchterl et al. 2000). In the case of Jupiter, the metal fraction in the atmosphere is estimated to be a factor of 2–3 above solar (Lunine et al. 2000), and the fraction is likely to be higher in the other giant planets (Pollack & Bodenheimer 1989). The core mass can be derived from a comparison of theoretical models of the planets with observations of the mass, radius, and gravitational moments. The main uncertainty is the theoretical equation of state for high-pressure hydrogen-helium mixtures. The core masses of Jupiter and Saturn fall in the range of 0–14 M⊕ and 0–22 M⊕ , respectively, according to the summary of Wuchterl et al. (2000). However, in the case of Jupiter, if the core mass were actually zero, the metal enhancement of the envelope with respect to solar abundances would have to be the full factor of 4 referred to above. For a planet of ∼1 MJ, a higher core mass for a given total mass results in an overall higher mean density and smaller radius. Evolutionary calculations (Bodenheimer et al. 2001) for the companion to HD 209458 give radii at the present time of 1.07 and 1.2 RJ, with and without a solid core of 40 M⊕ , respectively [the calculations by Burrows et al. (2000) referred to above assumed no core]. The measured value of the radius favors a model without a core. However, in order to explain the discrepancy between the calculated and observed radii, Bodenheimer et al. (2001) suggest that there is an additional source of energy produced in a planet in a close orbit as a result of the dissipation of the stellar tidal disturbance. Processes that would cause such dissipation include the synchronization of the planet’s spin with its orbital motion and the circularization of its orbit. The amount of internal dissipation necessary to explain the observed radius would be approximately 10−7 L¯ and 10−8 L¯ for the cases with and without a core, respectively. These numbers are small, but in the case of HD 209458, there is no obvious source for the dissipation, since presumably the orbit is already synchronized and circular. In fact, a model with a core is not ruled out, given the presence of sufficient dissipation. Additional possible energy sources include dissipation of orbital eccentricity induced by perturbations from other planets in the system (Bodenheimer et al. 2001) or dissipation of kinetic energy induced in the atmosphere by stellar heating (Guillot & Showman 2001). To eliminate the complicating effects of stellar heating and tidal dissipation, it is necessary to observe the radius of a planet 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 123 somewhat farther away from its star, which, for example, the Kepler mission could accomplish. The presence or absence of a core could then be established with more certainty. Multiple Planetary Systems It is likely that many of the ESPs now known will be shown, on the basis of more data in the future, to be members of planetary systems (Fischer et al. 2001). The first example of this kind of development is the system υ Andromedae, which was found by Butler et al. (1997) to have a planet of Mp sin i = 0.71 MJ and a semimajor axis of 0.056 AU. It was later (Butler et al. 1999) found to be accompanied by two other planets, with Mp sin i = 2.11 and 4.61 MJ and semimajor axes 0.83 and 2.50 AU, respectively. The quoted value of the orbital eccentricity of the inner planet is 0.035 and is consistent with zero, but the Lick Observatory data give the eccentricities of the outer planets as 0.23 and 0.3, respectively. This configuration, with rather eccentric orbits and high-mass planets relatively close to the star, has general properties highly different from those of the Solar System and remains to be explained by a formation theory. The actual mass of the outermost planet is constrained by Hipparcos measurements (Mazeh et al. 1999) to be 10 ± 5 MJ; within these limits the system is found to be dynamically stable over periods comparable to the lifetime of the star (Laughlin & Adams 1999, Rivera & Lissauer 2000, Stepinski et al. 2000). Laughlin & Adams (1999) find that because of the relatively high eccentricity of the two outer planets, the evolution of the system is chaotic; nevertheless there are significant parts of the observationally allowed parameter space where these two planets remain in noncrossing orbits over the lifetime of the system. Contributing to this stability is the fact that the longitudes of periastron for the two outer planets are almost the same (Rivera & Lissauer 2000). Note that this system is nonresonant, namely, the orbital periods are not simple multiples of each other. Another system, HD 168443 (Marcy et al. 1999, 2001b), with two planets of Mp sin i = 7.7 and 17.2 MJ and periods of 58 days and 5.85 years, respectively, is also nonresonant, as is the Solar System itself, with the exception of Neptune and Pluto, which are very close to a 3:2 resonance. Other systems do exhibit orbital resonances. In fact, the two originally discovered pulsar planets (Wolszczan & Frail 1992) have practically circular orbits and a period ratio again very close to a 3:2 resonance. A more recently discovered system is GJ876 (Marcy et al. 1998, 2001a), an M4 dwarf with an estimated mass of 0.32 M¯ , the lowest mass of a host star discovered so far. The companions have Mp sin i = 0.56 and 1.89 MJ, semimajor axes of 0.13 and 0.21 AU, eccentricities of 0.12 and 0.27, and periods of 30.1 and 61.02 days, respectively. The measurement accuracy for the period is 0.03 day, so the periods are very close to, but significantly different from, a 2:1 resonance. Again, the longitudes of periastron for the two planets are the same to within the measurement accuracy. Gravitational interactions between the two planets should, in time, allow the actual masses to be determined. Laughlin & Chambers (2001) have developed models for this purpose and have derived a possible solution with sin i ≈ 0.4. 20 Mar 2002 7:46 124 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN Planets in Cluster Environments Alternatives to the Doppler method for planet searches have been employed in a few situations, particularly in connection with stellar clusters. Evolutionary calculations (e.g., Burrows et al. 1997) for objects of planetary mass and brown dwarf mass show that the luminosity is highest when they are young, that is, a few million years in age. Thus, young clusters have been identified as targets for near-infrared and visual searches for such objects. A particularly good example is the young cluster around the star σ Orionis, which has an estimated age of 1–5 Ma and low extinction from dust. Deep photometry (Zapatero Osorio et al. 2000) reveals the presence of a sequence of very low-luminosity objects which are likely to be cluster members. Spectroscopy of a few of the objects shows that the surface temperatures are low, around 2000 K. Comparison with evolutionary tracks (Baraffe et al. 1998, Chabrier et al. 2000) yields mass estimates; there is some uncertainty in the masses, but it is probable that the lowest mass objects are in the planetary mass range, approximately 10 MJ. The mass spectrum follows the relation d N /d M ∝ M −0.8 (Bejar et al. 2001). This result suggests that isolated objects in the planetary mass range could be relatively abundant; searches in other young clusters yield isolated objects down to the mass range of 10–20 MJ, if they are cluster members (Tamura et al. 1998, Lucas & Roche 2000, Hillenbrand & Carpenter 2000, Najita et al. 2000). A search by Hubble Space Telescope using the photometric transit method for planets in the globular cluster 47 Tuc was carried out (Gilliland et al. 2000). The cluster is metal-deficient with respect to the Sun by a factor of 5. The search was continued for 8.3 days, sufficient time to detect two transits of a planet with period 4.1 days or less. Based on the statistics of the occurrence of close-in giant planets in the solar neighborhood and the probability of observing a transit, they concluded that their sample of 34,000 stars should contain about 30 transiting planets, of which they should have been able to detect 17. In fact no transits were observed; thus, the frequency of 51 Peg-type planets in the cluster is at least an order of magnitude less than in the solar neighborhood. It is not clear whether the formation rate of planets there was reduced because of low metallicity or because of disk truncation caused by stellar encounters, whether the planets did in fact form but did not migrate inwards, or whether gravitational