# THE TRANSITION FROM THE KUIPER BELT TO THE JUPITER-FAMILY COMETS

Wesley C. Fraser Herzberg Astronomy and Astrophysics Research Centre, National
Research Council,
5071 West Saanich Road, Victoria, BC, V8T 1E7, Canada Department of Physics
and Astronomy, University of Victoria, Victoria, BC, V8P 5C2, Canada Luke
Dones Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO,
80504, USA Kathryn Volk Lunar and Planetary Laboratory, The University of
Arizona, 1629 E University Blvd, Tucson, AZ, 85721 Planetary Science
Institute, 1700 East Fort Lowell Rd., Suite 106, Tucson, Arizona, 85719 Maria
Womack National Science Foundation, 2415 Eisenhower Ave, Alexandria, VA 22314
Department of Physics, University of Central Florida, Orlando, FL 32816 David
Nesvorný Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder,
CO, 80504, USA

###### Abstract

  * Kuiper Belt Objects, or more generally Trans-Neptunian Objects (TNOs), are planetesimals found beyond the orbit of Neptune. Some TNOs evolve onto Neptune-crossing orbits and become Centaurs. Many Centaurs, in turn, reach Jupiter-crossing orbits and become Jupiter-family comets (JFCs). TNOs are the main source of the JFCs. TNOs offer a different window than the JFCs, of more primordial bodies and over a different size and temperature range. It is in that context that this chapter is written. Here we discuss the dynamical pathways taken from the trans-Neptunian region to the JFCs, and the most important properties of TNOs that relate to the JFC population, including considerations of their origins, compositions, morphologies, and size distributions. We relate these properties to the JFCs whenever possible. We reflect on a few key outstanding issues regarding our incomplete knowledge of TNOs as they pertain to the Centaurs and JFC populations. We finish with a short discussion of notable new and upcoming facilities and the impacts they will have regarding these outstanding questions.

##  1 Introduction

_Oort_ (1950) proposed the first, and for some time the only, reservoir for
comets. He noted that, of nineteen long-period comets with well-determined
orbits and semi-major axes $a\gtrsim 1,000$ au, ten had $a>20,000$ au before
they entered the planetary region. These “near-parabolic” comets had a wide
range of inclinations to the ecliptic, both prograde and retrograde. Oort
proposed that the solar system was surrounded by a roughly spherical cloud of
$\approx 10^{11}$ comets that extended beyond $\approx 10^{5}$ au from the
Sun, about half the distance to the nearest star.

In the wonderful words of _Kazimirchak-Polonskaya_ (1972), the major planets
can indeed serve as “powerful transformers of cometary orbits,” with some
evolving from near-parabolic orbits onto orbits like those of Jupiter-family
Comets (JFCs), which we discuss in Section 1.2 (_Everhart_ , 1972). However,
the “capture” of Oort Cloud comets into short-period orbits is far too
inefficient to produce the observed number of JFCs (_Joss_ , 1973). This
mismatch suggested that there must be another source of short-period comets.
Several astronomers, notably _Edgeworth_ (1949) and _Kuiper_ (1951), suggested
the existence of a belt of low-inclination comet-like bodies beyond Neptune’s
orbit, $\approx$ 35–50 au from the Sun (see _Davies et al._ (2008) and
_Fernández_ (2020) for historical accounts of such ideas, which percolated
even before the discovery of Pluto in 1930). _Fernandez_ (1980) calculated
that such a belt could be the source of short-period comets if it contained
bodies up to the mass of Ceres ($\approx 10^{24}$ g, or 7% the mass of Pluto).
_Duncan et al._ (1988) performed extensive numerical integrations and
confirmed that only a low-inclination source could produce enough JFCs and
proposed that this source be called the Kuiper Belt. The first Kuiper Belt
Object, 15760 Albion (1992 QB1), was discovered four years later (_Jewitt and
Luu_ , 1993).111The community has referred to the objects beyond Neptune as
Kuiper Belt Objects and Trans-Neptunian Objects, largely interchangeably. We
adopt the latter here as a more generalized and less historically charged
term. _Duncan et al._ (1988) also remarked that Chiron, the only Centaur known
at the time, “may well be a bright member of the parent population of [short-
period] comets.” Hundreds of Centaurs are now known, including P/2019 LD2
(ATLAS), an active body which passed within $\approx 0.1$ au of Jupiter in
2017 and will do again in 2028 and 2063 (_Steckloff et al._ , 2020). The 2063
encounter, the closest of the three, is expected to place the comet on an
orbit with a semimajor axis $a\approx 4$ au and a perihelion distance $q<3$
au, making it a Jupiter-family comet.

Because of the inverse-fourth-power dependence on reflected flux density with
distance, the known Trans-Neptunian Objects (TNOs) are typically much larger
than the Centaurs, which, in turn, are generally larger than the nuclei of
JFCs. Most known TNOs have diameters of order 100 km, ranging up to Pluto and
Eris (2300–2400 km); Centaurs are generally in the range of 10 to 100 km, with
Chariklo the largest at 300 km; the nuclei of Jupiter-family comets range from
$\approx 0.3$ km up to more than 10 km. These size differences should be kept
in mind when comparing different classes of bodies.

In the remainder of this section, we summarize basic orbital properties of
TNOs, Centaurs, and comets, particularly the JFCs. Section 2 discusses how the
Kuiper Belt attained its complex structure and the orbital evolution of TNOs
to Centaurs and JFCs. In Section 3, we discuss the compositions of TNOs and
Centaurs revealed by broadband colors and reflectance spectroscopy. Section 4
treats the active Centaurs, whose activity must be driven by substances more
volatile than water ice; the issue of whether the frequent appearance of
bilobed structures in JFCs reflects morphological evolution after leaving the
Kuiper Belt or dates to the formation of these bodies billions of years ago;
and the size distributions of TNOs, Centaurs, and JFCs. Section 5 concludes
with a discussion of outstanding questions and future observations that may
clarify many of the issues we discuss. This chapter addresses a variety of
different topics regarding TNOs. Rather than providing a detailed review of a
specific topic, this chapter aims to provide an overview of the most relevant
TNO science relating to the field of cometary astronomy.

Many chapters in Comets III discuss subjects which we have no room to
describe. We particularly note the chapters on the dynamical populations of
comet reservoirs by Kaib and Volk; planetesimal and comet formation by Simon
et al.; the chapters on cometary nuclei by Guilbert-Lepoutre et al., Pajola et
al., Filacchione et al., and Knight et al.; past and future comet missions by
Snodgrass et al.; and the chapter by Jewitt & Hsieh on transition objects,
especially their discussion of asteroids on cometary orbits.

