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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
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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
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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
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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,
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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
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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.
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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,
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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
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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.
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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).
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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.
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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.
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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
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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
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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
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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
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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)
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PLANET FORMATION
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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
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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
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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
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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
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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.
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Visit the Annual Reviews home page at www.annualreviews.org
LITERATURE CITED
Adams FC, Benz W. 1992. In Complementary
Approaches to Double and Multiple Star Research, ed. HA McAlister, WI Hartkopf, pp.
185–94. San Francisco: Astron. Soc. Pac.
Adams FC, Lada CJ, Shu FH. 1987. Ap. J.
312:788–806
Adams FC, Lada CJ, Shu FH. 1988. Ap. J.
326:865–83
Adams FC, Ruden SP, Shu FH. 1989. Ap. J.
347:959–75
Artymowicz P. 1997. Annu. Rev. Earth Planet.
Sci. 25:175–219
Artymowicz P, Lubow SH. 1996. Ap. J.
467:L77–80
Artymowicz P, Lubow SH, Kley W. 1998. In
Planetary Systems—The Long View, ed. LM
Celnikier, J Tran Thanh Van, p. 381. Editions
Frontiéres
Baliunas SL, Henry GW, Donahue RA, Fekel
FC, Soon WH. 1997. Ap. J. 474:L119–22
Baraffe I, Chabrier G, Allard F, Hauschildt P.
1998. Astron. Astrophys. 337:403–12
Bate MR. 2000. MNRAS 314:33–53
Beckwith SVW. 1999. See Lada & Kylafis
1999, pp. 579–611
Beckwith SVW, Sargent AI. 1993. See Levy &
Lunine 1993, pp. 521–41
Beckwith SVW, Sargent AI, Chini RS, Güsten
R. 1990. Astron. J. 99:924–45
Béjar VJS, Martı́n EL, Zapatero Osorio MR,
Rebolo R, Barrado y Navascués D, et al.
2001. Ap. J. 556:830–36
Bell KR, Cassen PM, Klahr HH, Henning Th.
1997. Ap. J. 486:372–87
Bertout C. 1989. Annu. Rev. Astron. Astrophys.
27:351–95
Black DC. 1997. Ap. J. 490:L171–74
Bodenheimer P, Burkert A, Klein RI, Boss AP.
2000. See Mannings et al. 2000, pp. 675–701
Bodenheimer P, Grossman AS, DeCampli
WM, Marcy GW, Pollack JB. 1980. Icarus
41:293–308
Bodenheimer P, Hubickyj O, Lissauer JJ. 2000.
Icarus 143:2–14
Bodenheimer P, Lin DNC, Mardling RA. 2001.
Ap. J. 548:466–72
Bodenheimer P, Pollack JB. 1986. Icarus
67:391–408
Bonnell IA, Smith KW, Davies MB, Horne
K. 2001. MNRAS 322:859–65
Boss AP. 1997. Science 276:1836–39
Boss AP. 1998. Ap. J. 503:923–37
Boss AP. 2000. Ap. J. 536:L101–4
Briceno C, Vivas AC, Calvet N, Hartmann L,
Pacheco R, et al. 2001. Science 291:93–96
Brown TM, Charbonneau D, Gilliland RL,
Noyes RW, Burrows A. 2001. Ap. J.
552:699–709
Bryden G, Chen XM, Lin DNC, Nelson RP,
Papaloizou JCB. 1999. Ap. J. 514:344–67
Bryden G, Lin DNC, Ida S. 2000. Ap. J.
544:481–95
Burrows A, Guillot T, Hubbard WB, Marley
MS, Saumon D, et al. 2000. Ap. J. 534:L97–
100
Burrows A, Marley M, Hubbard WB, Lunine
JI, Guillot T, et al. 1997. Ap. J. 491:856–75
Burrows CJ, Stapelfeldt KR, Watson AM,
Krist JE, Ballester GE, et al. 1996. Ap. J.
473:437–51
Butler RP, Marcy GW. 1996. Ap. J. 464:L153–
56
Butler RP, Marcy GW, Fischer DA, Brown
TM, Contos AR, et al. 1999. Ap. J. 526:916–
27
Butler RP, Marcy GW, Williams E, Hauser H,
Shirts P. 1997. Ap. J. 474:L115–18
Cabrit S, Edwards S, Strom SE, Strom KM.