encounters with other stars in the dense cluster could have stripped the planets from the stars. Bonnell et al. (2001) perform a simple dynamic analysis to show that planetary orbits in a globular cluster at distances greater than 0.3 AU are likely to be disrupted, but that the close-in planets are likely to survive in their orbits. Properties of the Host Stars The main-sequence stars that harbor planetary-mass companions range in spectral type from M4 (surface temperature 3300 K) to F7 (surface temperature 6300 K). The target stars are generally chosen to be old, several Ga, because the surface activity declines with age, and thus the radial velocity measurements can be made more 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 125 accurately. Detailed observations have been made for these stars (e.g., Baliunas et al. 1997), and ages have been determined by comparisons of these observed properties with stellar evolutionary tracks (e.g., Fuhrmann et al. 1997, 1998). The most interesting characteristic of the planet-bearing stars is that they tend to be metalrich as compared with the Sun, as determined by spectroscopic abundance analysis (Gonzalez & Laws 2000, Gonzalez et al. 2001, Santos et al. 2001). The average overabundance is estimated to be 0.17 ± 0.20 dex, with respect to the sun, which itself is slightly metal-rich with respect to the average F-G field star in the solar neighborhood. Laughlin (2001) further finds that 1% of the solar-type stars have short-period planets (P < 20 days), but that among the metal-rich stars (above 0.125 dex with respect to solar), 10% have short-period planets. The most metalrich stars with planets, 55 Cancri and 14 Her, are overabundant by a factor of 3 (Gonzalez 1998). The most underabundant is HD 37124 (−0.32 dex). Laughlin (2001) also suggests that among the stars with planets, the metallicity increases slightly with stellar mass. Two explanations have been given concerning the association of metal-rich stars with planets. First, migration of metal-rich planets into their central stars could have enriched the outer layers of the star in metals (Lin 1997, Laughlin & Adams 1997). Or, second, the enhanced metallicity in the planet-forming disk could have been more conducive to planet formation. In fact, the planetary formation models of Pollack et al. (1996) show that the timescale for planet formation by the accretion process is very strongly dependent on the surface density of solid material in the disk. OBSERVATIONS OF PROTOSTELLAR DISKS Signature and Frequency of Occurrence of Disks It is clear from observations that many young stars are surrounded by disk-like structures (Bertout 1989, Beckwith & Sargent 1993, Strom et al. 1993, Beckwith 1999). Central stars over a considerable mass range (0.2–10 M¯ ) give indications that disks are present. A number of techniques are used to deduce the presence of both gas and dust in disks. Direct imaging has been accomplished at various wavelengths. Radio maps of the 13CO emission of the star HL Tauri showed an elongated structure with a radius of about 2000 AU (Sargent & Beckwith 1987). The velocities in this system were later interpreted as a rotating infall onto a small inner disk (Hayashi et al. 1993). Another disk observed in 13CO is that around GM Aur (Koerner et al. 1993), which is deduced to have a mass of approximately 0.08 M¯ in orbit around a star of 0.72 M¯ and to show the signature of Keplerian rotation. A circumbinary disk has been imaged in the near-IR with adaptive optics techniques around the young star GG Tau (Roddier et al. 1996). The Hubble Space Telescope has provided spectacular optical and near-IR images of disks, particularly in the Orion region (O’Dell & Wen 1994, McCaughrean & O’Dell 1996). HH 30 shows a flared disk with an optically detected outflow perpendicular 20 Mar 2002 7:46 126 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN to it (Burrows et al. 1996). The circumstellar disks in the binary L1551 IRS 5 have been resolved in the radio continuum at 7 mm (Rodriguez et al. 1998). More general, indirect techniques indicate that disks are common phenomena. First, young stars show excess infrared, sub-mm, and mm radiation over what one would expect from a normal stellar photosphere. This radiation, generally attributed to dust, arises either from a passive disk, which merely reprocesses the radiation from the central star, or from an active disk, which generates its own energy, for example, through turbulent friction. In many cases, synthetic spectra computed from active or passive disk models are found to agree with the observed emission (Adams et al. 1987, 1988; Chiang & Goldreich 1997). If the amount of absorbing material consistent with the infrared excess were spherically distributed around the star, the star would not be visible. Thus, it is deduced that the material must be arranged in a highly nonspherical geometry. Second, near infrared spectroscopy (Chandler et al. 1993, Carr et al. 1993) shows the presence of gas in the inner parts of disks, within 1 AU of the central star. Third, the classical T Tauri stars exhibit excess ultraviolet radiation, beyond that expected from a normal photosphere, as well as filling in of photospheric absorption lines (“veiling”). These effects suggest the presence of a “boundary layer” (Lynden-Bell & Pringle 1974) in which the rapidly orbiting disk material, channelled most probably by magnetic field lines (Shu et al. 1994), settles onto the more slowly rotating stellar surface. Typically, a star with a disk also shows characteristics of a wind, as diagnosed by forbidden line radiation and broad emission in Hα (Edwards et al. 1993). It is suggested (Cabrit et al. 1990, Hartigan et al. 1995) that there is a correlation between the mass accretion rate from disk to star and the mass loss rate in the wind, with the latter being roughly 10% of the former. The frequency of occurence of disks around young stars is best estimated by surveys in the mid-IR, around 10 µm. As summarized by Beckwith (1999), the fraction of stars with disks varies according to the sample and to the definition of “young star,” but overall, approximately half of young stars have disks. It is consistent with the observations to say that all young stars have disks when they are formed. Mass, Temperature Distribution, and Mass Transfer Rates of Disks Various types of observations allow many physical properties of protostellar disks to be determined. The radial extent of these disks is in the range of 10–1000 AU, and the corresponding masses (Figure 7) are roughly estimated to be 0.01–0.1 M¯ (e.g., Beckwith et al. 1990). From the UV radiation associated with matter accreting from the disk onto the star, the mass accretion rate is ∼10−8 M¯ year−1 for stars with an age of 106 year, and, in a rough correlation, decreases with age (Calvet et al. 2000). Fits of models to observed spectral energy distributions allow the run of midplane temperature TC, surface temperature TS, and surface density 6 as a function of distance from the star (R) to be estimated (Beckwith 1999). Such fits typically give TC ∝ R −0.5 , TS ∝ R −0.6 , and 6 ∝ R −1.5 . A standard 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 127 Figure 7 Histogram of the estimated total masses of disks, in M¯ , from observations in the millimeter, in the Taurus and Ophiuchus star formation regions. Adapted with permission from Beckwith (1999). reference model of a disk known as the “minimum mass solar nebula”(MMSN; Hayashi et al. 1985), reconstructed from the distribution of mass in the planets of the Solar System and assuming solar composition and no migration of planets, gives 6 ∝ R −1.5 and TC ∝ R −0.5 , the latter from the equilibrium temperature of dust in the stellar radiation field. More detailed equilibrium models of disks (Lin & Papaloizou 1980, 1985; Bell et al. 1997; Papaloizou & Terquem 1999) assume the disk is optically thick in the vertical direction, that the accretion rate Ṁ is constant as a function of R, that energy is transported in the vertical direction by radiation and convection, and that energy generated in the interior of the disk by some viscous process is all radiated locally (at approximately the same R) at the surface. The resulting distributions are not simple power laws with R; in general, 6 is less steep and TC is steeper than in the MMSN outside 1 AU. Radio observations of the disk around TW Hydrae, considered to be a close analog of the MMSN, are interpreted in terms of 6 ∝ R −1 and TC ∝ R −0.5 (Wilner et al. 