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\chapter{12}% insert your chapter number here
\title[Outer Satellites and Trojans]
  {Jupiter's Outer Satellites and Trojans}
\author[Jewitt, Sheppard and Porco]
  {David C. Jewitt\\ 
 Institute for Astronomy, University of Hawaii
  \and
  Scott Sheppard\\
 Institute for Astronomy, University of Hawaii
  \and
  Carolyn Porco\\
  Southwest Research Institute
}

\begin{document}
\maketitle

\section{Introduction}

Jupiter's irregular satellites possess large, eccentric and highly
inclined orbits.  They are conventionally considered separately from
the temporarily captured satellites and the Trojans (the latter
co-orbiting the Sun leading and trailing Jupiter by 60 deg).  However,
there is reason to believe that objects in these three groups share
many similarities, both in terms of their physical properties and their
origins. Accordingly, in this review we jointly discuss the irregular
and temporary satellites and the Trojans.

In the modern view of the solar system, different
populations of small bodies can be traced back to their origin in the
protoplanetary disk of the Sun.  Most planetesimals that formed near
the orbits of the giant planets were promptly ejected from the
planetary region.  A small fraction of those ejected (perhaps 10\%)
remain bound to the Sun in the $\sim 10^5$ AU scale Oort Cloud which
provides a continuing source of the long-period comets.  Planetesimals
growing beyond Neptune were relatively undisturbed and their
descendants survive today in the Kuiper Belt.  The Kuiper Belt in turn
feeds the giant-planet crossing Centaurs, which are then converted by
planetary (largely Jovian) perturbations into Jupiter Family Comets
(JFCs; short-period comets which are strongly interacting with Jupiter,
formally those with Tisserand invariants $2 \leq T \leq 3$).  During
their interaction with Jupiter, the comets sometimes become temporarily
trapped. Main-belt asteroids near resonances with Jupiter can also be
excited into Jupiter-crossing orbits, and may contribute to the
populations of temporarily trapped objects.  Since there is currently
no effective source of energy dissipation, neither the temporary
satellites nor the Trojan librators can be captured as permanent
members of these populations.  Temporary members will be either flung
out of the Jovian system or impact the planet or one of the Galilean
satellites. However, at very early epochs, at the end of Jupiter's
$\leq 10^{6}$ to $\leq 10^{7}$ yr growth phase, several mechanisms
might have operated to permanently trap objects from these and other
reservoirs.  Therefore, populations which are not now interacting may
once have been so.  Given the dynamical interrelations (Figure 1), it
is to be expected that the physical and compositional natures of the
various bodies should be related. \\


-----------------------------------------------------------------------
Figure 1: Interrelations  among the populations considered in this
chapter.  Solid arrows denote established dynamical pathways.  At the
present epoch, in which sources of energy dissipation are essentially
absent, no known pathways (dashed lines) exist between the temporary
and permanent satellite and Trojan populations. Numbers in parentheses
indicate the approximate dynamical lifetimes of the different
populations. \\
----------------------------------------------------------------------- \\

The irregular satellite and the Trojan populations both became known
about 100 years ago from early photographic surveys.  The first
irregular satellite, JVI Himalia, was discovered photographically in
1904 (Perrine 1905).  Additional members have been slowly added to this
group throughout the 20th Century (Figure 2).  The photographic surveys
and the implied limits to completeness are well described in Kuiper
(1961), while a later photographic survey was reported by Kowal et al.
(1978).  A second wave of discovery, driven by the use of large format
charge-coupled devices (CCDs) to survey the near-Jupiter environment,
is underway.  The number of known irregular Jovian satellites 
jumped from 8 to 50 (as of April 2003) within the last 3 years
(Sheppard et al.  2001, 2002).  In this review, however, we confine our
attention to the 32 having well determined orbits.

The first Trojan, 588 Achilles, was recognized in 1906 in a separate
photographic observation by Max Wolf in Heidelberg (Wolf 1906).  Later
wide field photographic (van Houten et al. 1991) and CCD surveys have
further increased the sample.   The currently known Trojan population
exceeds 1200 (Figure 2). \\

-----------------------------------------------------------------------
Figure 2:  Known populations of the Jupiter irregular satellites (solid
line) and Trojans (dashed line) as a function of date.  Both
populations became known at the start of the 20th century, as a result
of the application of photographic imaging.  The surge in the known
populations towards the end of the century results from new imaging
surveys using wide-field charge-coupled devices. \\
-----------------------------------------------------------------------
\\

Information on the small objects in the Jupiter system has been
obtained almost entirely from ground-based observations.  The main
spacecraft observations include a series of Voyager 2 images of the
second largest outer irregular satellite, JVII Elara, and a series of
resolved images of the largest irregular, JVI Himalia, taken by the
Cassini cameras (Figure 3) during that spacecraft's Jupiter flyby in late
2000 (Porco et al.  2003).  The Trojans have yet to be
visited by any spacecraft. \\

-----------------------------------------------------------------------
Figure 3:  The disk of Himalia illuminated from the left at a phase
angle of 70 deg. and observed by the Cassini ISS over $\sim$4.5 hours.
One unprocessed image from each of four observation sequences is shown
in the top row. The observation times were (from left to right): 18
December 2000, 20:30 UTC, 22:00 UTC, 23:30, UTC, and 19 December 2000,
01:04. The bottom row shows the same data, but smoothed by bicubic
interpolation.  Figure from Porco et al (2003).

-----------------------------------------------------------------------
\\

Irregular satellites are known around the other gas giants.  Saturn,
Uranus and Neptune have 13, 6 and 4 (or 5, if Triton is so counted),
respectively (Kuiper 1961, Gladman et al. 2000, 2001, Holman et al.
2003).  A single Trojan (2001 QR322) has been detected in association
with Neptune and simulations suggest that such objects should be
dynamically stable on $10^7$ year timescales and longer around all four
giant planets (e.g. Holman and Wisdom 1993, Nesvorny and Dones 2002).
Another type of 1:1 resonance, in which the object librates around the
longitude of the associated planet, has also been found to be
long-lived at Uranus and Neptune but not at Jupiter or Saturn (Weigert,
Innanen and Mikkola 2000).  No such "quasi-satellites" have yet been
detected.

The irregular satellites have been previously reviewed by Cruikshank,
Degewij and Zellner (1982).  The Trojans were previously reviewed by
Shoemaker, Shoemaker and Wolfe (1989), while their physical properties
have been more recently discussed by Barucci et al. (2003).  The
temporary satellites have been recognized as a group for some decades
but have not been extensively discussed in the literature. They are
important both for the clues they provide about the dynamics of capture
and because we possess compelling examples of temporary satellites that
interact with the Jovian system in interesting ways (e.g. the
Jupiter-impacting comet D/Shoemaker-Levy 9: see chapter by Harrington
et al.). In this review, we discuss the nature of, origin of and
interrelations among this collection of bodies. \\


\section{The Irregular Satellites}

The irregular satellites of Jupiter occupy orbits that are large,
eccentric and highly inclined relative to those of the regular system
(the Galilean satellites and attendant small inner bodies: for the
latter, see the chapter by Burns et al.).   A majority of the known
examples are retrograde (inclination $i \geq$ 90 deg.; Table 1)
and they reach vast jovicentric distances (up to 474 $R_J$ (0.22 AU)
for the apojove of JXIX).  For comparison, Jupiter's region of
gravitational control extends out roughly to the edge of the Hill
sphere, of radius

\begin{equation}
r_H = a_J\left(\frac{m_J}{3(m_J + m_{\odot})}\right)^{1/3}
\end{equation}

where $a_J$ and $m_J$ are the orbital semi-major axis and the mass of
Jupiter, respectively, and $m_{\odot}$ is the mass of the Sun.  With
$m_J$/$m_{\odot} \sim 10^{-3}$ and $a_J$ = 5 AU, we obtain $r_H \sim$
0.35 AU (735 $R_J$), corresponding to an angular radius of 5 degrees
when viewed at opposition from the Earth.  The semi-major axes of the
known irregular satellites extend out to about 0.5 $r_H$ and, as of
January 2003, their total number stands at 50 (the 32 with
well-determined orbits are listed in Table 1).  However, this is a
strong lower limit to the intrinsic population because observational
coverage of the Hill Sphere is incomplete and because many smaller
irregulars remain undetected.  The fraction of the Hill sphere that has
been searched for Jovian satellites is a function of the survey
limiting magnitude.  For apparent V-band (0.55 $\mu$m) magnitude $m_V
\leq$ 20, the coverage is probably close to complete over the whole
Hill Sphere, although even this assertion is difficult to justify given
the lack of documentation regarding past satellite surveys,
particularly those conducted photographically.  In our own work, only
$\sim$ 25\% of the Hill Sphere has yet been examined to a limiting red
($0.65\mu$m wavelength) magnitude $m_R \sim$ 23.5.