###  1.1 Meet the Kuiper Belt

Three decades after the discovery of the first Trans-Neptunian Object (besides
Pluto/Charon), the dynamical structure of the Kuiper Belt has proven to be
more complex than that of the asteroid belt (see _Gladman and Volk_ 2021 for a
recent review). TNOs are typically classified based on 10-Myr orbital
integrations, as this timescale reveals the population’s relevant key
dynamical behaviors (a scheme that began with early observational surveys;
e.g., _Elliot et al._ 2005).  _Gladman et al._ (2008) established a widely-
used classification scheme (Figure 1) that divides outer solar system objects
into the following categories:

  * •

Jupiter-coupled: Objects with semimajor axes exterior to Jupiter, but with
Tisserand parameters with respect to Jupiter222The Tisserand parameter $T$ of
a comet with respect to a planet with semimajor axis $a_{P}$ is
$T=a_{P}/a+2\cos i\sqrt{a(1-e^{2})/a_{P}}$. Here $a$, $e$, and $i$ are the
semimajor axis, eccentricity, and inclination of the comet with respect to the
planet’s orbital plane. The Tisserand parameter is an approximation to the
Jacobi integral, which is a constant of motion for the circular restricted
three-body problem. For Jupiter-coupled comets, the Tisserand parameter varies
more gradually than other orbital parameters, such as the comet’s period of
revolution around the Sun (_Kresák_ , 1972; _Carusi and Valsecchi_ , 1987;
_Levison_ , 1996). less than 3.05, consistent with cometary orbits

  * •

Centaurs: Non-Trojan objects with semimajor axes between those of Jupiter (5.2
au) and Neptune (30.1 au)

  * •

Resonant: Objects in mean-motion resonances (MMRs) with Neptune

  * •

Scattering: Objects whose semimajor axes vary by at least 1.5 au over 10 Myr,
which typically coincides with perihelion distances $\lesssim$ 38-40 au

  * •

Classical: Non-resonant, non-scattering objects with eccentricities $<0.24$,
an arbitrary cutoff that restricts this population largely to semimajor axes
between 30 and $\approx 50$ au

  * •

Detached: Objects on stable orbits that fall into none of the previous
categories

The population of classical objects residing between Neptune’s 3:2 and 2:1
resonances (39.4 $<a<$ 47.8 au) is often referred to as the ‘main belt’, with
classical objects interior and exterior to those resonances referred to as
inner and outer classical belt objects. Figure 2 shows a set of classified
observed outer solar system objects that illustrates a few key dynamical
features of this population: the prevalence of resonant objects, a bimodal
inclination distribution extending to quite high $i$, and a mix of scattering
and detached objects with a wide range of perihelion distances in the high-$a$
population.

Figure 1: Nomenclature scheme for objects with semi-major axes beyond
Jupiter’s orbit (_Gladman et al._ , 2008, from). This taxonomy primarily
focuses on TNOs, and, by design, excludes most JFCs. We use a similar
classification.

Populations of dynamically stable objects in Neptune’s MMRs were apparent from
early surveys (e.g. _Chiang and Jordan_ , 2002; _Elliot et al._ , 2005) and
predicted by early theoretical studies (e.g. _Duncan et al._ , 1995;
_Malhotra_ , 1995). Although the 3:2 MMR, which hosts Pluto and numerous
“Plutinos,” contains more known TNOs than other resonances, the raw numbers
are misleading. This is because bodies in the 3:2 have shorter orbital periods
and smaller perihelion distances than most TNOs, and so are easier to
discover. Analyses accounting for observational biases imply that a wide range
of Neptune’s resonances in the classical belt and in more distant regions have
large populations, comparable to that of the 3:2 MMR (e.g. _Gladman et al._ ,
2012; _Adams et al._ , 2014; _Volk et al._ , 2016; _Chen et al._ , 2019;
_Crompvoets et al._ , 2022). This has important implications for the dynamical
history of the outer solar system (see Section 2.1). By the late 1990s, it was
clear that the orbits of observed TNOs extended to higher inclinations than
did orbits of main-belt asteroids. However, there is a concentration of low-
inclination orbits in the classical belt from $a=42-45$ au.  The bimodal
nature of the inclination distribution in the classical Kuiper belt region was
first demonstrated by _Brown_ (2001). The low-inclination classical belt
objects also tend to have low eccentricities; this sparked the division of TNO
populations into categories of dynamically ‘hot’ and ‘cold’ subpopulations
[meant to invoke thermodynamics because the ‘hot’ population have larger
radial and vertical velocities than ’cold’ objects] (_Levison and Stern_ ,
2001). The cold population is essentially entirely constrained to $a=42-45$ au
(though with possible extensions just beyond 50 au; see, e.g., _Bannister et
al._ 2018), while the scattering, detached, and the majority of the resonant
populations all fall into the dynamically hot category (the implications of
which are discussed in Section 2.1).

Figure 2: Eccentricity and inclination vs. semimajor axis of $\sim 1800$
observed TNOs color-coded by dynamical class; the set of TNOs is the full
OSSOS sample (_Bannister et al._ , 2018) combined with a subset of other TNOs
in the Minor Planet Center database with classifications taken from _Smullen
and Volk_ (2020). The three solid lines in the top panel labeled with values
between 30, 40, and 50 represent lines of constant perihelion distance.
Modified from _Gladman and Volk_ (2021). See Figure 8 of _Bernardinelli et
al._ (2022) for a similar plot of discoveries by the Dark Energy Survey.

At large semimajor axes, the observed population is a mix of resonant,
scattering, and detached objects spanning an unexpectedly wide range of
perihelion distances from 30 to 80 au. The existence of a scattered disk (_Luu
et al._ , 1997; _Duncan and Levison_ , 1997; _Volk and Malhotra_ , 2008) or
scattering population (_Gladman et al._ , 2008; _Gladman and Volk_ , 2021)
with perihelion distances less than $\approx 37-40$ au is a natural
consequence of objects being fed onto Neptune-crossing orbits, either today or
in the early solar system (e.g., _Levison and Duncan_ 1997; _Lykawka and
Mukai_ 2007; also see the discussion in the Kaib & Volk chapter). Objects with
these smaller perihelion distances can experience perturbations from Neptune
at perihelion that are strong enough to cause significant changes in orbital
energy, resulting in a random walk in semimajor axis. This creates the fan-
like structure in $a-e$ space seen in Figure 2, where objects are dispersed in
semimajor axis along lines of constant perihelion distance (the dashed
curves). Interactions with Neptune’s resonances can cause some objects’
perihelia to be raised and lowered, causing them to cycle between scattering,
resonant, and detached states; other objects appear to be permanently stranded
in high-perihelion detached orbits, some likely via resonant interactions
during planet migration (reviewed in, e.g., _Gomes et al._ 2008). There is a
subset of detached objects with such large perihelia (90377 Sedna with $q=76$
au, 2012 VP113 with $q=80$ au; _Brown et al._ 2004; _Trujillo and Sheppard_
2014; _Sheppard et al._ 2019) that they require another explanation beyond the
perturbations of the giant planets (see, e.g., _Gladman and Volk_ 2021).
Additional large-$a$, large-$q$ objects that might bridge gaps between the
scattering, detached, and perhaps the inner Oort cloud populations are also
beginning to be discovered (e.g., 541132 Leleakuhonua (2015 TG387) with $q=65$
au and $a\approx 1000$ au). As these ‘extreme’ objects do not contribute to
the supply of short-period comets, we will not discuss them at length here
(their implications for the solar system’s history are touched on in Section
2.1, and their possible relationship to the inner Oort cloud is discussed in
the Kaib & Volk chapter).