2000). The midplane temperature in the MMSN is 280 K at 1 AU and 125 K at 5 AU. Corresponding surface densities of gas are 1700 and 150 g cm−2, respectively. Dust surface densities are a factor of 50–200 less. These physical characteristics are of great importance with regard to planet formation. The frequency of planet formation depends on the distribution of dust with radius; the final mass of the planets is determined by the properties of the gas; and the occurrence of multiple systems may be connected with the size of the disk, in the sense that a large 20 Mar 2002 7:46 128 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN disk with relatively low surface density would have reduced chances of forming a second planet. Depletion Timescale for Dust and Gas in Disks Although disks are apparently common among young stars, their lifetime in a phase where conditions are appropriate for forming planets is short. Disk lifetimes, in the phase of evolution when the dust component radiates significantly in the infrared, range from <3 Ma to 10 Ma, for stars in the solar-mass range. Lada (1999) estimates the mean lifetime of a disk at a few Ma, and Beckwith (1999) states that by 10 Ma the fraction of stars with disks has decreased to near zero. Briceño et al. (2001) find that the mean lifetime of disks in the Orion OB1 association is a few Ma, and Haisch et al. (2001), in a near-IR survey of several young clusters with a range of ages, find that half of the stars lose the dust component of their disks in 3 Ma, and that the overall disk lifetime is 6 Ma (Figure 8). The near-IR techniques probe the disks at radii of only 0.1 AU from the star. Further observations from the ISO satellite at 25 and 60 µm probe the disks at roughly 0.3–3 AU, and within the uncertainties the lifetimes are very similar, with a maximum at 10 Ma (Robberto et al. 1999). Thus, there is no obvious trend that suggests that disks clear from the inside out or from the outside in. The details of the process are difficult to determine, however, because the clearing timescale is thought to be short, ≈105 years (Wolk & Walter 1996). These disk ages are based upon the presence of emission from dust; thus, the “disappearance” of a disk could mean simply that the dust has coagulated into much larger objects that radiate much less efficiently. The disks also contain gas, which is much less extensively observed. The molecule CO has been observed (Zuckerman et al. 1995), but its abundance was found to be a factor of 100–1000 less than would be expected for solar composition, suggesting that there is little gas contained in disks. However, observations of molecular hydrogen from space (Thi et al. 2001) show that in three objects the gas-to-dust ratio is close to normal. The lack of CO can be attributed to condensation onto grains or destruction by UV starlight. However, there is little or no evidence that the lifetime of the gaseous component is any longer than that of the dust (Haisch et al. 2001). Thus, there is a rather severe observed constraint on the formation time of a gaseous giant: 107 years or less. There are not many exceptions, but, for example, Thi et al. (2001) find significant amounts of molecular hydrogen, enough to make Jovian-mass planets, around one particular star with age 17 Ma, and the TW Hydrae disk, thought to be similar in mass to the MMSN, has an age of approximately 10 Ma (Jensen et al. 1998). Structure of Residual Disks Disks in a later stage of evolution, around main-sequence stars with ages in the 5–30 Ma range, have been detected in the infrared and visible (see Lagrange et al. 2000 for a review). They consist of a relatively low mass (less than the MMSN) of dust, although the presence of gas is also suspected (Zuckerman et al. 1995, 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 129 Figure 8 The fraction of stars in a young cluster that show evidence for the presence of disks, as determined by excess in the infrared J, H, K, and L bands, is plotted as a function of cluster age. The bar labelled “systematic error” refers to the uncertainty in using different pre-main-sequence evolutionary tracks for determining the age. Reproduced with permission c The American Astronomical Society. from Haisch et al. (2001). ° Thi et al. 2001). The first and perhaps best case in which such a disk has been directly imaged is β Pic, a main-sequence star whose disk was first detected by the IRAS satellite and then imaged in the visible (Smith & Terrile 1984). This presumed remnant of a protostellar disk is composed of small dust particles and has been observed out to a radius of 1835 AU from the star (Larwood & Kalas 2001). A central gap in the dust distribution (Lagage & Pantin 1994), along with suspected nonaxisymmetric distortions of the disk (Kalas & Jewett 1995), has led to speculations that planets are present (Mouillet et al. 1997, Artymowicz 1997, Heap et al. 2000). On the other hand, the asymmetry could also be caused 20 Mar 2002 7:46 130 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN by a close stellar flyby (Larwood & Kalas 2001). Other well observed systems include Vega, Fomalhaut, ² Eridani, and HR 4796. The overall frequency of such dust disks around young main-sequence stars is estimated to be ≈20%, and the ratio of disk luminosity to stellar luminosity declines with age (Spangler et al. 2001). Another interesting example is the young main-sequence A star HD 141569. Coronagraphic observations from the Hubble Space Telescope at 1.1 µm show a resolved disk with peak surface brightness at 180 AU from the star, decreasing to larger and smaller radii (Weinberger et al. 1999). An annulus of reduced surface brightness (“gap”) is present at 250 AU. The presence of a planet or brown dwarf with mass >3 MJ in that region is ruled out by the observations. A planet in the 1 MJ range could account for the gap, but it could also be caused by the combined effects of radiation pressure and gas drag (Klahr & Lin 2001, Takeuchi & Artymowicz 2001). An analysis of two likely companions in the pre-mainsequence evolutionary stage gives an age for the system of 5 Ma (Weinberger et al. 2000). IMPORTANT ISSUES The summary of observational data on extrasolar planetary systems and their precursor disks indicates that there are numerous problems in connection with the elucidation of the planetary formation process. The observations of ESPs and planetary systems show such striking differences in properties as compared with the Solar System that one must infer that the formation process is very complex. It is also possible that more than one mechanism is at work. Some of the important questions that are raised can be stated as follows: 1. What is the primary mechanism for formation of objects of planetary mass (assumed here to be 10 MJ or below)? There are three main mechanisms that must be considered. The first is fragmentation of a rotating collapsing interstellar cloud core during its dynamical phase. This is the process that is thought to produce at least some of the stellar-mass binary systems, but it can produce low-mass fragments as well, down to roughly 7 MJ (Rees 1976, Low & Lynden-Bell 1976), so it must be considered as a possibility to explain the higher-mass ESPs. In the second process, the protostellar collapse resolves itself into a central star and a surrounding disk. If the disk is massive enough relative to the central star, or cold enough, it can become gravitationally unstable and fragment into small subcondensations (Kuiper 1951, DeCampli & Cameron 1979, Boss 1997). The third mechanism also takes place in a disk, and involves accretion of small particles to form a solid core, followed by capture of gas from the disk. The buildup of small particles to form large solid objects is in fact the process by which terrestrial planets are assumed to have formed (Safronov 1969, Wetherill 1980); at a few AU from a solar-mass star, conditions are also favorable for this process to provide the initial step in the formation of a gaseous giant. 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 131 2. Is the MMSN really the appropriate initial condition for planet formation? Its ratio of surface densities of gas and solid material is based on solar abundances and an equilibrium condensation model for the presence of various species of grains as a function of temperature. However, most of the material that eventually ended up in the star was first processed through the disk. As a result of accretion of new material onto the disk surface, growth of solid particles, turbulence, and gas drag, the surface density of solids could have evolved quite differently from that of the gas. In the early phases of the evolution of a disk, the surface density of solids was probably much higher than that in the MMSN. The evolution of the solid surface density must be considered in connection with planet formation models. 