For objects at Jupiter's distance and at opposition, $m_V$, and
diameter, $D$ [km], are approximately related through

\begin{equation}
m_V = 25.73 - 5log(D) - 2.5log\left[\frac{p_V}{0.04}\right]
\end{equation}

where $p_V$ is the V-band geometric albedo.  We take $p_V$ = 0.04
(Cruikshank 1977), which means that the deeper satellite surveys
(limiting magnitude $m_V \sim$ 23.5), can detect satellites of diameter
$\sim$ 2.8 km.  The largest irregular satellite, JVI Himalia, is
aspherical with an effective circular diameter of roughly 150 km
(Cruikshank 1977, Porco et al. 2003).  The smallest known irregular
satellites have effective diameters of order 2 km (Table 1).
Presumably, much smaller satellites exist: the timescales for orbit
decay by Poynting-Robertson and plasma drag exceed the age of the
solar system for diameters in excess of a few centimeters.

The irregular satellites are extremely susceptible to solar
perturbations, particularly when near apojove.  Large retrograde orbits
are more stable against these perturbations than prograde orbits (Henon
1970) consistent with the observation that the most distant satellites
are all retrograde.  This also suggests that the current satellites are
survivors of a once larger population that has been progressively
depleted due to dynamical instabilities.  Kozai (1962) considered the
effect of time-averaged solar perturbations on the motion of a
planetary satellite.   He found that the normal component of the
satellite angular momentum is conserved, such that variations in
eccentricity and inclination must be correlated.  Satellites which
develop high inclinations in response to external forcing also acquire
high eccentricities.  The resulting small perijove and apojove 
distances render these satellites susceptible to collision with Jupiter
or the Galilean satellites or, more usually, to escape from the Hill
sphere.  Long term ($10^9$ yr) integrations reveal a zone of depletion
at inclinations $55 \leq i \leq 130$ deg caused by solar and planetary
perturbations that drive the perijoves of satellites to small values
(Carruba et al 2002).  For a satellite with perijove inside the region
of the Galileans, the probability of collision per orbit is roughly
given by $P \sim (r_s/2R_s)^2$, where $r_s$ and $R_s$ are the Galilean
satellite physical radius and orbital radius, respectively.  Taking
Callisto as an example, with $r_s \sim$ 2400 km and $R_s \sim$ 23
$R_J$, we obtain $P \sim 5\times 10^{-7}$.  Highly eccentric satellite
orbits with periods $\tau \sim$ 1 yr would survive for only $\tau /P
\sim 2\times10^6$ yrs before colliding with or being scattered by the
Galileans.  For this reason, it is not surprising that the known
irregular satellites completely avoid the Galileans: the smallest
perijove is 80 $R_J$, for JXVIII.  The long term stability of orbits
exterior to the Galilean satellites but interior to the innermost known
irregulars has not been explored. In some models, this region would
have overlapped with the outer parts of the disk which seeded the
growth of the Galilean satellites.  Detection of surviving bodies here
would be particularly interesting.  \\

-----------------------------------------------------------------------
Figure 4: Orbital semi-major axis (in $R_J$) vs. eccentricity, for the
Jovian irregular satellites.  The symbols are coded for satellite size,
computed from assumed 0.04 albedos, as indicated. \\
----------------------------------------------------------------------- \\

The orbital elements of the irregular satellites are non-randomly
distributed.  We name the dynamical groups after the largest known
member of each (Sheppard and Jewitt 2003).  The Themisto (semimajor
axis $a \approx$ 105 $R_J$, inclination $i \approx$ 43 deg.) and
Himalia ($a \approx$ 160 $R_J$, $i \approx$ 28 deg) groups are prograde
(Table 1). Themisto is currently the only known member of the former
group, while five Himalias have been detected.  The many retrograde
satellites show evidence for division into at least three groups named
for Ananke ($a \approx$ 295 $R_J$, $i \approx$ 148 deg), Pasiphae ($a
\approx$ 325 $R_J$, $i \approx$ 152 deg) and Carme ($a \approx$ 325
$R_J$, $i \approx$ 165 deg, see Figures 4 and 5).   The satellites
within each group may be fragments produced by collisional shattering
of parent bodies (Kuiper 1956, Pollack, Burns and Tauber 1979).  If so,
the individual satellite clusters should be regarded as analogues of
the dynamical families found amongst the main-belt asteroids.  Many
properties of the asteroid families are still not well established but
it is instructive to attempt a comparison between them and the
irregular satellite groups.  The size distributions offer one basis for
comparison.

The size distributions of the asteroid families are sharply peaked,
with the largest bodies probably consisting of gravitationally reaccumulated
blocks produced after catastrophic failure of the target body (Michel
et al. 2001).  Very roughly, the size distributions can be represented
by differential power laws

\begin{equation}
n(r)dr = \Gamma r^{-q} dr
\end{equation}

in which $n(r)dr$ is the number of objects having radius between $r$
and $r+dr$ and $\Gamma$ and $q$ are constants.  The size distributions,
of both real dynamical families (Tanga et al. 1999) and numerical model
families (Michel et al. 2001), are compatible with $q \geq$ 3.  This
compares with the $q \sim$ 3 size distribution of the non-family
asteroids and the $q \sim$ 3.5 index produced by an equilibrium
cascade, in which particles are progressively shattered to smaller and
smaller fragments (Dohnanyi 1969).  \\

-----------------------------------------------------------------------
Figure 5: Orbital semi-major axis (in $R_J$) vs. inclination, for the
Jovian irregular satellites.  The symbols are coded for satellite size,
computed from assumed 0.04 albedos, as indicated. \\
------------------------------------------------------------------------ 
\\
Figure 6: Cumulative luminosity function of the irregular satellites.
Different symbols show the data and data corrected for survey
inefficiencies.  The straight line has a slope corresponding to a
$q$ = 2 power law.  \\

----------------------------------------------------------------------- \\

The irregular satellite cumulative luminosity function (number of
satellites brighter than a given apparent magnitude) is shown in Figure
6, based on our survey observations on Mauna Kea.  The satellites are
best fit by $q \sim$ 2 over the magnitude range $14 \leq m_R \leq 18.5$
(approximate diameter range $20 \leq D \leq 180$ km), while
asteroid-like size distributions steeper than $q =$ 3 are inconsistent
with the data.  This observation suggests that, if the irregular
satellites are members of collisionally produced families, some other
process has acted to modify the post-breakup size distribution (c.f.
Gehrels 1977).  One possibility is that the smaller irregular
satellites have been preferentially removed by gas drag in an early
extended Jovian atmosphere, as we discuss below.  The size distribution
at $m_R >$ 18.5 is less well determined.  Our best estimates of the
correction for survey sky-plane incompleteness suggest a depletion
relative to the $q$ = 2 distribution (Figure 6).  It is also true that
the mass within each of the five satellite groups is dominated by the
largest member.  In the context of collisional disruption this suggests
formation by impacts with energies barely above the disruption
threshhold, allowing gravitational reaccumulation of many fragments
into the largest object.

Physical observations provide a second basis for comparison of the
satellite groups with the asteroid families. As in the main belt, there
is hope that close examination of the fragments might provide a glimpse
of the interior structure of the parent body.  For example,
differentiated asteroids should, upon disruption, produce fragments
consisting of core (nickel-iron), mantle (olivine) and crustal
(silicate) materials.  The satellites, with their presumed rock-ice
composition, might fragment into low-density (icy) and high density
(rocky) components. These expectations in the main belt at first seemed
borne-out by colorimetric and spectroscopic data, but recent
measurements have shown that compositional differences among family
members are muted, and much smaller than the full compositional range
observed in the main belt.  Objects originally identified as metallic
core fragments, for instance, seem not to be metallic upon subsequent
examination (see discussion in Bus 1999).  The implications of this
observational result are not clear. \\


-----------------------------------------------------------------------
Figure 7:  Optical colors of the eight brightest irregular satellites,
from Rettig (2001). \\
-----------------------------------------------------------------------
\\

Evidence from physical observations of the satellites is limited.
The colors of the satellites range from neutral ($V-R \sim$ 0.35, the
color of the Sun on the Johnson-Kron-Cousins system) to moderately red
($V-R \sim$ 0.50, Luu 1991).  The satellites generally lack the ultra-red
material found on the Centaurs and Kuiper Belt Objects (Jewitt and Luu
2001, Jewitt 2002). In the optical, Rettig et al. (2001) and Grav et al.
(2003) find that the bright retrogrades are redder and less uniform in
color than the bright progrades (Figure 7).  This may be because the
retrograde objects belong to several discrete families, each with
different parents, whereas the measured prograde satellites are all
from the Himalia group and share a common parent.  Sykes et al. (2000)
used near infrared photometry to find that the retrograde satellites
(other than JXII Ananke) are systematically redder than the prograde
satellites and suggested that the retrogrades are fragments of a D-type
body while the progrades result from breakup of a C-type.   The available color
observations are consistent with the breakup of a single object of
internally uniform composition to form the prograde Himalia group (JVI,
JVII, JX and JXIII).  The wider dispersion among the colors of the
retrograde satellites may suggest more than one parent body, as
suggested in the scatter of the a-i and, to a lesser extent, a-e plots
(Figures 4 and 5).  The least arguable conclusion is that many more
observations are needed to define and interpret color systematics in
the irregular satellites.  \\