###  1.2 Meet the Comets

Most comets likely formed beyond the water “snow line” $\approx 3$ au from the
Sun [however, the snow line’s location changes as the protoplanetary disk
evolves (_Öberg et al._ , 2011; _Marboeuf et al._ , 2014; _Harsono et al._ ,
2015; _Cieza et al._ , 2016; _Drozdovskaya et al._ , 2016)] and within
$\approx 30$ au (_Nesvorný_ , 2018) in the solar system’s initial planetesimal
disk.

Comets are commonly divided into groups based on their orbital periods. In the
traditional taxonomy, long-period comets (LPCs) are defined as those with
orbital periods $P>$ 200 years, corresponding to $a>34.2$ au, and short-
period, or periodic, comets have $P<$ 200 years. The 200-year boundary has no
fundamental significance dynamically or compositionally (see, e.g. _A’Hearn et
al._ , 1995; _Mumma and Charnley_ , 2011).

Long-period comets are thought to have been gravitationally scattered by
interactions with the giant planets from their closer-in formation regions
($\approx 3$–30 au) out to distances between 2,000 and $\sim$ 100,000 au to
form a collective known as the Oort Cloud (see, e.g. _Duncan et al._ , 1987;
_Vokrouhlický et al._ , 2019). At those distances, perturbations external to
the solar system, including passing stars and galactic tides, raise and lower
comets’ perihelion distances in and out of the giant planet region and cause
their orbits to take on nearly random orientations (see for example,
_Weissman_ 1996; _Dones et al._ 2004; also see the chapter by Kaib & Volk in
this volume for further discussion of long-period comets and Oort Cloud
formation).

The short-period comets can be further divided into sub-populations (_Horner
et al._ , 2003; _Seligman et al._ , 2021). Most are classified as Jupiter-
family Comets (JFCs), many of which have aphelion distances near Jupiter’s
distance from the Sun (Figure 3). Most JFCs and Centaurs originate from the
dynamically hot trans-Neptunian populations (Section 1.1) and orbit the Sun on
prograde orbits with inclinations smaller than $\sim 30^{\circ}$, which is why
they are also sometimes referred to as ecliptic comets, e.g., _Levison and
Duncan_ 1997. While most JFCs originate from the TNO populations, other
populations likely contribute as well; Section 2.1 discusses this in further
detail. The smaller semimajor axes and inclinations of JFC orbits, which are
not consistent with an Oort Cloud origin, pointed the way to the existence of
the Kuiper belt/TNO populations prior to their discovery (e.g. _Edgeworth_ ,
1949; _Fernandez_ , 1980; _Duncan et al._ , 1988). This connection was later
confirmed by models of the newly observed reservoir (e.g. _Levison and Duncan_
, 1997; _Duncan and Levison_ , 1997).

Historically, JFCs were often defined as comets with $P<20$ years ($a<7.4$
au), although a variety of definitions appear in the literature. JFCs are now
often taken to be comets with Tisserand parameters with respect to Jupiter,
$T_{J}$, between 2 and 3 (_Carusi and Valsecchi_ , 1987). This is the
definition suggested by _Levison and Duncan_ 1997 as being the most indicative
of an origin in the Kuiper belt. Slight variations on the upper $T_{J}$ limit
for JFCs exist. We adopt the upper limit for JFCs of $T_{J}<3.05$ from
_Gladman et al._ (2008). By contrast, _Jewitt et al._ (2015) set the dividing
line between Jupiter-family comets and active asteroids, some of which are
main-belt comets, at $T_{J}=3.08$.

_Levison_ (1996) defined “Encke-type comets” (ETCs) as comets with $a<a_{J}$
and $T_{J}>3$ to distinguish “decoupled” comets like 2P/Encke, whose aphelion
distance is $\approx 1$ au interior to Jupiter’s orbit, from typical JFCs that
undergo close encounters with Jupiter. We do not find this category useful, as
objects defined this way are a mix of asteroids and comets, as we discuss
below. We consider Encke, which has $T_{J}=3.025$, to be a JFC on an unusual
orbit.

Encke’s perihelion distance $q=0.34$ au (smaller than Mercury’s semimajor
axis) is unique among comets with $T_{J}>3$. Encke is generally assumed to
originate in the Kuiper belt, but numerical simulations that reproduce the
comet’s decoupled orbit require it to remain active for an implausibly long
time (_Valsecchi et al._ , 1995; _Fernández et al._ , 2002; _Levison et al._ ,
2006b).

About half of the other “Encke-type comets” listed in the JPL Small-Body
Database are active asteroids (see chapter by Jewitt & Hsieh). The other half
are JFCs that do not cross Jupiter’s orbit, but still come within 2 Hill radii
of the planet and interact strongly with it. Many of these JFCs are quasi-
Hilda comets (_Tancredi et al._ , 1990; _Di Sisto et al._ , 2005; _Toth_ ,
2006; _Ohtsuka et al._ , 2008; _Gil-Hutton and García-Migani_ , 2016), which
undergo slow, and thus strong encounters with Jupiter, sometimes leading to
temporary captures by the planet. Indeed, D/1993 F2 (Shoemaker–Levy 9) may
have been a quasi-Hilda before its capture by Jupiter and impactful demise
(_Chodas and Yeomans_ , 1996).

Halley-type comets (HTCs) were once defined as periodic comets with orbital
periods between 20 and 200 years (_Carusi et al._ , 1987), but now are
typically classified as periodic comets with $T_{J}<2$ (e.g. _Levison and
Duncan_ , 1994; _Levison_ , 1996). HTCs generally have larger semimajor axes
(and higher inclinations) than the JFCs, but the new classification includes
“sun-skirting” comets like 96P/Machholz with $a\approx 3$ au and perihelion
distances well within the orbit of Mercury (_Jones et al._ , 2018).