3. What is the timescale and efficiency of planetary formation? The first two mechanisms just mentioned tend to form planetary-mass objects rather quickly; the third requires a more extended period of time. Which processes are capable of forming planets within the time constraint allowed by the lifetime of protoplanetary disks? The ratio of the timescale of planet formation and the disk lifetime will determine the frequency of planetary systems. 4. How can the role of various formation processes be established through analysis of the initial mass function and composition of the ESPs? What determines the range of planetary masses? 5. Once formed, how do the planets’ internal structure, total radiation, and observable spectrum evolve with time? Are forming planets detectable during the phase when they are still embedded in the parent disk? Are disk signatures induced by planet formation, such as holes and gaps, detectable? 6. What is the origin of orbital diversity? What role do the processes of orbital evolution, accretion, encounters, and mergers have in establishing this diversity? How can the unique properties of specific systems, such as the resonant system GJ 876, be explained? If orbital migration is an important process in extrasolar planetary systems, how can we explain the positions of the giant planets in the Solar System? 7. Once a system of several planets has formed, under what conditions is it stable over periods of time required for life to be established in the habitable zone? What is the survival rate of planetary systems around isolated stars or in clusters? PROCESSES IN PLANETARY FORMATION The first question of the previous section is the focus of this section. Some of the remaining questions are associated with dynamical evolution of planetary systems, and they will be analyzed in a later paper by Lin & Bodenheimer. We discuss some of the issues connected with the formation of planets by gravitational instability and by the core accretion–gas capture process. The formation of binary systems by collapse and fragmentation is discussed in detail by Bodenheimer et al. (2000). 20 Mar 2002 7:46 132 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN Grain Condensation and Sedimentation In a typical nebular disk model, temperatures outside approximately 2.5 AU are cool enough so that ices can condense, with the solid component accounting for 1–2% of the mass. Interior to that radius, only mineral grains such as silicates and iron can survive, so that the solid fraction is lower by a factor of 2–3. Above approximately 2000 K, the solid component is expected to have essentially evaporated. When the disk forms, it inherits the dust particles, which have a range of sizes with a typical value of a few tenths of a micron, from the interstellar medium. The vertical component of gravity in the disk tends to force the dust to settle toward the midplane. For micron-sized grains, the settling time is too long to be of interest. However, the larger grains fall faster than the smaller grains, so coagulation of grains into larger particles occurs during the settling process. Growth of grains is also aided by turbulence, gas drag (Supulver & Lin 2000), and the formation of vortices (Tanga et al. 1996). The combined growth and settling times in a typical disk are 5 × 103 years at 1 AU and 5 × 104 years at 5 AU. A dense layer of solid particles, typically in the 1 cm to 1 m size range, builds up in the midplane of the disk. Further collisions of these particles lead to the formation of “planetesimals,” objects of 1 to 100 km in size that are decoupled from the gas and move in Keplerian orbits around the star. The important physical processes during this early phase of planet formation are discussed by Hayashi et al. (1985), Lissauer (1993), Weidenschilling & Cuzzi (1993) and Ruden (1999). Gravitational Instability Scenario The formation of gravitationally unstable subcondensations in the solar nebula as a mechanism for the formation of giant planets was first proposed by Kuiper (1951) and further discussed by Cameron (1978). The early phases of the collapse and contraction of fragments were followed numerically by DeCampli & Cameron (1979), Bodenheimer et al. (1980), and Cameron et al. (1982). Adams et al. (1989) consider eccentric spiral modes in disks, find a gravitational instability if the disk is massive enough, and speculate that this instability could result in the formation of a binary companion. Numerical simulations by Adams & Benz (1992) and Boss (1997) show that the formation of a low mass companion (≈10 MJ) on an eccentric orbit is possible in a gravitationally unstable disk. However, Tomley et al. (1994) showed numerically that gravitationally unstable disks tend to transfer angular momentum outward by spiral waves that involve several different modes. Only if the disk is efficiently cooled is there some evidence for fragmentation. Also, Laughlin & Bodenheimer (1994) calculated the collapse of a rotating interstellar cloud core, and they resolved the structure of the disk that formed in the interior. The disk became gravitationally unstable, and they followed its evolution with a three-dimensional numerical hydrodynamics code. Spiral waves developed that resulted in transfer of angular momentum outward and most of the mass inward. The spiral wave amplitude saturated, and no fragmentation was observed. 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 133 The main criterion that must be satisfied for this mechanism to work is that the Toomre gravitational stability parameter Q= κCs π G6 (1) must locally be about 1 or less, where Cs is the sound speed, 6 the surface density, and κ the epicyclic frequency at some point in the disk [κ 2 = R −3 ddR (R 4 Ä2 ), where Ä is the orbital frequency]. Strictly speaking, this criterion applies to axisymmetric perturbations only. However, nonaxisymmetric numerical simulations show (e.g., Laughlin & Różyczka 1996) that if Q ≈ 1.3, then the gravitational instability appears with a growth time of a few orbits, but the solution involves saturated spiral waves with no fragmentation. On the other hand, if they reduce the minimum Q in the disk to 1.0, then fragments appear. Whether the regime Q ≈ 1.0 can be reached depends on the evolutionary history of the disk formation process. As a specific example, Boss (2000) has constructed a low-mass disk (10% of the mass of the central star). The temperature is aproximately 100 K at the orbital distance of Saturn, and the disk radius is approximately 20 AU. A three-dimensional numerical code shows it is gravitationally unstable, and it produces a fragment of 5 MJ at ≈10 AU. The fragment has uniform chemical composition with no core initially. Detailed calculations in one space dimension of the structure of such a fragment (Bodenheimer et al. 1980, Lin et al. 1998) show that at its probable initial size of 1013 cm it is in hydrostatic equilibrium with a central temperature of 1000 K, a central density of 3×10−8 g cm−3, log L/L ¯ = −4.19, and Tsurf = 36 K. The object then contracts in quasi-static equilibrium until the central temperature reaches 2000 K, at which point the hydrogen molecules dissociate and induce rapid collapse. After the whole object collapses, it regains hydrostatic equilibrium at a much smaller size, ≈1010 cm. From that point, it contracts slowly and cools, as calculated by Burrows et al. (1997), D’Antona & Mazzitelli (1994), and Baraffe et al. (1998). An important question is whether the fragment can form a core. At its relatively high initial central temperature, less than 1% by mass of the gas can condense into grains. It has been suggested (Slattery et al. 1980, Boss 1998) that in the early low-temperature contraction phase of a giant planet, the silicate and iron grains can sink to the center and that the water would be insoluble in the molecular hydrogen. The timescales for coagulation and sinking of grains have been estimated in the previous section, and for the particular model under consideration, they give approximately 3000 years, as compared to the contraction timescale of 104 years from formation to the point where all grain species have evaporated at the center. Since the coagulation and settling times are only estimates, it is not clear that a core can form. More detailed future work must also take into account the fact that the inner quarter of the mass of the protoplanet is convective. One might imagine that planetesimals captured by the planet later, during its final phase of contraction and cooling, could be a source of material for the core, but Stevenson (1982) showed that material added during this phase would be soluble in the planet’s envelope and would not settle to the center. 