-----------------------------------------------------------------------
Figure 8: Time-resolved optical reflection spectra of JXII Ananke.  The
spectra have been carefully normalized to the spectrum of the Sun, and
are vertically offset from one another for clarity.  Each spectrum is
marked by the Universal Time and date on which it was taken.  Figure
provided by Jane Luu. \\
----------------------------------------------------------------------- \\

Jarvis et al. (2000) reported weak 0.7 $\mu m$ absorption in the
optical spectrum of JVI Himalia and attributed this to an $Fe^{2+}$ to
$Fe^{3+}$ transition in phyllosilicates.  This latter material is
typically produced by aqueous alteration, requiring the presence of
liquid water for an extended period of time.  The Jarvis et al. spectra
show an optically blue object from which spectral class $F$ is
assigned.  Since most $F$-types are found in the main belt, they
speculate that JVI Himalia is a captured main-belt object.  However,
the magnitude of the spectral slope in their data appears to vary from
night to night:  rotational modulation caused by compositional
variations is a possible explanation.  Their spectra appear
inconsistent with broadband (ECAS) photometry of Tholen and Zellner
1984.  The near infrared ($1.4 - 2.4 \mu m$) spectrum of JVI Himalia is
featureless and specifically lacking the $1.5 \mu m$ and $2.0 \mu m$
water ice bands (Geballe et al. 2002). A marginal detection of the
deeper $3\mu m$ water ice feature has been recently reported (Brown et
al.  2002).  The $1.4 \leq \lambda \leq 2.4 \mu m$ spectra of JVII
Elara and JVIII Pasiphae are featureless.  Small but probably
significant rotational variations in optical spectral gradient are seen
in JXII Ananke (Figure 8).

\subsection{Irregular Satellites of Other Planets}
Irregular satellites have also been detected at Saturn (13, the largest being
110 km radius Phoebe), Uranus (6)
and Neptune (5, including Triton) but are not known to be associated
with any of the (much less massive) Terrestrial planets.  At the vast
distances of the outer planets, only the larger irregulars can be
easily detected and the known populations are correspondingly smaller
and less well characterised than at Jupiter.  Conversely, it is easier
to search the entire Hill spheres of the more distant planets than at
Jupiter, so that meaningful estimates of population completeness are
possible.  Some properties are found in common with those of the Jovian
irregulars, including evidence for inclination clustering in the Saturn
and Uranus systems that is suggestive of an origin by fragmentation of
a small number of parent bodies (Gladman et al. 2001, Sheppard and
Jewitt 2003).

Their distended nature leaves the irregular satellite systems
susceptible not only to external perturbations from the Sun, but
potentially also from other heliocentric bodies.  Beauge et al. (2002)
have explored the interaction between the irregular satellites and the
circumsolar disk.  They find that the planetary migration inferred to
explain the population of Kuiper Belt Objects trapped in the $3:2$ mean
motion resonance with Neptune would have had a disruptive effect on the
irregulars of this planet and of Uranus.

\subsection{Origin of the Irregular Satellites}

No plausible models exist to explain the large, highly eccentric and
inclined (including retrograde) orbits of the irregular satellites by
accretion in a bound, circum-Jovian nebula.  Instead, the irregular
satellites must have been formed elsewhere and then captured by
Jupiter.  The existence of the dynamical groupings (Figures $4$ and
$5$) argues that the current satellites are fragments of precursor
objects (Kuiper 1956), but it is not clear whether fragmentation
occurred as part of the capture process, or was a product of later,
unrelated bombardment by the flux of interplanetary projectiles.
The latter seems more plausible given that the velocity dispersion
imparted to fragments by aerodynamic forces is small compared to the
escape velocity of satellites as large as Himalia or Pasiphae.

Jupiter can capture nearby objects by at least three mechanisms.  
Temporary libration point capture is possible when a body moving in
heliocentric orbit approaches Jupiter through its L1 Lagrangian point
at less than about 1\% of the orbital velocity of Jupiter (Heppenheimer
and Porco 1977).  In the absence of energy dissipation, the capture is fully
reversible and temporary satellites leak out through L1 after a small
number of orbits about the planet (Heppenheimer and Porco 1977, Benner
and McKinnon 1995).  For an object to be captured by a fixed-mass
Jupiter from heliocentric orbit requires the dissipation of energy.
Frictional dissipation in the extended envelope of proto-Jupiter has
been suggested (Heppenheimer and Porco 1977; Pollack, Burns and Tauber
1979), as has dissipation by collision with pre-existing satellites
near Jupiter (Columbo and Franklin 1971).   Regardless of the specific
form of the dissipation, the capture of the irregular satellites must
have occurred very early:  Jupiter's extended gas envelope collapsed
within the first million years after formation while the density of
planetesimals near Jupiter was high enough for collisions to be
probable only during the planet formation phase (perhaps lasting a few
million years after Jupiter's envelope collapse).

The lifetime of a satellite orbiting within a gas of density $\rho$
[$kg~m^{-3}$] is roughly given by the time needed for the satellite to
intercept its own mass in gas.  For a spherical satellite of diameter
$D$, neglecting numerical factors of order unity the gas drag lifetime,
$\tau_d$, is given by

\begin{equation}
\tau_d \approx \left(\frac{\rho_s}{\rho}\right)\left(\frac{D}{C_d \Delta V}\right)
\end{equation}

where $\rho_s$ is the density of the satellite, $C_d \sim$ 1 is the
drag coefficient, and $\Delta V$ is the relative velocity of the
satellite through the gas.   Objects larger than a critical maximum
size cannot be significantly retarded by drag within the lifetime of
the gas envelope.  Conversely, objects smaller than a certain minimum
size can be stopped by gas drag: their fate is to spiral out of orbit
into the body of the planet (Pollack et al. 1979). Indeed, gas drag has
been suggested as a mechanism by which the ice giant planets Uranus and
Neptune might have accreted much faster than otherwise possible
(Brunini and Melita 2002). Gas drag sufficient to enable capture could
also lead to modification of the size distribution of the fragments
between these extremes, reducing the power law index and truncating the
size distribution below a critical diameter.   An observational
assessment of the minimum satellite size has yet to be made, but the
shallow size distribution is at least qualitatively consistent with the
action of gas drag.  Friction from gas drag should also lead to orbit
circularization, on a timescale given by Eq. (4).  Figure 4 shows that
the largest satellites in each group have eccentricities higher than
the respective mean eccentricities of the smaller members,
qualitatively consistent with the action of drag, but the effect is
not statistically significant.

Another form of capture of bodies from adjacent heliocentric orbits
could occur if Jupiter's mass were to suddenly increase (or,
equivalently, the Sun's mass were to suddenly decrease) by a large
factor, leading to rapid expansion of the Hill sphere (Eq. (1),
Heppenheimer and Porco 1977).  This so-called "pull-down" capture,
which favors retrograde satellites, requires the mass to change on
timescales comparable to the crossing time of the Hill sphere, perhaps
only a few years.  Unlikely as this seems, some models of Jupiter's
formation indeed predict very rapid mass growth.  Provided mass is
added isotropically to Jupiter, the change in the satellite orbit
radius, $a$, is given by (Jeans 1961)

\begin{equation}
a(m_J + m) = C
\end{equation}

where $m$ is the satellite mass and $C$ is a constant.  Depending on
the exact timing of capture relative to Jupiter's exponential growth,
it is clear from Eq. (5) that satellite orbits could be reduced in size
by a considerable factor, leading to permanent capture.  One appeal of
"pull-down" capture is that the same mechanism might also stabilise the
Trojans at $L4$ and $L5$, as we later discuss.  One potential problem
with "pull-down" is that Jupiter formation might occur so rapidly that
no macroscopic bodies would have time to grow before Jupiter reached
full mass.  Proto-gas-giant clumps in the disk instability model of
Boss (2001), for instance, have free fall times of 1 yr, too short for
solid bodies to grow to 100 km scale through collisional
agglomeration.   This would be less a problem if Jupiter grew by the
slower core accretion process, in which the heavy-element core grows
slowly (on $10^6$ to $10^7$ yr timescales) followed by a rapid growth to full
mass from capture of nebular gas.  In this case, the irregular
satellites and the Trojans could be nearby solid bodies that escaped
incorporation into the core and were later trapped by the envelope.
Still another possibility is that the satellites were captured through
a hybrid process: Lagrange point capture attended by Jupiter mass
growth coupled with dissipation due to remnant planetary gas.  Lastly,
the data do not preclude the possibility that different satellites were
captured through different processes.  For example, the prograde
satellites could have been trapped by libration-point capture and weak
gas drag and the retrogrades by pull-down capture attended by both
mass-growth and nebular drag.  The problem of the origin of the
irregulars is severely under-constrained.