Halley-type comets have often been taken to be the shortest-period tail of the
distribution of returning Oort Cloud comets. However, the population of known
HTCs is small, about 10% that of JFCs, in large part because HTCs’ (generally)
infrequent appearances provide few opportunities for discovery. The orbital
distribution of Halley-type comets is therefore not very well constrained
(e.g. _Wiegert and Tremaine_ , 1999). HTCs can be produced both from the
scattering TNO population (e.g. _Brasser et al._ , 2012; _Levison et al._ ,
2006a) and from the Oort Cloud (e.g. _Wang and Brasser_ , 2014; _Nesvorný et
al._ , 2017). More discussion of Encke- and Halley-type comets can be found in
the Kaib & Volk chapter.

Figure 3: Plot of short-period comets (orbital period $<200$ years, equivalent
to $a\lesssim 34.2$ au) listed in the JPL Small-Body Database browser. We use
the definition of _Gladman et al._ (2008) for Jupiter-family comets (JFCs),
Tisserand parameter relative to Jupiter $2<T_{J}<3.05$. JFCs are denoted by
circles; active asteroids ($T_{J}\geq 3.05$, $a<a_{J}$) by downward-pointing
arrows); active Centaurs ($T_{J}\geq 3.05$, $a\geq a_{J}$) by stars; and
Halley-type comets ($T_{J}\leq 2$) by upward-pointing arrows. The top panel
shows perihelion distance vs. semimajor axis, while the bottom panel shows
inclination vs. semimajor axis. The color scale shows $T_{J}$ for each comet
(right colorbars). The lines in the top panel denote circular orbits and
aphelion distance equal to Jupiter’s semimajor axis of 5.2 au. Objects between
the lines have orbits entirely within Jupiter’s orbit.

The population of Centaurs, small bodies with orbits in the giant planet
region, provides the link between the outer solar system TNO populations and
the inner solar system short-period comets. Most Centaurs are former TNOs that
evolved onto Neptune-encountering orbits and were scattered inward to the
giant planet region. There they have relatively short dynamical lifetimes of
$\sim$1–10 Myr (_Tiscareno and Malhotra_ , 2003; _Horner et al._ , 2004; _Di
Sisto and Brunini_ , 2007; _Bailey and Malhotra_ , 2009; _Fernández et al._ ,
2018) and either evolve inward onto short-period comet orbits or outward onto
highly eccentric orbits in the outer solar system; the details of this
evolution are discussed in Section 2.2. Cometary activity has been detected on
some Centaurs with perihelion distances as large as $\approx 12$ au (e.g.
_Jewitt_ 2009; _Lilly et al._ 2021; see discussion in Section 4.1), further
demonstrating that they are the transition population between the TNOs and
JFCs. However, the presence of activity does not by itself show that the
populations are related. For instance, although some active asteroids have
sublimation-driven activity and are thus bona fide comets, most are thought to
have resided in the asteroid belt for billions of years.

##  2 Origins of Trans-Neptunian Objects and Ecliptic Comets

###  2.1 Dynamical Origins of Trans-Neptunian Objects

How was the Kuiper Belt populated? The belt is thought to be a relic of an
ancient massive planetesimal disk outside the orbits of the giant planets
(_Nesvorný_ , 2018). _Fernandez and Ip_ (1984) showed that gravitational
interactions of the giant planets with small bodies cause Jupiter to lose
angular momentum (because it ultimately ejects most such bodies from the solar
system) and Saturn, Uranus, and Neptune to gain angular momentum. If the
planetesimal disk is massive enough (comparable to Uranus or Neptune), these
interactions can change the planets’ orbits substantially. _Malhotra_ (1993,
1995) showed that the outward planetesimal-driven migration of Neptune would
result in capture of Pluto and “Plutinos” into the 3:2 MMR.  This model
predicted that TNOs would also be captured into other MMRs, notably the 2:1
resonance near 48 au. TNOs in the 2:1 and many other MMRs were soon found by
surveys such as DES (_Elliot et al._ , 2005), CFEPS (_Petit et al._ , 2011),
and OSSOS (_Bannister et al._ , 2018) [see Section 1.1].

In these migration scenarios, the original orbits of the giant planets would
have been more closely spaced than they are now. In the Nice model (_Tsiganis
et al._ , 2005), Jupiter and Saturn are initially closer together then cross a
mutual 2:1 resonance as a result of interactions with the planetesimal disk,
exciting their eccentricities and triggering an instability in the orbits of
all the giant planets (_Tsiganis et al._ , 2005; _Levison et al._ , 2008;
_Brasser et al._ , 2009; _Morbidelli et al._ , 2010; _Levison et al._ , 2011;
_Nesvorný and Morbidelli_ , 2012; _Izidoro et al._ , 2016; _Gomes et al._ ,
2018; _Quarles and Kaib_ , 2019; _Nesvorný et al._ , 2021).  More recent
models of planetary instabilities have addressed problems with the Nice model,
such as the excitation of excessively large eccentricities and inclinations in
the terrestrial planets (_Brasser et al._ , 2009; _Agnor and Lin_ , 2012).
Efforts to match the intricate orbital distributions of the trans-Neptunian
populations, asteroid belt, and other small body reservoirs have also led to
substantial revision of the Nice model (see reviews by _Dones et al._ 2015;
_Nesvorný_ 2018; _Malhotra_ 2019; _Morbidelli and Nesvorný_ 2020; _Raymond and
Nesvorný_ 2022). For instance, most current models invoke a fifth giant planet
that was later ejected from the solar system by Jupiter (_Nesvorný_ , 2011;
_Nesvorný and Morbidelli_ , 2012; _Batygin et al._ , 2012; _Cloutier et al._ ,
2015) and find that the instability probably took place early, in the first
10–100 Myr of the solar system (_Deienno et al._ , 2017; _Mojzsis et al._ ,
2019; _De Sousa et al._ , 2020), rather than after hundreds of Myr (_Gomes et
al._ , 2005a). Our evolving understanding of the timing of the instability has
implications for the pre-migration evolution of the disk, including the likely
collisional histories of the planetesimals that eventually become the TNOs
that feed the short-period comet populations (e.g. _Morbidelli and Rickman_ ,
2015).