20 Mar 2002 7:46 134 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN To summarize, this model has a number of strengths: ■ ■ ■ ■ The formation time is roughly the dynamical time which, at distances of 5–10 AU from the star, is only 100 to a few hundred years. Planets form on eccentric orbits, as observed in extrasolar planetary systems. The model can explain the ESPs that have been found in the mass range of 5–10 Jupiter masses or higher. In general, once a protoplanet has obtained a mass of approximately 1 M⊕ or more, torques are exerted upon it by the surrounding disk and it tends to migrate toward the star on a timescale shorter than the disk lifetime (Goldreich & Tremaine 1980, Lin & Papaloizou 1986, Ward 1997). The migration is called Type I before the planet is massive enough to open a gap in the disk (cf. Growth Termination, see below) and Type II after this time. In the gravitational instability picture, the Type I migration problem does not exist. Once the planet has formed, it will undergo Type II migration, which can be relatively slower than Type I and which could explain the presence of ESPs very close to their stars (Lin et al. 1996). A number of problems have also been identified: ■ ■ ■ ■ The fragments are relatively large, approximately 10 Jupiter masses, so it is difficult to form Jupiter and Saturn and most ESPs. Relatively massive disks are required, at least 0.1 times the mass of the star, which is not consistent with the typical observed disk mass, although it is at the upper end of the range. The mechanism has problems explaining the presence of solid cores, particularly in the case of Uranus and Neptune. As discussed above, gravitationally unstable disks don’t necessarily fragment. Mechanism of Core Accretion—Gas Capture In view of some of the difficulties of the gravitational instability model, the standard accretion scenario has generally been favored, at least for the case of the Solar System. A giant planet forms according to the following steps: 1. Accretion of dust particles results in a solid core of a few M⊕ , accompanied by a very low-mass gaseous envelope. 2. Further accretion of gas and solids results in the mass of the envelope increasing faster than that of the core until a crossover mass is reached. 3. Runaway gas accretion occurs with relatively little accretion of solids. 4. Accretion is terminated by tidal truncation or dissipation of the nebula. 5. The planet contracts and cools at constant mass to its present state, with a peak L ≈ 10−3 –10−4 L¯ . This model is not without its own problems. The principal one is that in a MMSN, the formation times for Jupiter and Saturn are over 107 years; thus, one must postulate that the actual disk was several times denser than the MMSN in the 5–10 AU zone at the time these planets formed. Furthermore, the model, in and of itself, does not predict highly eccentric orbits, as observed for ESPs. Some other 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 135 process must be found to explain the eccentricities. Another important problem is that orbital decay by Type I migration occurs on a timescale shorter than that of planetary growth, once the solid core has reached a mass of ≈1 M⊕ . On the other hand, the main strengths of the model are that it predicts masses in the solid component of 15–20 M⊕ , consistent with the values deduced for the giant planets, and it shows that the mass of the solid component is relatively independent of the position of the planet in the disk, also in agreement with observations. In particular, the model can explain the properties of Uranus and Neptune, which are not at all consistent with the gravitational instability picture. The following subsections describe the core accretion–gas capture model in somewhat more detail. PLANETESIMAL COAGULATION AND THE FORMATION OF SOLID EMBRYOS Once planetesimals in the size range of 1–100 km have been formed, the rate of accretion of solid material onto a forming planet in a background swarm of planetesimals is Ṁ cor e = π Rc2 6 Z ÄFg , (2) where Fg = 1 + (ve /v)2 is the ratio of the total cross section to the geometric cross section, also known as the gravitational enhancement factor. Here, Rc is the capture radius of the planet, Ä is its orbital frequency in the disk, 6 Z is the surface density of solid material, ve is the escape velocity from the surface of the planet, and v is the mean relative velocity of planetesimals and the planet far from encounter. The success of the accretion model in making Jovian-mass planets at 5–20 AU depends on two important factors (Lissauer 1987): First, 6 Z must be larger by a factor of 3–4 than the value given by the MMSN, and second, v must be small compared to ve so that Fg is large. The latter requirement can be met if runaway growth of one planetary core takes place. As reviewed by Lissauer (1993) and Ruden (1999), equipartition of energy between particles tends to be established through longrange gravitational encounters, so that the larger particles have smaller velocities and therefore enhanced Fg , so they tend to accrete each other. The plausibility of runaway accretion, first discussed by Greenberg et al. (1978), has been verified by a number of other calculations, for example, Weidenschilling et al. (1997). A problem arises in the later stages once the larger particles have accreted. They tend to excite velocity dispersion among the smaller particles, reducing Fg , and inhibiting further accretion. The effect of gas drag on the small particles, however, can counteract this effect. A forming planet can accrete only that material within its gravitational reach. The Roche radius, or “Hill sphere” radius, outside of which material is not gravitationally bound to the planet because of the tidal effect of the central star, is given by µ ¶ Mp 1/3 , (3) RH = a p 3M∗ where a p is the distance to the central star, which has mass M∗ . The planet excites eccentricity in particle orbits in the nearby disk, and numerical simulations (see 20 Mar 2002 7:46 136 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN Lissauer 1993) show that the effective “feeding zone” of the planet extends to 4 R H on either side of the planet, assuming that the orbit is circular. When all of the material within that zone has been collected by the planet, it reaches its “isolation mass”, given by ¢3/2 ¡ 16πa 2p 6 Z ¡ ¢3/2 Miso = = 1.56 × 1025 a 2p 6 Z g (4) 1/2 (3M∗ ) if M∗ = 1 M¯ , a p is in AU, and 6 Z is in g cm−2. At 5 AU in an MMSN, Miso ≈ 1.5 M⊕ , but if 6 Z is increased by a factor of 3 above that of the MMSN, Miso ≈ 8 M⊕ . Of course, if gas is also present, or if the orbit is eccentric, or if the planet migrates, true isolation will never occur. GAS ACCRETION ONTO PROTOPLANETARY CORES When the growing core achieves a mass of 1 M⊕ , it has gravitationally attracted a small amount of nebular gas around it, ≈10−5 M⊕ , and this gaseous envelope increases in mass along with the core mass. Since initially there is a continuous distribution of gas between the core and the surrounding disk, it is appropriate to define the outer edge of the protoplanet (R B ) as the point inside of which gas is gravitationally bound to it, meaning either the tidal radius R H or the accretion radius, RA = GMp , Cs2 (5) where Cs is the sound speed in the disk, whichever is smaller. A key concept regarding gaseous envelopes is the so-called critical core mass (Perri & Cameron 1974, Mizuno 1980). A low-mass envelope is presumed to be in hydrostatic equilibrium as a result of the heat, and consequent thermal pressure, generated by infalling planetesimals that either hit the core or, at later stages, are ablated and destroyed in the envelope before reaching the core. An energy balance is established, with the gravitational energy released by the infalling planetesimals balanced by the radiation from the surface of the envelope. However, once the envelope mass is of the same order as the core mass, the infalling planetesimals are not able