The action of (weak) gas drag on the post-fragmentation
satellites is consistent with the finding that some of these objects
occupy resonances.  In a $10^5$ yr numerical integration of the motions
of the satellites, Whipple and Shelus (1993) found a resonance between
the longitude of perijove of JVIII Pasiphae and the longitude of
perihelion of Jupiter, with a libration period of 13,500 years.  JIX
Sinope also locks intermittently in this same resonance and is
additionally trapped in a 1:6 mean motion resonance (Saha and Tremaine
1993).  The resonances, which act to protect the satellites from solar
perturbations, occupy a small fraction of phase space suggesting
that they are not populated by chance.   Weak gas drag would drive slow
orbital decay and allow trapping of some of the satellites in
resonances, as is observed.  Note that the required weak gas drag is qualitatively
different from the strong gas drag invoked above to explain capture.
Orbital evolution under the latter proceeds too rapidly for resonance
trapping to occur.  Weak drag could result from a tenuous gas
atmosphere persisting after the hydrodynamic collapse of the planet.
Capture into resonance could also be driven by late-stage, slow mass
growth of Jupiter, with or without the assistance of weak drag (Saha
and Tremaine 1993).  Recent numerical orbital integrations (R.
Jacobson, personal communication) suggest that one of the new jovian
satellites, 2001J10, is a Kozai resonator.  Its inclination, 145.8 deg,
falls within the stable zone below the critical value of about 147
degrees found for the jovian retrograde group in numerical simulations
(V. Carruba and M. Cuk, private communication).

In any case, given that capture after the formation epoch is
unlikely, the existence of the irregular satellites and Trojans implies
that sufficient time elapsed for 100 km and larger solid bodies to grow
in the solar nebula near proto-Jupiter's orbit.  This fits naturally
with the "standard" model of gas giant planet formation, in which a
rock/ice core grows to 5 - 10 $M_{\oplus}$ on timescales $\sim10^7$ yr
before precipitating gravitational instability and collapse of the
surrounding gas nebula (Pollack et al.  1996).  In this scenario, the
irregular satellites and Trojans are pre-Jovian planetesimals that
escaped both incorporation into the body of Jupiter and ejection from
the solar system by gravitational slingshot.  Compositionally, they
must be related to Jupiter's high molecular weight core but may be
partially devolatilized by their continued exposure to the Sun.  As
remarked by Boss (2001) and others, the standard model has difficulty
in forming Jupiter in the $\sim10^6$ yr lifetime of the protoplanetary
gas.  Instead, Jupiter might have grown by coreless spontaneous gravitational
collapse of the protoplanetary nebula on timescales possibly only $\sim
10^3$ yr (Boss 2001).   It is hard to see how these models allow 
100 km scale solid bodies, like those present in the irregular satellite
and Trojan populations, to form fast enough to then be captured. \\

\subsection{Collisional Lifetimes}
The estimated collisional lifetimes of the irregular satellites in
their present orbits are very long.  As a result of their small size
and large orbital separation, the timescale for satellite-satellite
collisions is comparable to or longer than the age of the solar system
(Kessler 1981).  Collisions between the irregular satellites and
short-period comets are also exceedingly rare.  Statistically, there
should have been no impacts of kilometer sized cometary nuclei with any
of the irregular satellites in the entire age of the solar system
(Nakamura and Yoshikawa 1995).  These authors calculate that, if the
cometary size distribution measured at diameters $>$ 1 km can be
extrapolated to diameters $\ll$ 1 km, only $\sim$ 1 collision will have
occurred with a 70 meter or larger diameter nucleus, in the past 4.6
Gyr.  Even allowing that this calculation is intrinsically uncertain,
perhaps by an order of magnitude in impact flux, it is clear that the
collisional lifetimes of the irregular satellites to cometary impact
are very long.  The existence of the dynamical groups (Figures $4$ and
$5$) therefore implies that the fragmentation occurred early, either as part of
the capture process or soon after it when the interplanetary projectile
flux was many orders of magnitude higher than now. 

Evidence for an on-going but very low rate of collisional production of
dust from the satellites has been identified in data from the Galileo
spacecraft impact detector by Krivov et al.  2002 (see also chapter by
Kruger et al).  They find prograde and retrograde micron-sized grains
in the 50 $R_J$ to 300 $R_J$ radius range and suggest an origin by
erosion of the satellites by the fluxes of interplanetary and
interstellar dust.  This dust orbits largely outside Jupiter's
magnetosphere and so is dynamically influenced mostly by gravity (from
Jupiter and the Sun) and radiation forces.  The number density (10
$km^{-3}$) is about 10 times the value in the local interplanetary
medium, but far too small to permit optical detection.


\section{The Temporary Satellites}
Backwards numerical integrations of the motions of Jupiter-family
comets show frequent involvement with, and occasional temporary
captures by, Jupiter (Carusi and Valsecchi 1979, Carusi et al. 1985).
For example, comets P/Gehrels 3, P/Oterma and P/Helin-Roman-Crockett
have recently been trapped as temporary satellites while
P/Smirnova-Chernykh, P/Gehrels 3 and P/Helin-Roman-Crockett are
expected to become temporary satellites in the next century (Tancredi,
Lindgren and Rickman 1990).

The most famous example of a temporarily captured object is
D/Shoemaker-Levy 9 (hereafter SL9), which was a short-lived companion
to the planet for several decades to a century before its demise in
1994 (Benner and McKinnon 1995, Kary and Dones 1996).  If it had not
collided with the planet, SL9 would have been eventually ejected by
Jupiter, either to leave the solar system completely or to circulate
amongst the planets as a short-period comet (or peculiar asteroid,
depending on its volatile content).

In fact, comet P/Brooks 2 provides an excellent 19th Century example of
a comet meeting the latter fate.  It passed within 2$R_J$ of Jupiter in July
1886 and, like SL9, was apparently tidally disrupted as a result
(Sekanina and Yeomans 1985).  The perihelion distance decreased from
5.45 AU before encounter to 1.94 AU afterwards.  P/Brooks 2 was
discovered 3 years after breakup as a multiple object, with up to 9
distinct components being reported.  One fragment, perhaps $\sim$ 0.8
km in diameter, survives to this day (Sekanina and Yeomans 1985).

These examples of temporary capture show the intimate involvement
between Jupiter and the minor bodies of the solar system.  We may thus
envision a loose swarm of temporarily captured satellites in orbit
about Jupiter. This swarm is distinct from the permanently captured
irregulars in that its members change from decade to decade.  A small
steady-state population probably exists.  The best empirical
limits to this swarm (fewer than 210 members larger than 16 km in
diameter) are not very tight and should be improved (Lindgren et al.
1996).

Object SL9 (Figure 9) is the best studied temporary satellite and
merits special discussion here.   The object was discovered in March
1993, after being broken up in July 1992 by tidal stresses induced in a
close pass by Jupiter.   Soon after discovery, the orbit was found to have
perijove inside the body of the planet and a collision was accurately
forecast.  The longer-term motion of SL9 was highly chaotic (Lyapunov
exponent $\gamma$ = 0.1 $yr^{-1}$, Benner and McKinnon 1995),
preventing meaningful backwards integrations beyond $\sim$10 yrs before
discovery.  However, a consideration of the statistical nature of the
orbits suggests that SL9 may have been orbiting Jupiter for up to 100 yrs
prior to discovery (Benner and McKinnon 1995; Kary and Dones 1996).
That it had escaped detection for so long demonstrates our lack of
knowledge of the interloper population.   Presumably, had it not broken
up and consequently brightened by factors of hundreds due to the
release of dust, SL9 would have remained undiscovered.   \\

-----------------------------------------------------------------------
Figure 9: Comet D/Shoemaker-Levy 9, a temporary satellite of Jupiter,
imaged on 17 May 1994 about 22 months after breakup and 2 months prior
to impact with Jupiter.  The string of fragments was at this time about
$1.2 \times 10^6$ km ($17~R_J$) in length.  Image from Weaver et al.
1995. \\
----------------------------------------------------------------------- \\

Dynamical chaos makes it impossible to decide whether the pre-capture
SL9 was a Jupiter-family comet, a Centaur or (less likely) a Trojan or
a main-belt asteroid.  Spectral observations showed no gas in SL9,
giving rise to speculation that it might have been an escaped
asteroid.  However, at heliocentric distances $R >$ 5 AU, many comets
appear devoid of coma and emit no measurable gas so these observations
cannot be uniquely interpreted as showing an asteroidal nature.
Substantial dust comae were observed around each of the fragments in
SL9, however.  In active comets, dust is expelled against nucleus
gravity by drag forces due to gas released by sublimating ice.  In SL9,
in contrast, the bulk of the dust was produced by the break-up of the
nucleus, and the comet as a whole underwent substantial fading with
time, as the dust dissipated into circum-Jovian space (Jewitt
1995).  Perhaps the best evidence for low-level outgassing (at $\sim$
22 $kg~s^{-1}$) is provided indirectly by the sustained circularity of
the inner isophotes of the comae (Rettig and Hahn 1997).   In the
absence of resupply, these isophotes would become stretched by
radiation pressure distortion and Keplerian shear.