1990. Ap. J. 354:687–700
Calvet N, Hartmann L, Strom SE. 2000. See
Mannings et al. 2000, pp. 377–99
Cameron AGW. 1978. Moon Planets 18:5–40
Cameron AGW, DeCampli WM, Bodenheimer
P. 1982. Icarus 49:298– 312
Carr JS, Tokunaga AT, Najita J, Shu FH,
Glassgold AE. 1993. Ap. J. 411:L37–40
Chabrier G, Baraffe I, Allard F, Hauschildt P.
2000. Ap. J. 542:464–72
20 Mar 2002
7:46
AR
AR154-05.tex
AR154-05.SGM
LaTeX2e(2001/05/10)
P1: GKD
PLANET FORMATION
Chandler CJ, Carlstrom JE, Scoville NZ, Dent
WRF, Geballe TR. 1993. Ap. J. 412:L71–
74
Charbonneau D, Brown TM, Latham DW,
Mayor M. 2000. Ap. J. 529:L45–48
Chiang EI, Goldreich P. 1997. Ap. J. 490:368–
76
Ciecielag P, Plewa T, Rózyczka M. 2000. Astron. Nachr. 321:171–74
Cochran WD, Hatzes AP, Butler RP, Marcy
GW. 1997. Ap. J. 483:457–63
D’Antona F, Mazzitelli I. 1994. Ap. J. Suppl.
90:467–500
DeCampli WM, Cameron AGW. 1979. Icarus
38:367–91
Edwards S, Ray T, Mundt R. 1993. See Levy
& Lunine 1993, pp. 567– 602
Fischer DA, Marcy GW, Butler RP, Vogt SS,
Frink S, Apps K. 2001. Ap. J. 551:1107–18
Ford EB, Joshi KJ, Rasio FA, Zbarsky B.
2000. Ap. J. 528:336–50
Fuhrmann K, Pfeiffer M, Bernkopf J. 1997.
Astron. Astrophys. 326:1081–89
Fuhrmann K, Pfeiffer M, Bernkopf J. 1998.
Astron. Astrophys. 336:942–52
Gilliland RL, Brown TM, Guhathakurta P,
Sarajedini A, Milone EF, et al. 2000. Ap.
J. 545:L47–51
Goldreich P. 1965. MNRAS 130:159–81
Goldreich P, Soter S. 1966. Icarus 5:375–89
Goldreich P, Tremaine S. 1980. Ap. J. 241:425–
41
Gonzalez G. 1998. Astron. Astrophys. 334:221–
38
Gonzalez G, Laws C. 2000. Astron. J. 119:390–
96
Gonzalez G, Laws C, Tyagi S, Reddy BE.
2001. Astron. J. 121:432–52
Greenberg R, Wacker JF, Hartmann WK,
Chapman CR. 1978. Icarus 35:1–26
Greenzweig Y, Lissauer JJ. 1992. Icarus
100:440–63
Guillot T, Burrows A, Hubbard WB, Lunine
JI, Saumon D. 1996. Ap. J. 459:L35–38
Guillot T, Showman AP. 2001. Astron. Astrophys. In press
Haisch KE, Lada EA, Lada CJ. 2001. Ap. J.
553:L153–56
145
Hartigan P, Edwards S, Ghandour L. 1995. Ap.
J. 452:736–68
Hayashi C, Nakazawa K, Nakagawa Y. 1985.
In Protostars and Planets II, ed. DC Black,
MS Matthews, pp. 1100–53. Tucson: Univ.
Ariz. Press
Hayashi M, Ohashi N, Miyama SM. 1993. Ap.
J. 418:L71–74
Heacox WD. 1999. Ap. J. 526:928–36
Heap SR, Lindler DJ, Lanz TM, Cornett RH,
Hubeny I, et al. 2000. Ap. J. 539:435–44
Henry GW, Marcy GW, Butler RP, Vogt SS.
2000. Ap. J. 529:L41–44
Hillenbrand LA, Carpenter JM. 2000. Ap. J.
540:236–54
Holman M, Touma J, Tremaine S. 1997. Nature 386:254–56
Hubickyj O, Bodenheimer P, Lissauer JJ. 2001.