to supply energy at the rate at which it is radiated, so the gas as a whole must contract to liberate additional energy. This contraction eventually becomes fast, and the rate of gas accretion from the disk increases rapidly until it becomes a runaway process. Mizuno (1980) showed that the critical core mass was ≈10 M⊕ and that it did not depend strongly on the position of the planet (a p ) in the disk. The agreement between this result and the approximately known core masses of the four giant planets in our Solar System is an important point in support of this theory. Bodenheimer & Pollack (1986) calculated the complete evolution, up to a few Ga, of giant planets with final masses equal to those of Saturn and Uranus, under the assumption of a constant Ṁcore , including both the planetesimals and the gas contraction as energy sources. The evolution started with a core of approximately 1 M⊕ , and the final core masses were in the range of 10–30 M⊕ . Improved 30 Mar 2002 8:13 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 137 calculations were published by Pollack et al. (1996) and Hubickyj et al. (2001). These calculations are composed of three major elements: (a) The core accretion rate is no longer assumed to be constant but is calculated according to Equation 2, with the gravitational enhancement factor obtained from numerical simulations of Greenzweig & Lissauer (1992). (b) The structure and evolution of the envelope is calculated from solutions of the equations of stellar structure, including radiative and convective energy transport. The mass accretion rate of the envelope Ṁenv is calculated according to the requirement that the actual radius of the planet be equal to R B . (c) The interaction of the infalling planetesimals with the envelope, including the effects of gas drag, vaporization, ablation, and deposition of energy are taken into account. Outer boundary values of density and temperature at R B are set to values obtained from disk models (Bell et al. 1997); once accretion has been completed and the planet contracts inside R B , standard photospheric boundary conditions are imposed. The results of these calculations show that the evolution is divided into three major phases. In the first, the solid core accretes to approximately 10 M⊕ on a timescale of about 106 years. At the end of Phase 1, Ṁcore decreases considerably as the core approaches Miso , and the envelope mass is still very low. In Phase 2, envelope and core masses both increase relatively slowly, with Ṁenv exceeding Ṁcore . Once Menv approaches Mcore , Phase 3 begins, in which Menv increases on a short timescale. An example of the evolution of mass with time for three cases is shown in Figure 9, and the evolution of the corresponding luminosities is shown in Figure 10. Several conclusions can be reached. First, the formation time for a Jupiter-mass planet at 5 AU with interstellar opacities is approximately 6 Ma, close to the typical disk lifetime, even with 6 Z enhanced over that in the MMSN by a factor of 3.3. Second, the length of Phase 2 is a critical quantity that determines the overall formation time. This timescale can be reduced if solid accretion proceeds beyond the isolation mass, for example, because of migration or if the rate of radiation from the protoplanet is increased. Third, the formation time is very sensitive to the value of 6 Z , so that values taken from the MMSN would give unacceptably long formation times. Fourth, an opacity reduction below interstellar values is appropriate because grains, once they enter the planetary envelope, settle and coagulate rapidly. An opacity reduction results in a significantly reduced formation time, because the radiated luminosity of the planet becomes larger, requiring faster contraction and enhanced Ṁenv during the lengthy Phase 2. The presence of ESPs near their stars has led to the suggestion (Lin et al. 1996) that giant planets form in the 5–10 AU region according to the picture just discussed, but during the formation process they migrate inwards. However, one must also consider the possibility that these planets could actually form at their present locations. The main difficulties in forming a planet at say 0.05 AU are: (a) According to many nebular models, the temperatures there are too high to allow solid particles to exist. (b) Even if solid particles could condense, there is too little mass in the inner regions of the disk to provide ≈1 MJ. (c) As long as the planet 20 Mar 2002 7:46 138 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN is embedded in a disk, the torques exerted on it would cause it to migrate into the star. Nevertheless, Bodenheimer et al. (2000) tested the hypothesis that close-in giant planets could form in situ. The first difficulty was solved through use of a nebular model by Bell et al. (1997), which shows that for a viscosity parameter α = 0.01 and a disk accretion rate Ṁ = 10−8 M¯ year−1 , the temperature at 0.05 AU is approximately 1500 K, cool enough to allow some grains to survive. The second difficulty is solved if one notes that the disk accretion rate given above corresponds to a delivery rate of condensible solids to 0.05 AU of Ṁ ≈ 10−5 M⊕ year−1 . Thus, Ṁcore was assumed to be constant at that rate. Ward (1997) also proposed that migration of chunks of solid material inward to 0.05 AU could result in accretion of a planet at that radius. The third difficulty can be averted if one assumes that the inner part of the disk has been cleared, for example, by magnetic effects (Lin et al. 1996), out to about 0.1 AU. In that case, the tidal torques on the planet would be negligible. However, this solution to the migration problem leads to the problem that there would be little gas to accrete onto the planet. The results of the calculations indicate that a 51 Peg-type planet can form in 5 Ma, with Mcore = 45 M⊕ and Menv = 120 M⊕ . The authors conclude that in situ formation is possible, given reasonable disk models, but there are problems, indicating that migration may well have been an important component of the formation for close-in giant planets. A problem with migration occurs, however, for planets at distances >0.1 AU, where there is no obvious mechanism for stopping the migration at their present distances except disk dispersal, for example, by steller winds, by photoevaporation caused by the UV radiation from the central star, or by accretion onto the star. GROWTH TERMINATION Two mechanisms have been discussed for the termination of the rapid gas accretion onto a protoplanet; first, disk dispersal, and second, gap opening. It may seem counterintuitive that Phase 3, which involves gas accretion on a timescale of only 103–104 years, is suddenly followed, at the critical moment, by a process of nebular dissipation in which the gas density is suddenly reduced by a factor of 1000 from its initial value. However, this mechanism could work to explain the structure of Uranus and Neptune (Pollack et al. 1996, Bryden et al. 2000). For a substantial period of time, ≈2 Ma during Phase 2, a planet has Mcore ≈ 10 M⊕ and Menv ≈ 2−4 M⊕ . In the outer parts of a disk (10–20 AU) the formation time for the core could be long enough so that substantial disk dissipation occurs during Phase 2, causing the planet to never reach critical core mass. An analogous situation could occur for the lower-mass ESPs. But for planets in the Jovian mass range, it seems as though gap opening must be the critical factor. The tidal truncation conditions (Lin & Papaloizou 1986, 1993) give the planetstar mass ratio at which a gap appears in the disk: 40ν ¢ M∗ Äa 2p M p,G A P = ¡ (6) 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 139 and µ M p,G A P = 3 Cs Äa p ¶3 M∗ , (7) where ν is the disk viscosity. In a low-mass disk, Mp must typically be above ≈1 MJ to satisfy these conditions. Numerical simulations (Bryden et al. 1999, Artymowicz & Lubow 1996, Kley 1999) show that, in fact, gaps do begin to open at the mass predicted by these equations, but that accretion onto the planet can continue through the gap until its density is reduced by a factor of 1000, leading to a final planet mass up to 5–10 MJ, depending on the disk viscosity. Further accretion is possible if the protoplanet has an eccentric orbit. Thus, the maximum mass of a planet formed by the accretion process appears to be close to the lower limit of the mass of an object formed by direct fragmentation during collapse. The ESPs in the Saturn mass range, if not limited in mass by disk dissipation, would have to