The break-up of the nucleus by the small stresses induced by perijoval
tides indicates that the nucleus must be weak (in tension).  Models of
gravitationally bound aggregates convincingly fit the astrometric data
and suggest a parent body diameter $D \sim$ 1.5 km and density $\rho
\sim$ 500 $kg~m^{-3}$ (Asphaug and Benz 1996).  A globally weak
structure could result from internal fractures produced by collisions
or, in the cometary context, could result from agglomeration of
constituent planetesimals (Weidenschilling 1997).  Again, no definitive
conclusions about the nature and origin of SL9 are possible based on
photometric or spectroscopic observations but the data and model results are
compatible with its being a cometary nucleus or small Centaur.  \\

-----------------------------------------------------------------------
Figure 10: Impacts of SL9 on Jupiter taken UT 1994 Jul 21 at 06:50:03
at $2.3 \mu m$ wavelength, where the disk of the planet appears dark due to
strong methane absorption in the atmosphere.  The bright object to the
upper left is Io.  The impact sites appear bright because they scatter
sunlight at high altitudes above the methane.\\
----------------------------------------------------------------------- \\

The rate of impact of similarly sized bodies into Jupiter is uncertain,
but can be estimated in several ways.  The average time between
collisions, $T_c$, obtained by integration of the motions of the known
short-period comets is $T_c \sim$ 950 yrs (Nakamura and Yoshikawa
1995).  A similar exercise using a larger number of test particles to
more fully sample the parameter space and correct for observational
bias gives $30 \leq T_c \leq 500$ yrs for 1km nuclei, with a most
probable value $T_c$ = 240 yrs (Kary and Dones 1996).  

Observations provide an independent estimate of the impact frequency.
A search through the observational records for Jovian cloud markings
that might be impact debris clouds (see Figure 10) has produced some
interesting but not wholly convincing candidates (Hockey 1996).  One of
the most believable was recorded by the Italian-French astronomer
Cassini in 1690 (Tabe, Watanabe and Jimbo 1997).  It was observed over
an 18 day period, during which its morphology evolved from round to
elongated in a fashion consistent with stretching by the known zonal
wind shear.  The size of the feature suggests an impactor mass like
that of SL9.  If this is indeed an impact scar, an interval of $T_c
\sim$ 300 yrs for $\sim$km sized comets is indicated.  \\

-----------------------------------------------------------------------
Figure 11: Number of comets within a given perijove in the last 250
years, adapted from Kevin Zahnle (private communication). The orbits of
Io and Europa are marked. \\
----------------------------------------------------------------------- \\

The impact timescale can also be observationally estimated from the
number of close involvements between comets and Jupiter in modern
history.  Altogether, 5 cometary approaches to Jupiter with perijove
distance $q_J \leq 3R_J$ have been recorded in the past 250 years
(Zahnle, Dones and Levison 1998).  Given that the number distribution
of perijove distances is uniform in $q_J$, (i.e. the cumulative
number of comets with $q_J \leq q$ is proportional to $q$, see Figure
11) this allows an estimate of the number of impacts with the planet.
If 5 comets approach to within 3 $R_J$ in 250 years, then the number
reaching 1 $R_J$ is 5/3 in 250 years, or a characteristic timescale
between impacts of 150 years.  This is an upper limit to the true
timescale because only a fraction of the comets involved are likely to
have been subsequently detected.  In particular, comets scattered
outwards by Jupiter are far less likely to be detected than those
scattered towards the Sun.  At face value, this effect alone would
require an increase of the impact flux by a factor of two, and a
reduction of the impact timescale to only 75 years. \\

-----------------------------------------------------------------------
Figure 12:  Enki Catena on Ganymede, a $\sim$150 km long chain of 13
craters thought to have been produced by the impact of a tidally split
comet.  Galileo image courtesy NASA. \\
----------------------------------------------------------------------- \\

Distinctive crater chains on the Galilean satellites Ganymede and
Callisto provide still another constraint (Figure 12).  Based on their
peculiar morphology, these chains have been attributed to impacts by
recently disrupted nuclei (Melosh and Schenk 1993).  The limited range
of lengths of the crater chains, from $\sim$60~km to $\sim$600 km
(Schenk et al.  1996), restricts the interval between break-up and
impact, basically requiring impact on the outbound leg of the orbit
immediately following break-up.  The fraction of disrupted comets that
strike a satellite of radius $r_s$ moving in an orbit of radius $R_s$
is given, to within geometric factors near unity, by $(r_s/2R_s)^2$.  The
rate of formation of crater chains thus provides a direct measure of
the rate of disruption of nuclei, which should be interpreted as the
number of comets passing per unit time within the effective Roche
radius ($\sim$2 $R_J$) of Jupiter's center.  In this way, Schenk et al.
(1996) find a mean disruption interval $\sim$ 550$\pm$225 yrs for
comets with diameters $D \geq$ 2 km.  Scaling for perijove distance (as
$1/q_J$) and nucleus size (assuming a $d^{-2}$ power law for the
cumulative distribution of nucleus diameters) gives a mean interval for
impacts of $D \geq$ 1 km nuclei into Jupiter $T_c \approx$ 140 $\pm$ 60
yrs.  The principal uncertainties in this estimate include the
unmeasured ages of the surfaces of Ganymede and Callisto (assumed,
based on crater counts, to be 4 Gyr and 3.5 Gyr, respectively), and the
scaling from crater chain dimensions to projectile size.    Given that
many of the numbers used in this calculation (e.g. the surface ages)
are little more than guesses, it is remarkable that the timescale
derived from the crater chains bears any resemblance to the timescale
deduced by other methods:  indeed, this is probably the most compelling
evidence for the correctness of the crater chain formation model.

A reasonable conclusion from these estimates would be that kilometer
sized comets strike Jupiter once every century.   The corresponding
average mass flux into the atmosphere is $dM/dt \sim$ 1000 $kg~s^{-1}$
($10^{-14}$ $kg~m^{-2}~s^{-1}$), most of this in oxygen, silicon,
carbon and heavier elements.  The upper atmospheres of
Jupiter (Lellouch et al 2002) and the other gas giant planets
(Feuchtgruber et al. 1997) are known to contain $H_2O$, $CO_2$ and $CO$
delivered from external sources.  In Jupiter, the total mass flux from
all sources needed to explain the upper atmospheric abundances of these
oxygen bearing molecules is $dM/dt \sim$ 200 $kg~s^{-1}$ ($3 \times
10^{-15}~kg~m^{-2}~s^{-1}$) (Lellouch et al 2002 and see the chapter
by Moses et al.).  This is in good agreement with the flux estimated
from SL9 type impactors, and suggests that comets are likely to be
major contributors to this oxygen flux in the stratosphere.  

Deeper in the atmosphere, a factor of $2$ to $4$ overabundance of
metals relative to hydrogen has been recorded in Jupiter by the Galileo
probe (Owen et al. 1999).  When integrated over the 4.6 Gyr age of the
solar system, the total mass delivered by comets is only
$10^{-5}~M_{\oplus}$.  This is far too small to account for the
measured overabundance in the deep atmosphere and a different source
must be invoked.

Temporary captures of comets can also occur at the major mean motion
resonances.  For example, comets P/Whipple and P/Russell 3 recently
occupied horseshoe orbits in 1:1 resonance with Jupiter, while
P/Kowal-Vavrova was similarly trapped at the 4:3 resonance (Carusi et
al. 1985).   Knowledge of these captures has given rise to the idea
that the Trojans, or some fraction of the Trojans, might consist of
captured comets.  \\

\section{The Jovian Trojans}
The leading (L4) and trailing (L5) Trojans share Jupiter's semi-major
axis but are separated from Jupiter by about 60 degrees in orbital
longitude (Figure 13).  In the idealised planar, restricted three body
(Sun-Jupiter-Trojan) approximation, these objects exhibit simple
harmonic motion around the L4 and L5 Lagrangian points, described by

\begin{equation}
\frac{d^2\phi}{dt^2} + \left(\frac{27}{4}\right)\mu n_J^2\phi = 0
\end{equation}

where $\phi$ is the angular separation between the Trojan and the
relevant Lagrangian point, $t$ is time, $\mu$ is approximately the
ratio of Jupiter's mass to that of the Sun and $n_J$ is the mean motion
($yr^{-1}$) of Jupiter.  This has the solution

\begin{equation}
\phi = \frac{A}{2}cos(\omega t + B)
\end{equation}

with $A$ and $B$ constants representing the amplitude and phase of
the motion and angular frequency given by

\begin{equation}
\omega = \left(\frac{27}{4}\mu\right)^{1/2} n_J
\end{equation}

With $\mu \sim$ 0.001, $n_J \sim$ 0.52 $yr^{-1}$, Equation (8) gives
$\omega \sim$ 0.043 $yr^{-1}$, corresponding to a characteristic
libration period $2\pi/\omega \sim$ 150 yrs.  The libration amplitudes
of the various Trojans, $A$, are spread over a wide range with a mean
near 30 deg. (Shoemaker et al. 1989, Milani 1993).