During the planetary instability, most bodies in the proto-trans-Neptunian
disk are ejected from the solar system, but some reach quasi-stable niches,
where they survive to the present. Models predict that the Oort Cloud and TNO
populations contain the overwhelming majority of the survivors. Based on the
known populations of small bodies, particularly Jupiter Trojans, and the
capture efficiency found by modeling the instability, the disk is estimated to
have originally contained about $6\times 10^{9}$ bodies with diameters
$d\gtrsim 10$ km (_Morbidelli et al._ , 2009b; _Nesvorný_ , 2018). The
instability model of _Nesvorný et al._ (2019b), evolved to the present,
predicts the number of Centaurs of this size that OSSOS discovered to within a
factor of two (also see _Bottke et al._ 2022). However, we know little about
how many such objects reside in the TNO populations and especially the Oort
Cloud. The fraction of those objects that reach the Oort Cloud and TNO
populations and survive today are estimated to be $\eta=0.05\pm 0.01$
(_Vokrouhlický et al._ , 2019) and 0.004 (_Nesvorný et al._ , 2017),
respectively, corresponding to $6\times 10^{9}\times 0.05=3\times 10^{8}$
$d>10$ km bodies in the Oort Cloud and $2\times 10^{7}$ in the TNOs. Bodies
from the disk are also implanted into the asteroid main belt ($\eta\approx
5-8\times 10^{-6}$, _Levison et al._ 2009; _Vokrouhlický et al._ 2016), as
Hildas and Trojans of Jupiter (each with $\eta\approx(6\pm 1)\times 10^{-7}$,
_Nesvorný et al._ 2013; _Vokrouhlický et al._ 2016), and as irregular
satellites of Jupiter, Uranus, and Neptune (each with $\eta\approx 2--
3~{}\times 10^{-8}$) and Saturn ($\eta\approx 5\times 10^{-8}$, _Nesvorný et
al._ 2014), yielding some 40,000 main-belt asteroids, 4,000 Hildas, 4,000
Trojans, and 100–300 irregular satellites of each giant planet.

Finding scenarios for the early evolution of the outer planets that are
consistent with the complex orbital distribution of TNOs (Section 1.1) is
difficult and a topic of active research. In general, some amount of
planetesimal-driven migration (e.g. _Fernandez and Ip_ , 1984; _Malhotra_ ,
1993, 1995) is invoked to explain the large number of resonant TNOs, while
some sort of dynamical instability amongst the giant planets (e.g. _Tsiganis
et al._ , 2005) is invoked to help explain both the planets’ orbits and help
dynamically excite the TNOs. Three main migration models have been proposed,
which depend on the value of Neptune’s eccentricity $e_{\rm N}$ at that time:
(A) very low-eccentricity ($e_{\rm N}\lesssim 0.01$) migration of Neptune from
$<25$ au to 30 au (e.g. _Malhotra_ , 1993, 1995; _Hahn and Malhotra_ , 2005);
(B) instability-driven scattering of Neptune from $<20$ au to an eccentric
orbit ($e_{\rm N}\sim 0.3$) at $\sim 30$ au, and subsequent circularization of
Neptune’s orbit by dynamical friction from the planetesimal disk (e.g.
_Tsiganis et al._ , 2005; _Levison et al._ , 2008); and (C) an intermediate
case in which Neptune’s migration is interrupted by the instability, with its
eccentricity reaching a peak of $e_{\rm N}=0.03$-0.1, and then dropping to
$\simeq 0.01$ as Neptune slowly migrates toward 30 au (e.g. _Nesvorný and
Morbidelli_ , 2012; _Nesvorný and Vokrouhlický_ , 2016). As discussed below,
these different kinds of migration models result in different distributions of
the TNO populations that feed into the current comet populations.

The original mass and radial span of the Kuiper belt are unknown, but models
that initially put several Earth masses beyond 30 au run into problems with
Neptune’s migration, because Neptune continues to migrate past that distance
(_Gomes et al._ , 2004). Migration beyond 30 au can also result in excess mass
in the residual belt; today’s TNOs with $r<50$ au represent $<0.1$
$M_{\oplus}$ (_Di Ruscio et al._ , 2020). A sharp truncation of the original
massive disk, an exponential cutoff of the disk surface density near 30 au, or
some combination of the two is required to match Neptune’s orbit (_Nesvorný et
al._ , 2020). Specifically, the disk’s mass density at 30 au must have been
$\lesssim 1M_{\oplus}{\rm au}^{-1}$ for Neptune to stop at 30 au (_Nesvorný_ ,
2018). The original disk most likely continued, with a low surface density, to
45 au, where the cold classical TNOs formed and survived (_Batygin et al._ ,
2011).  The current mass of cold TNOs is estimated to be only $\sim 3\times
10^{-4}$ $M_{\oplus}$ (_Fraser et al._ , 2014) to $(3\pm 2)\times 10^{-3}$
$M_{\oplus}$ (_Nesvorný et al._ , 2020). These values assume that TNOs have
densities of 1 g cm-3. The vast majority of the dynamically hot TNO
populations that feed the Centaur and short period comet populations originate
in the more massive, closer-in portion of this original planetesimal disk.

The three models outlined above have different implications for the hot TNO
populations. A pure instability model (model B) does not explain the wide
orbital inclination distribution of hot TNOs (_Petit et al._ , 2011;
_Nesvorný_ , 2015) because the instability happens so fast that there is not
enough time to sufficiently excite the orbital inclinations. The existence of
cold classical TNOs also limits how large Neptune’s eccentricity can be when
it reaches its current semimajor axis ($e_{\rm N}<0.15$; _Dawson and Murray-
Clay_ 2012). In all three models, planetesimals originating from the $<30$ au
portion of the disk are scattered by Neptune to higher-$a$ and high-$e$
orbits; to end up in today’s metastable hot TNO populations, these orbits must
subsequently be stabilized by some dynamical mechanism that causes their
orbital eccentricities to drop.  The Kozai resonance (_Kozai_ , 1962) near and
inside mean-motion resonances with Neptune is presumably the dominant
implantation mechanism during periods of slow migration (_Nesvorný_ 2020). The
Kozai resonance produces anti-correlated oscillations of $e$ and $i$. As the
TNO’s orbital eccentricity decreases, its orbit can decouple from Neptune
scattering (i.e., the TNO’s perihelion distance can evolve to beyond Neptune’s
aphelion distance) or drop out of resonance while the TNO’s orbital
inclination increases. The $\nu_{18}$ secular resonance (which occurs when a
TNO’s orbital nodal precession rate matches one of the dominant nodal
precession rates of the giant planets, and is the mode most associated with
Neptune’s nodal rate) can also influence the inclination distribution (_Volk
and Malhotra_ , 2019), but it does not wipe out the Kozai signature.  When the
Kozai implantation dominates for smooth migration (model A), it is difficult
to obtain implanted hot TNO orbits with $i<10^{\circ}$ (Figure 4). The finer
details of these stabilization mechanisms and how they affect the efficiency
of implantation from the original planetesimal disk into the hot TNO
populations is still not fully explored, even in the simplest planetesimal
driven migration scenario (model A; see discussion in _Volk and Malhotra_
2019).