be explained by formation in a disk region with cold temperatures and low viscosity; otherwise it would not be possible for them to open a gap. Again, migration seems to be implied. Angular momentum is also transferred from the disk to the planet during the gap-opening process, leading to a subdisk around the planetary core (Ciecielag et al. 2000). One might think that the presence of this disk would slow down the accretion process onto the planet. However, the disk turns out to have a thickness comparable to its radial extent and to have a spiral structure, which results in transfer of angular momentum outward rapidly, on a dynamical timescale. FINAL CONTRACTION PHASE Once the accretion is terminated, the protoplanet evolves at constant mass on a timescale of several Ga with energy sources that include gravitational contraction, cooling of the warm interior, and surface heating from the star. The latter source is important for giant planets close to their stars because the heating of the surface layers delays the release of energy from the interior and results in a somewhat larger radius at late times than for an unheated planet (Burrows et al. 2000). For giant planets close to their stars, tidal dissipation in the planet, caused by circularization of its orbit and synchronization of its rotation with its orbital motion, can provide a small additional energy source (Bodenheimer et al. 2001). The energy transport in the interior during this phase is primarily by convection, but the rate of energy loss at the surface is controlled by the radiative opacity in the photospheric layers. The main sources of uncertainty in the theoretical models are (a) the complicated surface opacities, which depend on a wide variety of molecular transitions as well as poorly understood dust processes (Chabrier et al. 2000), and (b) the interior equation of state, which is primarily nonideal in this phase (Saumon et al. 1995). The initial conditions for this phase depend only weakly on the formation process. In case of models formed by gravitational instability the evolution goes through a phase of gravitational collapse induced by molecular dissociation, and equilibrium is regained, 105 to 106 years after formation, at a radius of only 1.5–2 20 Mar 2002 7:46 140 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN RJ (Bodenheimer et al. 1980). In the case of accretion models, calculations show (Bodenheimer & Pollack 1986, Bodenheimer et al. 2000) that after the formation phase, which lasts a few Ma, the radius declines on a timescale of 105 years to ≈1010 cm, or 1.4 RJ. The detailed evolution beyond this point has been calculated by Burrows et al. (1997), Guillot et al. (1996), Baraffe et al. (1998), and Chabrier et al. (2000). The calculations produce luminosity and surface temperature as a function of time for various masses. If a free-floating or orbiting planetary candidate is directly observed, and if its age, luminosity, and surface temperature can be determined, the evolutionary tracks yield estimates of the mass (Zapatero Osorio et al. 2000). The results of these calculations can also be compared with the radius of the one ESP for which it is known, as discussed in Radius and Internal Structure above. A useful calibration point can be obtained by comparison of the models with the known luminosity and surface temperature of Jupiter at its known age of 4.7 Ga (Burrows et al. 1997). SUMMARY AND DISCUSSION The main purpose of this article is to discuss the question: What do the properties of the ESPs tell us about their formation processes, and might these processes differ from what occurred in the Solar System? Simply from the large number of planets known, we deduce that the formation mechanism must be one that is robust, not just marginally possible. As outlined in Issues above, there are three possible formation processes: fragmentation during cloud collapse, fragmentation as a result of gravitational instability in a disk, and core accretion followed by gas capture. The first mechanism can likely produce isolated masses down to 5–10 MJ, although there remains the problem of producing the necessary initial condition of a high-density (∼10−15 g cm−3 ) fragment in the interstellar medium. Alternatively, a fragment in the 5–10 MJ range can form as a subregion during the collapse of a larger-mass molecular cloud core, say 1 M¯ , but then there is the problem that even if such a fragment does form, it would tend to accrete additional material. A third possibility is that a high-mass fragment and a low-mass fragment could form in the same cloud. In this case, further accretion tends to equalize the masses (Bate 2000) in a close binary system. Bate states “it is very difficult to form [by direct fragmentation] a brown dwarf companion to a solar-type star with a separation <10 AU.” Thus, the low-mass fragment would somehow have to escape from the system before substantial accretion has taken place. Although a more detailed understanding of protostellar fragmentation is needed, the isolated brown dwarfs and planetary-mass objects in young clusters are candidates for this process, but the highest-mass planets in orbit are unlikely to have formed this way. The second process can operate in a disk if it is gravitationally unstable with a minimum Toomre Q value of ≈1. It is still not clear under what conditions a disk that satisfies this requirement can actually form. In any case, the simulations that have been performed so far indicate that the masses of the fragments are 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 141 in the 5–15 MJ range, so they could explain the existence of the higher-mass planets. For example, the object with Mp sin i = 17 MJ in the system HD 168443 (Marcy et al. 2001b) would be hard to explain by the core accretion process. The presence of it and its companion with Mp sin i = 7 MJ (a p = 0.3 AU) could be consistent with the gravitational instability hypothesis (Boss 1998, Marcy et al. 2001b). However, there is a problem with the numerical simulations of this process, which show that dense condensations can form but they tend to be sheared out by the differential rotation in the disk. It also may be difficult to explain resonant planets or the nonnegligible number of nearly circular orbits outside 0.1 AU that have been detected. Furthermore, the process is not favored in the inner regions of standard accretion disks (a p < 1 AU) because high values of sound speed and angular velocity give a Q-value much greater than 1; however, a somewhat unusual disk, with a high accretion rate and low viscosity, could have Q < 1 even interior to 1 AU (Bell et al. 1997). Further studies are needed on the properties of disks during their early history, before the classical T Tauri phase, because this early phase may be crucial to planet formation. Variants on this scenario include fragment formation in a disk induced by a close encounter with another star-disk system (Watkins et al. 1998), or ejection of a filament in such an encounter, leading to gravitational instability in the filament and formation of an unbound object of 5–10 MJ (Lin et al. 1998). Roughly one half of the ESPs around main-sequence stars have masses Mp sin i < 1.5 MJ and are unlikely to have been produced by either of the above processes. The core accretion process can explain objects over a considerable range of masses, but it may be difficult to produce masses above 5 MJ (Nelson et al. 2000), which account for ∼20% of the observed planets. It is tempting to postulate that this mechanism accounts for most of the ESPs as well as the giant planets in the Solar System. The enhancement of metallicity in the stars with planets is consistent with this process, because higher solid surface densities in disks promote much faster formation times for giant planets (Pollack et al. 1996). But there are certain difficulties. 1. The process works best in the semimajor axis range of 5–10 AU, where ices can condense and where the masses that can be built up by solid accretion exceed 1 M⊕ . In the 1–2 AU region, where many ESPs exist, solid cores tend to become isolated, which means the accretion rate onto them slows down considerably, at only a small fraction of M⊕ . However, this argument neglects the possibility that the cores can migrate during formation, or that solid particles can migrate through the disk relative to the forming planet; in both cases, accretion could continue. 