Icarus. Submitted
Jensen EL, Cohen DH, Neuhäuser R. 1998.
Astron. J. 116:414–23
Kalas P, Jewitt D. 1995. Astron. J. 110:794–804
Klahr H, Lin DNC. 2001. Ap. J. 554:1095–109
Kley W. 1999. MNRAS 303:696–710
Koerner DW, Sargent AI, Beckwith SVW.
1993. Icarus 106:2–10
Kuiper GP. 1951. In Astrophysics, ed. J Hynek,
pp. 357–424. New York: McGraw-Hill
Lada CJ. 1999. See Lada & Kylafis 1999, pp.
143–92
Lada CJ, Kylafis ND, eds. The Origin of Stars
and Planetary Systems. Dordrecht: Kluwer
Acad.
Lagage PO, Pantin E. 1994. Nature 369:628–
30
Lagrange A-M, Backman DE, Artymowicz P.
2000. See Mannings et al. 2000, pp. 639–72
Larwood JD, Kalas PG. 2001. MNRAS
323:402–16
Latham DW, Mazeh T, Stefanik RP, Mayor
M, Burki J. 1989. Nature 339:38–40
Laughlin G. 2001. Ap. J. In press
Laughlin G, Adams FC. 1997. Ap. J. 491:L51–
54
Laughlin G,
Adams FC. 1998. Ap. J.
508:L171–74
Laughlin G, Adams FC. 1999. Ap. J. 526:881–
89
20 Mar 2002
7:46
146
AR
AR154-05.tex
BODENHEIMER
¥
AR154-05.SGM
LaTeX2e(2001/05/10)
P1: GKD
LIN
Laughlin G, Bodenheimer P. 1994. Ap. J.
436:335–54
Laughlin G, Chambers JE. 2001. Ap. J.
551:L109–13
Laughlin G, Różyczka M. 1996. Ap. J.
456:279–91
Levison HF, Lissauer JJ, Duncan MJ. 1998.
Astron. J. 116:1998–2014
Levy EH, Lunine JI, eds. 1993. Protostars and
Planets III. Tucson: Univ. Ariz. Press
Lin DNC. 1997. In Accretion Phenomena and
Related Outflows, ed. L Ferrario, D Wickramasinghe, pp. 321–30. San Francisco: Astron. Soc. Pac.
Lin DNC, Bodenheimer P, Richardson DC.
1996. Nature 380:606–7
Lin DNC, Ida S. 1997. Ap. J. 477:781–91
Lin DNC, Laughlin G, Bodenheimer P,
Różyczka M. 1998. Science 281:2025–27
Lin DNC, Papaloizou JCB. 1980. MNRAS
191:37–48
Lin DNC, Papaloizou JCB. 1985. In Protostars
and Planets II, ed. DC Black, MS Matthews,
pp. 981–1072. Tucson: Univ. Ariz. Press
Lin DNC, Papaloizou JCB. 1986. Ap. J.
309:846–57
Lin DNC, Papaloizou JCB. 1993. See Levy &
Lunine 1993, pp. 749–835
Lin DNC, Papaloizou JCB, Terquem C, Bryden G, Ida S. 2000. See Mannings et al. 2000,
pp. 1111–34
Lin DNC, Woosley SE, Bodenheimer P. 1991.
Nature 353:827–29
Lissauer JJ. 1987. Icarus 69:249–65
Lissauer JJ. 1993. Annu. Rev. Astron. Astrophys.
31:129–74
Low C, Lynden-Bell D. 1976. MNRAS
176:367–90
Lowrance P, Becklin EE, Schneider G. 2001.
In Young Stars Near Earth, ed. R Jayawardhana, T Greene. San Francisco: Astron. Soc.
Pac. In press.
Lucas PW,
Roche PFA. 2000. MNRAS
314:858–64
Lunine JI, Owen TC, Brown RH. 2000. See
Mannings et al. 2000, pp. 1055–80
Lynden-Bell D, Pringle JE. 1974. MNRAS
168:603–37
Mannings V, Boss AP, Russell SS, eds. 2000.
Protostars and Planets IV. Tucson: Univ.
Ariz. Press
Marcy GW, Butler RP. 1995. Int. Astron. Union
Circ. No. 6251
Marcy GW, Butler RP. 1996. Ap. J. 464:L147–
51
Marcy GW, Butler RP. 1998. Annu. Rev. Astron.