In general, the results of migration models better match the observed hot TNO
populations if Neptune’s orbit is modestly excited by an instability at some
point during migration (model C). This is particularly true for matching the
inclination distribution of the hot TNOs (Figure 4).  In this case, bodies are
implanted in the hot TNO populations as the eccentricities of high-$a$ and
high-$e$ orbits drop due to the $\nu_{8}$ secular resonance (which occurs when
a TNO’s perihelion precession rate matches one of the dominant perihelion
precession rates of the giant planets, the mode most associated with Neptune’s
perihelion precession rate), which is stronger in this case, because $e_{\rm
N}\neq 0$ (_Nesvorný_ , 2021); here the contribution of Kozai cycles is
relatively minor. As the $\nu_{8}$ resonance does not affect inclinations, the
inclination distribution is roughly preserved during implantation. The
inclination distribution is then primarily controlled by Neptune’s  scattering
and the $\nu_{18}$ secular resonance; in some simulations, the slower
Neptune’s migration is, the broader the inclination distribution becomes
(_Nesvorný_ , 2015), although this is not always a generic outcome of slow
migration simulations (_Volk and Malhotra_ , 2019).  This model, assuming that
Neptune’s migration was long-range and slow ($e$-folding time $\gtrsim 10$
Myr) better matches the Kuiper Belt’s orbital structure, such as its
inclination distribution (Figure 4) and the fraction of TNOs in resonant
orbits (_Nesvorný_ , 2018).

The scattered disk is thought to be the main source of ecliptic (or Jupiter-
family) comets (_Duncan and Levison_ , 1997; _Levison and Duncan_ , 1997;
_Volk and Malhotra_ , 2008; _Brasser and Morbidelli_ , 2013; _Nesvorný et al._
, 2017) (see Section 2.2 and _Dones et al._ 2015 for a review of this topic).
The dynamical structure of the inner detached disk (50–100 au), with dropout
bodies – objects that fell out of resonance during migration on the sunward
side of mean motion resonances (_Bernardinelli et al._ , 2022) – is an
important constraint on Neptune’s migration (_Kaib and Sheppard_ , 2016;
_Nesvorný et al._ , 2016; _Lawler et al._ , 2019). The efficiency of
implantation into these populations and how the inner detached disk may feed
the actively scattering population on long timescales depends on the details
of migration. The scattered disk decayed by a factor of $\sim 100$–300 since
its formation 4.5 Gyr ago (see, e.g., the scattered disk/Oort Cloud formation
and evolution models of _Brasser and Morbidelli_ 2013 and _Nesvorný et al._
(2017)). This is reflected by a rapidly decreasing number of ecliptic comets
and planetary impactors soon after the instability, and a gradual decrease
during the past $\approx 4$ Gyr.

Figure 4: The cumulative distribution function (CDF) of TNO orbital
inclinations obtained in dynamical models A (left panel) and C (right panel).
The intrinsic-model, biased-model and observed distributions are shown by
dotted, solid and red lines, respectively. The observed distribution shows all
detections from the Outer Solar System Origins Survey (OSSOS) with $40<a<47$
au, $q>36$ au and $i>5^{\circ}$ (_Bannister et al._ , 2018). The biased model
distribution was obtained by applying the OSSOS survey simulator (_Lawler et
al._ , 2018a) to the intrinsic model. In model A, Neptune migrated from 24 au
to 30 au with $e_{\rm N}\simeq 0.01$ on a 10-Myr timescale. In model C,
Neptune’s eccentricity was excited to $e_{\rm N}\simeq 0.1$ when Neptune
reached 28 au and slowly damped after that such that $e_{\rm N}\simeq 0.01$ in
the end. All planetesimals shown here started within 30 au of the Sun.

###  2.2 Dynamical Routes from the Centaurs to the JFCs

Figure 5: The colormap shows the time-weighted orbital distribution of
Centaurs (using a definition whereby Centaurs’ orbits are entirely enclosed in
the Jupiter-Neptune region) in a simulation of their evolution from the outer
solar system into the JFC population (figure from _Sarid et al._ 2019).

The short-period comets are fed into the inner solar system from the Neptune-
crossing population of TNOs. This is predominantly the population of
scattering objects (see discussion in the chapter by Kaib & Volk), though
other sub-populations of TNOs contribute as well (see Section 2.3). Some
objects on Neptune-crossing orbits will be scattered inwards into the Centaur
population, from which point their evolution is dominated by gravitational
scattering by the giant planets. Objects can spend upwards of $\sim 100$ Myr
in the scattering TNO population with perihelion very near or interior to
Neptune. Once an object has been transferred onto an orbit in the giant planet
region, it takes $\sim$ 1- 10 Myr for that object to either be ejected back
into the scattering population, or transferred into the JFC population (e.g.
_Tiscareno and Malhotra_ , 2003; _Di Sisto and Brunini_ , 2007; _Bailey and
Malhotra_ , 2009; _Sarid et al._ , 2019; _Di Sisto and Rossignoli_ , 2020).

Figure 5 illustrates the typical timespan objects spend traversing each part
of the Centaur region (which in this figure from _Sarid et al._ 2019 is
defined as an orbit entirely enclosed between Jupiter and Neptune, $q>5.2$ au
and $Q<30.1$ au, which is slightly more restrictive than the _Gladman et al._
2008 definition we typically use). Most of the time an object spends in the
Centaur population is spent in the Uranus-Neptune region because encounters
with these planets are gentler than those with Jupiter and Saturn. Even so,
20% of Centaurs will be ejected back into the outer solar system before making
it inside Uranus’s orbit; only roughly half the Centaurs will be transferred
onto orbits inside Saturn’s, with roughly one third making it past Jupiter to
become JFCs (_Sarid et al._ 2019; see also, e.g., _Tiscareno and Malhotra_
2003; _Di Sisto and Rossignoli_ 2020). Of order 1% of Centaurs will end their
journeys via impact with one of the giant planets (e.g., _Levison et al._ ,
2000; _Tiscareno and Malhotra_ , 2003; _Raymond et al._ , 2018; _Wong et al._
, 2021). Dynamical evolution in the Centaur region is relatively insensitive
to the exact source population in the outer solar system, though Centaurs with
high orbital inclinations do tend to have longer lifetimes in the giant planet
region due to the decreased probability of close encounters with the planets
(e.g., _Di Sisto and Rossignoli_ , 2020). Very high inclination and retrograde
Centaurs are not well-explained by the observed populations of TNOs described
in Section 1.1 because the journey through the giant planet region does not
radically alter the inclination distribution of Centaurs relative to their
source population (e.g., _Brasser et al._ , 2012; _Volk and Malhotra_ , 2013).
The observed high-inclination Centaurs and scattering objects (e.g., _Gladman
et al._ , 2009; _Chen et al._ , 2016) likely originate from non-TNO source
regions (see discussion in the chapter by Kaib & Volk).