The known Trojans have been discovered in a variety of wide-field and
other surveys.  Unfortunately, many of these surveys are not well
characterized in terms of areal extent and sensitivity; some even
remain unpublished.  For this reason, it is difficult to reliably
reconstruct the intrinsic size and orbital element distributions from
the apparent distributions (which are affected by observational
selection).   Therefore, the intrinsic properties of the Trojans as a
group are less well known than might be expected from the size of the
Trojan sample. \\


-----------------------------------------------------------------------
Figure 13:  Plan view of the Jovian Trojans at epoch UT 2002 Jan 01.
All numbered objects in the L4 (leading) and L5 (trailing) clouds are
shown.  The locations of L4 and L5 are marked, as is the orbit of
Jupiter.  A dashed circle shows the Hill sphere of Jupiter, to scale.
\\
-----------------------------------------------------------------------
\\

A classic example is provided by the relative numbers of L4 and L5
Trojans, which are often reported as $N4 > N5$ (e.g. Fleming and
Hamilton 2000).  It is true that, as of mid-1988, 105 of the known
Trojans were in the L4 cloud while only 52 were in the L5 cloud ($N4/N5
\sim 2$; Shoemaker, Shoemaker and Wolf 1989) while a synthesis of
Palomar Schmidt survey data suggested to van Houten et al. (1991) that
$N4/N5 = 2$.  However, as of February 2002, the IAU has assigned
numbers (indicating that the orbits are confidently known) to 530
Trojans and lists another 685 Trojans that have been less well
observed.  The ratio of the numbers in the two clouds is $N4/N5 =
696/519 \sim 1.3$.  The Trojan population is probably completely known
for absolute magnitudes $H_V <$ 9.0 to 9.5 (Jewitt, Trujillo and Luu
2000), corresponding to diameters $D \sim$ 84 to 105 km.  The
population ratios at these limiting magnitudes are $N4/N5 = 14/13 \sim
1$ and $N4/N5 = 41/28 \sim 1.4$, respectively.  Given that the best
characterized (brightest) Trojans show the smallest deviations of
$N4/N5$ from unity, it is reasonable to suppose that the larger values
of this ratio are produced by observational bias in favor of one cloud
over the other.  Such a bias could result from unequal observational
coverage of the $L4$ and $L5$ clouds, perhaps due to their placement
with respect to the Milky Way, making the detection of faint Trojans
more difficult in one cloud than in the other.  A careful experiment to
determine $N4/N5$ free of the effects of observational bias has yet to
be reported and is urgently needed.

The differential size distribution of the L4 Trojans is given by

\begin{equation}
n_1(r)dr = 1.5\times10^6 r^{-3.0\pm0.3}dr
\end{equation}

for $2.2 \leq r \leq 20$ km and

\begin{equation}
n_2(r)dr = 3.5\times10^9 r^{-5.5\pm0.9}dr
\end{equation}

for $r \geq 42$ km, where $r$ is the radius computed on the assumption
that the albedo is $p_R =$ 0.04 (Jewitt, Trujillo and Luu 2000).  A
smooth interpolation is presumed to exist in the radius range $20 \leq
r \leq 42$ km.  Integration of these equations gives the total
population of Trojans with $r \geq$ 1 km as N(1km) $\sim$ $1.6 \times
10^5$.  The number of main-belt asteroids with radius $r \geq$ 1 km is
about $2.7 \times10^5$ (Ivezic et al. 2001), showing that the two populations
are of the same order (c.f. Shoemaker et al. 1989).   The break in the
Trojan size distribution may indicate that the smaller objects (Eq. (9))
are collisionally produced fragments of a parent population whose size
distribution is given by Eq (10). Observational incompleteness at the
$1$ km scale is extreme: $>$ 99 \% of these objects remain
unobserved.\\

\subsection{Binaries}
One Trojan (617 Patroclus) has been found to be double (Merline et al.
2001) with the two components differing in brightness by only 0.2 mag
(Figure 14).  Based on a nominal 0.05 albedo, the primary and secondary
have diameters 105 km and 95 km, respectively.  The maximum projected
separation reported to date is 0.21 arcsec, corresponding to $\sim$650
km.  For comparison, the radius of the Hill sphere of the primary
(assuming density 1000 $kg~m^{-3}$) is 35,000 km showing that the
Patroclus binary is very tightly bound.  The origin of the binary is
unclear.  Numerical simulations of collisional disruption using N-body
codes do produce satellites, but not (so far) with mass ratios near
unity (Michel et al.  2001).  Determination of the orbit will, through
Kepler's Law, yield the binary mass.  If the sizes of the components
can then be accurately measured, the physically more interesting mean
density could also be found.   The fraction of binary Trojans has not
been measured but the identification of even one such object amongst
the few surveyed at sufficiently high angular resolution implies that
the fraction may be large.  In this regard, it has been suggested that
large object 624 Hektor could be a contact binary (Hartmann and
Cruikshank 1978).  Careful measurement of the number and properties of
binaries among the Trojans will place strong constraints on the
time-integrated collisional environment and on the formation process.
\\

-----------------------------------------------------------------------
Figure 14: H band ($1.6~\mu m$) image of Trojan 617 Patroclus taken
2001 October 13 by W. Merline et al and showing the two components
separated by 0.12 arcsec.  Image acquired
using the Gemini North Telescope and the Hokupa�a University of Hawaii
adaptive optics system.\\
----------------------------------------------------------------------- \\

\subsection{Families}
The search for dynamical families among the Trojans is more difficult
than in the main asteroid belt.  This is because the velocity
dispersion is similar to that among the asteroids while the available
orbital element phase space is considerably smaller.  Families are thus
proportionally more dispersed over the available phase space and so are
more difficult to identify against the background of unrelated objects.
In the limiting case, catastrophic collisions between Trojans can
impart velocities that carry family members out of the Lagrangian
populations.

Despite these difficulties, about a dozen dynamical families have been
reported (Shoemaker et al 1989, Milani 1993).  Perhaps the most
convincing are those with the smallest relative velocities between the
components and which were found by both Shoemaker et al (1989) and
Milani (1993).  These include the pairs 1583 Antilochus, 3801
Thrasymedes and 1437 Diomedes, 2920 Automedon, which have relative
velocities of a few $\times 10$ m $s^{-1}$.  On physical grounds, the
velocity dispersion should be comparable to the escape velocity from
the largest fragment in each collision, as is the case for these
pairs.

The reported Trojan families are also much smaller, in terms of numbers
of objects per family, than those in the main belt.  Milani (1993)
suggests 8 members of the largest (Menelaus) family, but the membership
of only a fraction of these appears secure.  This paucity of the Trojan
families is presumably an artifact of the much smaller number of
Trojans having well-determined orbits.  Our knowledge of the Trojan
families should increase dramatically as the sample of reliable orbital
elements is enlarged.\\

\subsection{Physical Properties}

What is the physical nature of the Trojans?  Thermal infrared and
optical measurements yield a mean geometric albedo $p_V = 0.056 \pm
0.003$ (standard error on the mean of 32 objects), with the maximum
reported value $p_V = 0.18 \pm 0.02$ (4709 Ennomos; Fernandez et al.
2003).  Similarly low albedos are characteristic of the nuclei of
comets (Fernandez et al. 2001), where they are presumed (but not yet
rigorously demonstrated) to indicate organic, perhaps carbonized
surface compositions.