Astrophys. 36:57–97
Marcy GW, Butler RP. 1999. See Lada & Kylafis 1999, pp. 681–708
Marcy GW, Butler RP. 2000. Publ. Astron. Soc.
Pac. 112:137–40
Marcy GW, Butler RP, Vogt SS, Fischer D,
Lissauer JJ. 1998. Ap. J. 505:L147–49
Marcy GW, Butler RP, Vogt SS, Fischer D,
Liu MC. 1999. Ap. J. 520:239–47
Marcy GW, Butler RP, Fischer D, Vogt
SS, Lissauer JJ, Rivera EJ. 2001a. Ap. J.
556:296–301
Marcy GW, Butler RP, Vogt SS, Liu MC,
Laughlin G, et al. 2001b. Ap. J. 555:418–25
Marcy GW, Cochran WD, Mayor M. 2000.
See Mannings et al. 2000, pp. 1285–311
Mayor M, Queloz D. 1995. Nature 378:355–59
Mazeh T, Krymolowski Y, Rosenfeld G. 1997.
Ap. J. 477:L103–6
Mazeh T, Zucker S. 2001. In The Formation
of Binary Stars, ed. H Zinnecker, R Mathieu,
pp. 519–28. San Francisco: Astron. Soc. Pac.
Mazeh T, Zucker S, Dalla Torre A, van
Leeuwen F. 1999. Ap. J. 522:L149–51
McCaughrean MJ, O’Dell CR. 1996. Astron.
J. 111:1977–86
Mizuno H. 1980. Prog. Theor. Phys. 64:544–57
Mouillet D, Larwood JD, Papaloizou JCB, Lagrange A-M. 1997. MNRAS 292:896–904
Najita JR, Tiede GP, Carr JS. 2000. Ap. J.
541:977–1003
Nelson RP, Papaloizou JCB, Masset F, Kley
W. 2000. MNRAS 318:18–36
Noyes RW, Jha S, Korzennik SG, Krockenberger M, Nisenson P, et al. 1997. Ap. J.
483:L111–14
O’Dell CR, Wen Z. 1994. Ap. J. 436:194–202
Papaloizou JCB, Terquem C. 1999. Ap. J.
521:823–38
Peale SJ. 1997. Icarus 127:269–89
20 Mar 2002
7:46
AR
AR154-05.tex
AR154-05.SGM
LaTeX2e(2001/05/10)
P1: GKD
PLANET FORMATION
Peale SJ. 2001. Ap. J. 552:889–911
Perri F, Cameron AGW. 1974. Icarus 22:416–
25
Perryman MAC. 2000. Rep. Prog. Phys. 63:
1209–72
Podsiadlowski P. 1993. In Planets Around Pulsars, ed. JA Phillips, SE Thorsett, SR Kulkarni, pp. 149–65. San Francisco: Astron.
Soc. Pac.
Pollack JB, Bodenheimer P. 1989. In Origin
and Evolution of Planetary and Satellite Atmospheres, ed. SK Atreya, JB Pollack, MS
Matthews, pp. 564–602. Tucson: Univ. Ariz.
Press
Pollack JB, Hubickyj O, Bodenheimer P, Lissauer JJ, Podolak M, Greenzweig Y. 1996.
Icarus 124:62–85
Rees MJ. 1976. MNRAS 176:483–86
Rivera EJ, Lissauer JJ. 2000. Ap. J. 530:454–63
Robberto M, Meyer MR, Natta A, Beckwith
SVW. 1999. In The Universe as Seen by ISO,
ed. P Cox, MF Kessler, p. 427. Garching bei
Muenchen: Eur. South. Obs.
Roddier C, Roddier F, Northcott MJ, Graves
JE, Jim K. 1996. Ap. J. 463:326–35
Rodriguez LF, D’Alessio P, Wilner DJ, Ho
PTP, Torrelles JM, et al. 1998. Nature
395:355–57
Ruden SP. 1999. See Lada & Kylafis, pp. 643–
80
Sackett PD. 2001. In Planetary Systems in the
Universe, Formation and Evolution, ed. AJ
Penny, P Artymowicz, A-M Lagrange, SS
Russell. San Francisco: Astron. Soc. Pac. In
press
Safronov VS. 1969. Evolution of the Protoplanetary Cloud and Formation of the Earth and
Planets. Moscow: Nauka
Santos NC, Israelian G, Mayor M. 2001. Astron. Astrophys. 373:1019–31
Sargent AI, Beckwith SVW. 1987. Ap. J.