The approximately one-third of Centaurs that become JFCs (_Levison and Duncan_
, 1997; _Tiscareno and Malhotra_ , 2003; _Di Sisto and Brunini_ , 2007;
_Bailey and Malhotra_ , 2009; _Fernández et al._ , 2018) typically transfer
into the inner solar system via a low-eccentricity orbit just exterior to
Jupiter like that of comet 29P/Schwassmann-Wachmann 1; this orbital region,
dubbed the JFC Gateway (_Sarid et al._ , 2019), represents an important phase
in the transition from Centaur to JFC because it coincides with thermal
conditions that allow for significant cometary activity from sublimation of
water ice (see, e.g., _Steckloff et al._ 2020). The Centaur to JFC transition
is, of course, reversible, with objects passing back into the Centaur
population (also typically through a Gateway orbit). How many JFCs survive,
and in what state, to re-enter the Centaur population remains an open
question.

Dynamical models of JFC orbital evolution indicate that, after becoming JFCs,
it can take up to $\sim 0.5$ Myr for a comet to be dynamically removed (e.g.,
_Levison and Duncan_ , 1994; _Di Sisto et al._ , 2009). However, during this
extended orbital evolution, the JFCs’ orbital inclinations are pumped up to
larger and larger values, driving the overall simulated JFC inclination
distribution to disagree with the observed one (e.g., _Levison and Duncan_ ,
1994; _Di Sisto et al._ , 2009; _Nesvorný et al._ , 2017).  To solve this
mismatch between simulated and observed JFC populations, it is usually assumed
that a comet becomes inactive after some number of orbits with a perihelion
distance below some threshold (often $q\lesssim 2.5$ au). Fits to the
inclination distribution of JFCs with diameters between 1 and 10 km suggest
physical lifetimes of $\approx$ 4000–40,000 years ($\approx$ 500-5000 orbits),
which is a small fraction of the dynamical lifetimes (e.g. _Levison and
Duncan_ , 1997; _Di Sisto et al._ , 2009; _Brasser and Wang_ , 2015; _Nesvorný
et al._ , 2017). Sub-km JFC nuclei must have much shorter physical lifetimes.
The exact nature of this fading (i.e., whether it is due to buildup of a
surface lag layer (“mantle”, e.g. _Rickman et al._ (1990)) or physical
destruction of small comet nuclei through spin-up or other mechanisms) is not
well-understood; observations of dormant comet nuclei in various solar system
regions (including the Centaur population) could help constrain this problem.
An additional complication is that the activity of JFCs can turn on and off
repeatedly. For instance, comet Blanpain (now known as 289P) was discovered in
1819, observed for two months, and not seen again for almost two centuries
until it was identified with the asteroid 2003 WY25 and found to have a weak
coma (_Jewitt_ , 2006).

###  2.3 Kuiper Belt Sources of Centaurs and Comets

Figure 6: A model of the TNO population (modeled from formation to the present
day) with the source-region orbits of eventual ecliptic comets highlighted.
The black dots show a snapshot of the TNO population from $\sim 3$ Gyr ago;
objects from that snapshot that later become ecliptic comets (defined as
$2<T_{J}<3$, $P<$ 20 years, $q<2.5$ au) are shown as larger red dots. About
75% of TNOs that become short-period comets in this simulation originate in
the scattered disk, with semimajor axes between 50 and 200 au; $\sim 20$%
originate from TNOs with $a<50$ au (some of which enter the 50-200 au
scattering population en route); about 3% come from the Oort Cloud. From
_Nesvorný_ (2018), which was adapted from _Nesvorný et al._ (2017).

Dynamical models of the evolution of trans-Neptunian populations confirm that
the dynamically hot populations, particularly the scattering population,
dominate the influx of new Centaurs and then JFCs in the inner solar system.
Figure 6, for example, highlights the original orbits of particles that evolve
onto cometary orbits from a model of the TNOs (_Nesvorný et al._ , 2017). Most
of these comet-supplying TNO orbits have perihelion distances below $\sim
37-38$ au, placing them in the scattering population, the one originally
argued to be the dominant supplier of JFCs (e.g. _Duncan and Levison_ , 1997).
However, it is clear that a few other TNO populations also contribute to the
influx. Figure 6 shows a number of JFCs sourced from Neptune’s resonant
populations (vertical features most evident in the top panel). Most notable
are the close-in 3:2 and 2:1 resonances, which are known to have large
populations (e.g. _Volk et al._ , 2016); chaotic diffusion within these
resonances (and others) can slowly feed objects onto Neptune-crossing orbits
that supply the JFCs (e.g. _Morbidelli_ , 1997; _Tiscareno and Malhotra_ ,
2009). Figure 6 also shows a handful of high-perihelion TNO orbits that
nonetheless evolve into JFCs. Most of these simulated objects appear to be in
Neptune’s more distant mean motion resonances, where secular effects cause
their perihelia to cycle in and out of Neptune’s reach (e.g. _Gomes et al._ ,
2005b). In the real TNO population, it is still not entirely clear how many of
the so-called ‘detached’ TNOs on high-perihelion orbits are still in Neptune’s
resonances (and thus could cycle back into the scattering population) and how
many are truly stranded at high perihelia (for example, by being dropped out
of resonance during the late stages of Neptune’s migration; e.g., _Kaib and
Sheppard_ 2016; _Lawler et al._ 2019); this is because the orbits of very
large semimajor axis TNOs are difficult to measure to high-enough precision
for this determination (discussed in, e.g., _Gladman and Volk_ 2021). The
orbital distribution of the detached TNOs and how much that population can
cycle in and out of the actively scattering population is one of the larger
uncertainties in determining the exact delivery rate of JFCs from the trans-
Neptunian region (also relevant to this are the effects of any unknown
perturbers in the distant solar system; see discussion in _Nesvorný et al._
2017). However, following the evolution of our best models of the TNO
populations into the inner solar system (_Levison and Duncan_ , 1997; _Di
Sisto et al._ , 2009; _Brasser and Morbidelli_ , 2013; _Nesvorný et al._ ,
2017) results in an excellent match to the observed orbital distribution of
comets (Figure 7), confirming that the majority of JFCs likely originate as
TNOs.

For completeness, we note that a few other solar system populations may
contribute to the observed JFCs. These include the low-inclination Themis
family in the outer main asteroid belt (_Hsieh et al._ , 2020) (also see the
chapter by Jewitt & Hsieh), the Hildas (_Di Sisto et al._ , 2005) in the 3:2
resonance with Jupiter near 4 au, and the Jupiter and Neptune Trojans (_Horner
and Lykawka_ , 2010; _Di Sisto et al._ , 2019). These sources are likely minor
suppliers of the JFC population compared to the TNOs. Bodies from the
primordial Kuiper Belt were implanted into all these populations (see Section
2.1), so JFCs from different present-day sources may not show clear signs of
their birthplaces. Indeed, two large asteroids near the middle of the asteroid
belt, 203 Pompeja and 269 Justitia, have recently been proposed to have
originated as TNOs, based on their colors, which are even redder than D-type
Trojans and Hildas (_Hasegawa et al._ , 2021).