The optical reflection spectra of Trojans are approximately linear with
wavelength and can be conveniently described in terms of the normalized
reflectivity gradient, $S'$ [\%/1000\AA ] (Jewitt and Luu 1990,
Fitzsimmons et al. 1994).  This is the rate of change of the
reflectivity with respect to wavelength, normalized to the continuum
height at some reference wavelength (often 5000~\AA).  Histograms of
$S'$ are shown in Figure 15.  There, the Trojans (Jewitt and Luu 1990)
are indistinguishable from the irregular satellites (Luu 1991, Rettig
2001) and cometary nuclei (Jewitt 2002) in terms of their optical
spectra, consistent with the comet nucleus analogy.  The neutral to
reddish colors and low albedos of the Trojans are close to those of
outer-belt asteroids, where the $P$ and $D$ spectral types are
numerically dominant (Gradie, Chapman and Tedesco 1989).  The color
distributions of the satellites, Trojans and nuclei are significantly
different from those of the reddish Kuiper Belt Objects, however.  The
transformation from KBO to comet nucleus probably involves the burial
of distinctive ultra-red material (material having $S' \geq$ 25
\%/1000\AA) on the KBOs by refractory debris ejected through outgassing
(Jewitt 2002).   Spectral observations of Trojans in the $1 \leq
\lambda \leq 2.5 \mu m$ near-infrared have failed to show any of the
bands characteristic of vibrational overtones and combination
frequencies in common molecular bonds, such as $OH$, $CH$, $NH$ (Luu,
Jewitt and Cloutis 1994; Dumas, Owen and Barucci 1998).  The water
bands at 1.5 $\mu$m and 2.0 $\mu$m are specifically absent, as is the
deeper (but harder to observe) 3.0 $\mu$m band (Jones et al. 1990,
Cruikshank et al. 2001).  These observations are all consistent with a
largely refractory surface composition, perhaps consisting of an
organic material (to provide the low albedos) with a large C/H ratio
(to explain the non-detection of the common molecular bonds).  A
suitable terrestrial analogue might be common charcoal, which is dark
and spectrally featureless.  However, it must be said that unique
interpretations of featureless reflection spectra, frequently with
modest signal-to-noise ratios, are impossible.  Plausible non-organic
compositions also fit the data (Cruikshank et al. 2001).  \\

-----------------------------------------------------------------------
Figure 15: Distributions of normalized optical reflectivity gradients
for (top to bottom) the irregular satellites of Jupiter (data from
Rettig 2001), Trojans (Jewitt and Luu 1990), cometary nuclei (Jewitt
2002) and Kuiper Belt Objects (Jewitt and Luu 2001). \\
-----------------------------------------------------------------------
\\

Remote measurements sample only the surface skin and reveal little
about the bulk composition of the Trojans.  As previously remarked
(Jewitt and Luu 1990), the available data are compatible with ice-rich
Trojan interiors buried beneath a thermally insulating skin (mantle) of
refractory matter.  This is exactly the stratigraphy inferred in the
nuclei of comets, where buried ice sublimates only from exposed vents
embedded in a low albedo mantle consisting of refractory debris.   The
Trojans, formed at or beyond the protoplanetary snow-line, could be
dormant comets.  The higher albedo of Ennomos (Fernandez et al. 2003)
hints at the possibility of surface ice, perhaps exposed by a recent
impact, although less exciting explanations are certainly possible.

If the Trojans really are planetesimals from the 5 AU region of the
protoplanetary disk trapped in dynamically stable niches, then they
form a potentially valuable complement to the nuclei of the comets.
Most long period comets formed in the 20 - 30 AU region and were
scattered to the Oort Cloud (their storage location) mainly by Uranus,
Neptune and, to a lesser extent Saturn (Hahn and Malhotra 1999).  The
Oort Cloud contribution from Jupiter was small (few percent) as a
result of its greater mass and large ejection velocity (most Jupiter
scattered planetesimals were launched above the escape velocity from
the solar system and are lost to the interstellar medium).  Conversely,
most Jupiter family comets originate in the Kuiper Belt and
therefore sample the disk in the 30 - 50 AU region.  In moving from the
Trojans, to the long-period comets to the Jupiter family comets, we
sample objects formed at 5 AU (temperatures $T \sim$ 150 K), 20 - 30 AU
($60 \leq T \leq$ 75 K) and 30 - 50 AU ($45 \leq T \leq  60$ K),
respectively.   A comet having compositional characteristics suggesting
formation near Jupiter's orbit has been reported (Mumma et al 2001).
Perhaps it is appropriate to think of this body as a close relation of
the irregular satellites and Trojans.

How might the suspected volatile nature of the Trojans be
observationally tested?  In the absence of in-situ spacecraft
investigation, we must rely on chance exposures of ice uncovered by
impacts.  The surface stability of water frost depends critically on
the ice temperature and hence on the albedo.  At Jupiter's distance,
the equilibrium sublimation rate of freshly deposited water ice frost
(albedo = 0.9) at the subsolar point (i.e.  the warmest location) of a
non-rotating Trojan body is $\sim$ 2 $\times 10^{-18}
kg~m^{-2}~s^{-1}$.  Such a frost would sublimate less than 1 mm in the
age of the solar system.  The same ice darkened to an albedo 0.1 by an
admixture of absorbing refractory particles ('dirt') would, in
equilibrium, sublimate at $5 \times 10^{-7} kg~m^{-2}~s^{-1}$,
corresponding to the loss of a 1 mm layer in $\sim$1 month.  
Dirty water ice would generate a weak gas coma that would be hard
to detect given existing instrumentation, and which would be
short-lived due to the rapid ($\sim 10^3$ yr) formation of a thermally
insulating rubble mantle over the sublimating surface (Jewitt 2002).
The extreme sensitivity of the sublimation rate to the albedo shows
that highly reflective fresh ice exposed by impact, for example, could
survive indefinitely against sublimation provided its albedo remained
high.  We imagine the formation of bright ray craters on the Trojans
caused by impacts puncturing the surface mantle and excavating buried
ice.  The persistence of exposed ice would probably be limited by other effects,
particularly impact gardening of the surface layers leading to mixing
with dark refractory grains.   But before being mixed with other
material, the ice should be identifiable both spectroscopically and in
accurate, rotationally resolved albedo measurements.\\

\subsection{Capture of Trojans}
We noted earlier that comets are sometimes temporarily captured into
the Lagrangian clouds.  Permanent capture would require the action of a
dissipative force or an increase in the Jupiter: Sun mass ratio.
Regarding the former, collisions with other Trojans and
non-gravitational forces due to asymmetrical mass loss from the comets
have both been suggested (Yoder 1979).  Quantitatively, in the present
epoch, neither mechanism seems plausible.  The probability of collision
within the Trojan clouds is currently too small to effect capture in
the limited ($\sim$few orbit) period of temporary capture, and
non-gravitational forces are so weak at 5 AU that only the smallest
bodies could possibly be influenced by them.  We consider it unlikely
that the Trojans are comets captured by outgassing forces.  On the
other hand, in the early solar system the numbers of objects moving in
Jupiter's orbit may have been very much larger than at present.
Collisional damping of the velocity dispersion could have stabilized
objects near the $L4$ and $L5$ points, leading to the in-situ
accumulation of the Trojans.  Solar nebular gas drag would not have impeded
this process (Peale 1993).

With regard to the planetary mass, the high abundance of H and He in
Jupiter requires that this planet formed quickly, prior to the
dissipation of the surrounding gas nebula.  Observations of nearby
young stars suggest gas disk survival times measured in millions of
years (e.g. Briceno et al. 2001) while the terminal, hydrodynamic
collapse phase of Jupiter's growth probably occurred on timescales
$\sim 10^3$ yr.   Objects in heliocentric orbit near the L4 and L5
points in the presence of a growing Jupiter could, in analogy with the
trapping of satellites (Heppenheimer and Porco 1977, Namouni 1999) find
themselves trapped by the rapidly strengthening gravitational potential
caused by Jupiter's growth (Fleming and Hamilton 2000).  Kozai's
mechanism may have played a role in trapping nearby bodies into
retrograde irregular satellite orbits (Marzari and Scholl 1998b).

Numerical experiments provide some support for this conjecture.  With a
Jovian growth timescale of $10^5$ yrs the capture efficiency is high
for heliocentric inclinations $\leq$ 20 deg and negligible for
inclinations $\geq$ 40 deg (Marzari and Scholl 1998).  This matches the
intrinsic inclination distribution of the Trojans: the bias-corrected
mean inclination has been independently measured as $\sim$17 deg.
(Shoemaker et al. 1989) and 13.7 $\pm$ 0.5 deg (Jewitt, Trujillo and
Luu 2000).  Only two numbered Trojans ((19844) 2000 ST317 and (12929)
1999 TZ1) have $i \geq$ 40 deg.  Small eccentricities are also highly
favored by the capture process.

However, capture by mass-growth predicts a distribution of libration
amplitudes that is much wider than the one observed.  The real Trojans,
with a median libration amplitude near 30 degrees, are more tightly
bound to the L4 and L5 points than expected from this model (for which
the modal libration amplitude is near 70 degrees).  One possible
explanation if, indeed, mass growth is the explanation for capture, is
that collisional dissipation of energy after capture has lead to the
progressive damping of the libration amplitudes (Marzari and Scholl
1998).  In this scenario, the smallest (highest velocity) fragments
produced by collisions would be selectively lost from the Trojan
clouds, leading to a flattening of the size distribution (c.f. Eq
(9)).  Alternatively, the current population may reflect selective loss
of the large amplitude Trojans: orbits with large libration amplitudes
are less stable than those of small amplitude (Levison, Shoemaker and
Shoemaker 1997).