2. Planet-planet interaction may have to be invoked to explain high eccentricities. Disk-planet interaction for a planet in the MJ range tends to circularize the orbit. For example, migration calculations of Nelson et al. (2000) show no orbital eccentricity excited for masses up to 5 MJ. 3. The low density for the companion to HD 209458 suggests it does not have a core and, thus, favors the gravitational instability process; however, there is a problem in this regard with its low mass. Fitting the observed radius by theoretical models may require an additional internal energy source, such as tidal dissipation, in which 20 Mar 2002 7:46 142 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN case either process could be consistent. Furthermore, the core mass could be small, in which case the effect on the radius would be negligible. The similarities of the period-eccentricity relations of the ESPs and of lowmass (0.1–0.3 M¯ ) secondaries in spectroscopic binaries (with similar periods and primary masses to those of the ESPs), as well as the close similarities between the period histograms and eccentricity histograms in these two types of systems, have led Black (1997), Heacox (1999), and Stepinski & Black (2000) to suggest that there is a common formation process. Since the core accretion process has great difficulties in explaining the secondary masses of the spectroscopic binaries and also the wide range of eccentricities, they suggest that gravitational instability in a disk could explain both populations. The main problem here is that the wide range in both the observed masses and the observed orbital distances has not been explained satisfactorily by this model. On the other hand, the slopes of the mass distributions of the two types of systems are quite different, with a break around 10–30 MJ (Mazeh & Zucker 2001). It is entirely possible that the formation mechanisms were indeed distinct, but that similar postformation orbital evolution generated the observed similarity in the period and eccentricity distributions (Heacox 1999). In both the gravitational instability model and the core accretion model, the favored site for planet formation is 5–10 AU from the star. Thus, migration may have played an important role during the formation period of giant ESPs (to be discussed in detail in a companion paper by Lin & Bodenheimer). The resonance lock in GJ 876 also implies migration (Goldreich 1965). The large value of the measured radius of HD 209458b implies either that it formed in situ or, more likely, it migrated to its present position early in its evolution (Burrows et al. 2000). In the case of the planets with periods of only 3 to 4 days, there exist mechanisms to halt the migration before the planets are consumed by the star. For planets in the longer-period range, there is no obvious mechanism to stop the migration, except by invoking clearing of the disk before the migrating planets reach the vicinity of the star (Trilling et al. 1998). The question still remains why Jupiter and Saturn have apparently not undergone significant migration. The pulsar planets also provide clues regarding the formation process. Although many mechanisms have been proposed for the system around PSR 1257 + 12 (Podsiadlowski 1993), the most likely one is ablation of a low-mass companion to the pulsar by radiation from the pulsar, producing a circumbinary disk that is forced outwards under the influence of both gas and radiation pressure. Assuming the disk has sufficient mass, the terrestrial-mass planets could form by accumulation of small particles, as outlined in a reasonably analogous context by Lin et al. (1991). This system thus suggests that planet formation, in this case by accretion, is a robust process, which can occur even under somewhat unusual circumstances. Gravitational instability is an unlikely mechanism, as the planets have low mass and the disk probably also had low mass. In the case of the pulsar planet around B1620–26, the object is the outer member of a hierarchical triple system, and its 20 Mar 2002 7:46 AR AR154-05.tex AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD PLANET FORMATION 143 probable mass shows it likely to be on the borderline between a planet and a brown dwarf. However, its presence in a globular cluster suggests it still could have been formed by accretion in a disk around a main-sequence star and then captured in an exchange interaction between that star and a binary pulsar (Ford et al. 2000). Could there have been a universal formation mechanism? The observed extrasolar planetary systems exhibit a wide range of properties, but their diversity could be due in large part to dynamical processes such as migration, mutual gravitational interactions among a large number of planetary embryos (Levison et al. 1998) or planets (Lin & Ida 1997), or interactions with other stars (Mazeh et al. 1997, Holman et al. 1997, Laughlin & Adams 1998). The supposition that the core accretion hypothesis does not produce eccentricities is based on simplified models that look at the formation of a single embryo. The underlying formation mechanism could be the same for most planetary systems, with a transition from planetary formation by core accretion to star formation by collapse and fragmentation occurring in a relatively small (and overlapping) mass range. Although there are numerous problems to be resolved in the core accretion–gas capture picture, it is clearly the favored mechanism to explain (a) the Solar System, (b) the pulsar system PSR 1257 + 12, (c) extrasolar planetary systems with nearly circular orbits at distances >1 AU, such as 47 UMa and HD 28185, (d ) “hot” Jupiters such as 51 Peg b, and (e) systems with eccentric orbits and masses <5 MJ. In the case of systems of type c, d, and e additional dynamical processes are required, including tidal circularization, orbital migration, and excitation of eccentricity by planet-planet interaction (Lin & Bodenheimer, manuscript in preparation). In the sixth type of system, the isolated planetary-mass objects in young clusters, observations have not yielded a sufficient number of very faint objects to show a break in the mass distribution, which would be expected if two different formation mechanisms were at work. The available evidence is consistent with the hypothesis that these objects formed in the way that the other objects in that cluster (stars and brown dwarfs) did, namely by protostellar fragmentation. However, in view of the difficulties in forming isolated small fragments, it can also be hypothesized that the objects formed by accretion in a disk and were then ejected by planet-planet interactions at speeds less than the cluster escape speed. Provided that the gas-capture process can be shown to yield masses up to ≈10 MJ, there remain very few exceptions that do not easily fit into the scheme just outlined; the most difficult one is HD 168443c (Mp sin i = 17 MJ), which could be a brown dwarf captured into orbit at an early stage of its history. ACKNOWLEDGMENTS We thank G. Marcy, S. Vogt, D. Fischer, and R. Mardling for useful conversation. This research has been supported in part by the NSF through grants AST-9618548, AST-9714275, and AST-9987417; by NASA through grants NAG5-4277, NAG57515, and NAG5-9661; and a special NASA astrophysics theory program which supports a joint Center for Star Formation Studies at NASA-Ames Research Center, UC Berkeley, and UC Santa Cruz. 20 Mar 2002 7:46 144 AR AR154-05.tex BODENHEIMER ¥ AR154-05.SGM LaTeX2e(2001/05/10) P1: GKD LIN Visit the Annual Reviews home page at www.annualreviews.org LITERATURE CITED Adams FC, Benz W. 1992. 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Red curves refer to a planet forming at 5 AU in a disk with 6 Z = 10 g cm−2, approximately a factor of 3.3 above that in the MMSN, and with interstellar grain opacities. Blue curves refer to a model with the same parameters but in which the grain opacity is taken to be 2% of the interstellar values. Green curves have the same parameters as the blue ones except that 6 Z = 6 g cm−2. Courtesy Olenka Hubickyj. 30 Mar 2002 14:44 AR AR154-05-COLOR.tex AR154-05-COLOR.SGM LaTeX2e(2002/01/18) P1: GDL Figure 10 Luminosities as a function of time for the same models shown in Figure 9. The first peak in each case corresponds to the phase of rapid accretion of solids. The second peak corresponds to runaway accretion of gas. The final portion of the red curve refers to the beginning of the contraction and cooling phase at constant mass for a Jupiter-mass planet. Other curves end during the phase of rapid gas accretion. Courtesy Olenka Hubickyj.