323:294–305
Saumon D, Chabrier G, Van Horn HM. 1995.
Ap. J. Suppl. 99:713– 41
Shu FH, Najita J, Ostriker E, Wilkin F, Ruden
SP, Lizano S. 1994. Ap. J. 429:781–96
Slattery WL, DeCampli WM, Cameron AGW.
1980. Moon Planets 23:381–90
147
Smith BA, Terrile RJ. 1984. Science 226:1421–
24
Spangler C, Sargent AI, Silverstone MD,
Becklin EE, Zuckerman B. 2001. Ap. J.
555:932–44
Stepinski TF, Black DC. 2000. Astron. Astrophys. 356:903–12
Stepinski TF, Malhotra R, Black DC. 2000.
Ap. J. 545:1044–57
Stevenson DJ. 1982. Planet. Space Sci. 30:755–
64
Strom SE, Edwards S, Skrutskie MF. 1993.
See Levy & Lunine 1993, pp. 837–66
Supulver KD, Lin DNC. 2000. Icarus 146:525–
40
Takeuchi T, Artymowicz P. 2001. Ap. J.
557:990–1006
Tanga P, Babiano A, Dubrulle B, Provenzale
A. 1996. Icarus 121:158–70
Tamura T, Itoh Y, Oasa Y, Nakajima T. 1998.
Science 282:1095–97
Thi WF, Blake GA, van Dishoeck EF, van
Zadelhoff GJ, Horn JMM, et al. 2001. Nature 409:60–63
Thorsett SE, Arzoumanian Z, Camilo F, Lyne
AG. 1999. Ap. J. 523:763–70
Tomley L, Steiman-Cameron T, Cassen P.
1994. Ap. J. 422:850–61
Trilling DE, Benz W, Guillot T, Lunine
JI, Hubbard WB, Burrows A. 1998. Ap. J.
500:428–39
Ward WR. 1997. Icarus 126:261–81
Watkins SJ, Bhattal AS, Boffin HMJ, Francis
N, Whitworth AP. 1998. MNRAS 300:1214–
24
Weidenschilling SJ, Cuzzi JN. 1993. See Levy
& Lunine 1993, pp. 1031–60
Weidenschilling SJ, Spaute D, Davis DR,
Marzari F, Ohtsuki K. 1997. Icarus 128:429–
55
Weinberger AJ, Becklin EE, Schneider G,
Smith BA, Lowrance PJ, et al. 1999. Ap.
J. 525:L53–56
Weinberger AJ, Rich RM, Becklin EE, Zuckerman B, Matthews K. 2000. Ap. J. 544:937–
43
Wetherill GW. 1980. Annu. Rev. Astron. Astrophys. 18:77–113
20 Mar 2002
7:46
148
AR
AR154-05.tex
BODENHEIMER
¥
AR154-05.SGM
LaTeX2e(2001/05/10)
P1: GKD
LIN
Wilner DJ, Ho PTP, Kastner JH, Rodriguez
LF. 2000. Ap. J. 534:L101–4
Wolk SJ, Walter FM. 1996. Astron. J.
111:2066–76
Wolszczan A. 1994. Science 264:538–42
Wolszczan A, Frail DA. 1992. Nature 355:145–
47
Wuchterl G, Guillot T, Lissauer JJ. 2000. See
Mannings et al., pp. 1081–109
Zapatero Osorio MR, Béjar VJS, Martı́n EL,
Rebolo R, Barrado y Navascués D, et al.
2000. Science 290:103–7
Zuckerman B, Forveille T, Kastner JH. 1995.
Nature 373:494–96
30 Mar 2002
14:44
AR
AR154-05-COLOR.tex
AR154-05-COLOR.SGM
LaTeX2e(2002/01/18)
P1: GDL
Figure 9 Evolution of the mass of a forming planet, according to the model of core
accretion and gas capture (Hubickyj et al. 2001). Solid curves give the core mass, dotted
curves the envelope mass, and dash-dotted curves the total mass. 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.
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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.