A realistic treatment of capture by the mass growth of Jupiter must
necessarily include planetary migration.  This is because the growing
Jupiter exchanges angular momentum with planetesimals and with the gas
disk of the solar nebula, allowing its orbit size to change on the same
timescale as its mass grows.  The semi-major axes of the orbits of all
the giant planets are thought to have been altered by such torques.
Saturn, Uranus and Neptune migrated outwards: the resonant structure in
the distribution of Kuiper Belt Objects provides evidence for the
magnitude (5 - 7 AU) and the timescale (1 - 10 Myr) of the outward
migration of Neptune (Hahn and Malhotra 1999).   Massive Jupiter
provided the ultimate source of the angular momentum and, in contrast
to the other planets, its orbit shrank, perhaps by only a few $\times$
0.1AU.  Resonant structure in the main-belt asteroid distribution may
attest to this inward motion (Liou and Malhotra 1997).   Fleming and
Hamilton (2000) show that adiabatic changes in Jupiter's mass and
semi-major axis relate to the Trojan libration amplitude, A, through

\begin{equation}
\frac{A_f}{A_i} =
\left(\frac{m_{Ji}}{m_{Jf}}\right)^{1/4}\left(\frac{a_{ai}}{a_{Jf}}\right)^{1/4}
\end{equation}

where subscript $'i'$ refers to the initial value and $'f'$ to the
final value.  The changes can be considered adiabatic if they occur on
timescales much longer than the 150 yr libration period given by  Eq.
(6).  An adiabatic inward migration of Jupiter at constant mass by 0.5
AU to $a_{Jf}$ = 5.2 AU would increase the libration amplitudes by a
modest 2\%.   Adiabatic growth of Jupiter from $\sim$10 $M_{\oplus}$
core mass to 317 $M_{\oplus}$ final mass would lead to a reduction in
the libration amplitudes by a factor of $A_f/A_i \sim$ 0.4.  Therefore,
the effects of migration are minor relative to those caused by mass
growth.

The significance of radial migration is that the planets may have
passed through mean motion resonances that would destabilize the
Trojans.   The current orbital periods of Jupiter (11.87 yrs) and
Saturn (29.45 yrs) fall in the ratio 2.48:1, very close to the mean
motion resonance at 5:2 (this is sometimes oddly known as the "Great
Inequality").  An inward displacement of the orbit of Jupiter by only
0.02 AU would cause these planets to fall exactly into the 5:2
resonance.  Perturbations on the Trojans of a growing, migrating
Jupiter have been modelled by Gomes (1998) and Michtchenko, Beauge and
Roig (2001).  Both find strong dynamical effects upon passage through
mean-motion resonances due to dynamical chaos.  For example, the timescale for
ejection of Trojans when at the 5:2 commensurability is only $\sim10^6$
years.  Much more severe effects are experienced at the 2:1
commensurability (corresponding to a Jupiter located at 6.00 AU), for
which the $10^3$ yr Trojan ejection lifetime is scarcely longer than
the characteristic libration period.  If the Jovian Trojans are
primordial, these results suggest that Jupiter and Saturn can have
never passed through the 2:1 commensurability, and therefore that the
separation of the orbits of these two planets, presently at 4.33 AU,
has not changed by more than 1 AU (Michtchenko et al. 2001).  This
inference is compatible with the relative motions of the planets needed
to explain resonant structure in the main asteroid belt (Liou and
Malhotra 1997) and in the Kuiper Belt (Hahn and Malhotra 1999). \\

\subsection{Trojan Stability}
Trojans are currently lost from the L4 and L5 clouds by two main
processes.  The dominant loss is from collisional shattering and the
ejection of fragments.  Collisions can occur between Trojans (the
relevant velocity dispersion is $\sim$ 5 $km~s^{-1}$), and between
Trojans and interplanetary projectiles (mostly long-period comets,
which impact at characteristic speeds near 15 $km~s^{-1}$).  In high
velocity, catastrophic impacts, the secondary fragment ejection
velocity varies inversely with fragment mass.  Therefore, the net
effect should be a depletion of the smaller Trojans relative to the large
ones, corresponding to a flattening of the size distribution relative
to the production function.  The rate of loss of kilometer-sized and
larger Trojans has been estimated at $dN/dt \sim 10^{-3} yr^{-1}$
(Marzari, Farinella and Vanzani 1995).  Given that the current
population with $r \geq$ 1 km is $N \sim 1.6 \times 10^5$ (Jewitt,
Trujillo and Luu 2000), this estimate would suggest that the small
Trojans are continually replenished (presumably by collisional
shattering of larger Trojans) on timescales $N/(dN/dt) \sim 160$ Myr.
Secondly, Trojan orbits appear to be weakly chaotic, but the Lyapunov
timescales are much longer than the collision time (few $\times 10^9$ yr;
Levison, Shoemaker and Shoemaker 1997) and the resultant loss rates
correspondingly small.  However, loss through dynamical instability is
independent of Trojan size, potentially allowing the escape of even the
largest Trojans, while collisional ejection affects small Trojans most
strongly.

Observational evidence for collisional processing of the Trojans is
apparent in the size distribution which shows a slope break near $r
\sim $30 km (Jewitt, Trujillo and Luu 2000).   The larger objects may
be primordial, the smaller ones are collisionally produced fragments of
these  parent bodies.  Other evidence for a size dependence of the
physical properties of the Trojans includes an optical color-diameter
trend (Jewitt and Luu 1990, Fitzsimmons et al  1994) that may suggest
the increasing prevalence of collisional fragments at smaller sizes.
Lastly, the rotational lightcurve amplitudes of large Trojans
statistically exceed those of small Trojans, possibly suggesting the
smoothing action of collisions (Binzel and Sauter 1992).

Objects scattered out of the Trojan clouds can encounter Jupiter, to
become temporarily involved with that planet before impact, or ejected
from the planetary system, or injected into planet-crossing orbits
(Marzari, Farinella and Vanzani 1995).  Escaped Trojans are dynamically
similar to Jupiter family comets (Rabe 1972, Marzari, Farinella and
Vanzani 1995). Estimates of the total Trojan population, when compared
with the flux of JFCs, suggest that the fraction of the JFCs that might
be escaped Trojans is $< 10\%$ (Marzari, Farinella and Vanzani 1995,
Jewitt, Trujillo and Luu 2000). As with the irregular satellites,
escaped Trojans whose perijoves fall into the realm of the Galilean
satellites are subject to quick removal by collision.  The fraction of
impact craters on the Galilean satellites that might be caused by
escaped Trojans has been estimated to fall in the 1 \% to 10 \% range
(Zahnle, Dones and Levison 1998), with the dominant impactors being
Jupiter Family Comets derived from the Kuiper Belt.  This fraction is
highly uncertain, however, not least because the size distributions of
the Trojans and, particularly, the nuclei of comets are not well
determined.  It is possible that escaped Trojans dominate the impactor
flux into the satellites, particularly at smaller diameters where the
comets are believed to be depleted relative to power law extrapolations
from larger sizes. \\


\section{Leading Questions}  

The big questions concern the sources and sinks of the irregular and
temporary satellites and the Trojan librators, and the variations in
the populations of these bodies with time.  In particular, we would
like to know if the irregulars and the Trojans are remnants of much
larger initial populations that have been depleted over time by
collisional or other effects.  We also hope to understand the
relationship between the bodies discussed in this review, and the
materials that are widely presumed to exist in Jupiter's high molecular
weight core: are they samples of the same material?  A better
understanding of this latter issue might one day motivate spacecraft
exploration of (and sample return from) the Trojans.  As always, the
big questions are unlikely to be easily answered, and so we list a set
of related but smaller, observationally more tractable questions that
will take us some way towards our goal. \\

\begin{itemize}
\item       Do the irregular satellites and/or the Trojans possess ice-rich
interiors?  This is suggested by their presumed formation at or beyond
the snow-line, but no relevant observational constraints on the
composition have been established. \\

\item   What is the size distribution of the irregular satellites as a
whole, and within the separate subgroups?  Is there a measurable
minimum size that would provide evidence for depletion of the smallest
bodies by gas drag? \\

\item       What correlations, if any, exist between the orbital and
physical parameters of the irregular satellites?   Correlations are
expected from gas drag (for example, the smallest satellites are more
strongly affected by drag, and should have orbits smaller and less
eccentric than their larger counterparts). \\

\item       What is the distribution of spectral (compositional) types
among the irregulars and how does this relate to their presumed origin
by fragmentation of a small number of precursor objects? \\

\item       What is the current population and what are the main
sources of temporary satellites (both planet impactors and others)?  \\

\item       What are the unbiased orbital element distributions of the
temporary and irregular satellites?  Unbiased distributions will provide the
strongest information about capture mechanisms and evolutionary
processes. \\

\item       What fraction of the Trojans is binary and what is the
distribution of separations and masses among the components of these
objects?  How do they form and what constraints do the binaries place
on the collisional history of the Trojans? \\

\item       What fraction of the Trojans belongs to identifiable
dynamical families? \\

\item       Can we identify escaped Jovian Trojans amongst the
near-Earth objects?  Low albedo, spectrally reddish near-Earth objects
are known.  How can we determine which, if any, of these are former
Trojans?


\end{itemize}

\section{Acknowledgements}
We thank Julie Moses for pointers about meteoric infall to Jupiter, Yan
Fernandez and Toby Owen for comments on the paper.  Bob Jacobson
computed the orbital elements listed in Table 1.  This work was
supported by grants to DCJ from NASA.


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