Figure 7: The cumulative orbital distributions of ecliptic comets with orbital
periods $P<20$ years, Tisserand parameter with respect to Jupiter $2<T_{J}<3$,
and perihelion distance $q<2.5$ au. The model results (solid lines; _Nesvorný
et al._ 2017) are compared with the distribution of known JFCs (dashed lines).
The model assumes that ecliptic comets remain active and visible for
$N_{p}(2.5)=500$ perihelion passages with $q<2.5$ au. From _Nesvorný_ (2018),
which was adapted from _Nesvorný et al._ (2017). The panels are normalized so
that the numbers of ecliptic comets with $q<2.5$ and with $2<T_{J}<3$ equal
one.

##  3 Compositions and Physical Properties

In this section, we discuss the compositions of TNOs, Centaurs, and JFCs as
observed from Earth- and spacecraft-based telescopic observations. Measured
properties of these objects are valuable for constraining solar system
formation models (_Barucci et al._ , 2011; _van der Wiel et al._ , 2014). As
Centaurs are thought to be an intermediate stage in the orbital evolution from
TNOs to JFCs, intercomparison of their compositions can provide insights into
how the journey from the scattering TNO population inward influences
outgassing behavior and observed coma composition. Where available, we discuss
the few compositional links between these dynamically connected populations.

###  3.1 Surface Compositions of TNOs and Centaurs

Beyond atmospheric escape through processes such as Jeans loss (_Lisse et al._
, 2021), TNOs are generally inactive bodies. As such, specific material
identification on surfaces is made entirely through reflectance spectroscopic
remote sensing. TNOs tend to have spectra that are largely devoid of
identifying features (Figure 8). The detection of specific materials on the
surfaces of TNOs and Centaurs is so scarce that we can easily tabulate them in
Table 1, which shows the limited list of surface ices detected on these
objects.

Table 1: Representative listing of molecules detected/inferred on surface ices and in comae or atmospheres (volatiles) of TNOs, Centaurs, and comets TNO surface ices | H2O | CH3OH | CH4 | N2 | CO | CO2 | NH3 | C2H6
---|---|---|---|---|---|---|---|---
TNO volatiles | N2 | CO | CH4 |  |  |  |  |
Centaur surface ices | H2O | CH3OH |  |  |  |  |  |
Centaur volatiles | CO | H2O | CO2 | HCN | CN | CO+ | N${}_{2}^{+}$ |
Comet ices | H2O | CO2 | COOH-group |  |  |  |  |
Comet volatiles | H2O | CO2 | CO | CH4 | HCN | CH3OH | H2CO | NH3
| HNC | C2H2 | C2H6 | HCOOH | HCOOCH3 | HNCO | H2S | OCS
| HC3N | SO | SO2 | CS | CH3CO | S2 | CN | C2
| NH2 | C3 | CO+ | N${}_{2}^{+}$ | H2O+ | CO${}_{2}^{+}$ | N2 |

The most frequently detected material on TNOs is water ice, in both amorphous
and crystalline forms (_Zheng et al._ , 2009; _Barucci et al._ , 2011). Water
ice is thought to be abundant in all TNOs and Centaurs (_Brown et al._ ,
2012), and it is clearly one of the major building blocks of those bodies.
Water ice absorption is most clearly seen in Haumea and its collisional family
(_Barkume et al._ , 2006; _Trujillo et al._ , 2011). Methanol was first
detected on the surface of the Centaur Pholus (_Cruikshank et al._ , 1998),
and has been detected with varying levels of confidence on only a handful of
TNOs through ground-based spectroscopy (_Barucci et al._ , 2011), and in the
spectrum of Arrokoth by the New Horizon spacecraft (_Grundy et al._ , 2020).
Its rarity of detection implies either that its spectral signatures are
usually too weak to detect, either because it is not common on TNO surfaces,
or because those signatures are masked by other materials. The former
condition might imply that methanol is a by-product of some post-formation
process, rather than a material that was abundant during the formation of
TNOs.

The remaining materials are only found on the largest TNOs, i.e., on “dwarf
planets”333We caution that dwarf planets should not be conflated with
volatile-rich TNOs. For an object to be considered a dwarf planet requires
only that it be massive enough for self-gravity to govern its shape. It is a
coincidence of their formation and current surface temperatures that the
dwarf-planet TNOs are the only bodies able to retain detectable levels of the
volatile ices, which is the condition we are interested in here., such as
Eris, Pluto, Makemake, and Quaoar (for a recent summary, see _Barucci and
Merlin_ , 2020). These are the known volatile ices at TNO temperatures
($\approx$ 30-50 K) that are unstable to sublimation on timescales shorter
than the age of the solar system: N2, CH4, CO, and CO2. It is only by virtue
of the masses of the largest TNOs that atmospheric retention of these ices is
sufficient to preserve a detectable abundance of these materials since
formation (_Schaller and Brown_ , 2007; _Brown et al._ , 2011; _Lisse et al._
, 2021). At the most basic level, the interplay between temperature and
gravity governs the retention of each volatile, resulting in dramatic
variations in relative abundances from object to object. This explains why
some objects have spectra that are N2 dominated (e.g. Eris), some are methane
dominated (e.g. Quaoar), and some exhibit features of all the above volatile
ices (e.g. Pluto). Figure 8 presents a small sample of spectra of the dwarf
TNOs, exhibiting the sheer diversity of their spectra. Much like water on the
Earth, the presence of these materials in a semi-stable state drives
interesting atmospheric and surface re-circulation cycles that dominate the
surface rheologies of these bodies (_Bertrand et al._ , 2018; _Hofgartner et
al._ , 2019). These processes and the loss rates, which are highly sensitive
to the surface and interior temperature histories of these bodies, greatly
complicate estimates of the primordial ice abundances. This interesting topic
is well beyond the scope of this chapter. For our purposes it is sufficient to
emphasize that these volatile ices are primordial in nature, and are not fully
depleted from the interiors of smaller TNOs, the interior presence of which is
betrayed by the presence of these ices in the comae of JFCs (see Section 3.2).

Of course, the compositions of TNOs are not limited only to the few ices that
have been spectrally identified. TNOs typically have red colors at optical
wavelengths. The most striking example of this is the New Horizons flyby
imagery of the small (36 km long) TNO Arrokoth (_Grundy et al._ , 2020). The
dynamic range of TNO/Centaur optical colors is enormous, spanning from nearly
neutral reflectors (e.g. the Haumea family members; _Brown et al._ 2007) to
some of the reddest objects in the solar system (e.g., Gonggong - 2007 OR10;
_Fraser and Brown_ (2012)). This red color is most commonly attributed to
chemical processing of organic materials by cosmic rays (_Thompson et al._ ,
1987; _Cruikshank et al._ , 1998; _Barucci et al._ , 2011; _Fraser and Brown_
, 2012). Such materials exhibit the so-called optical gap absorption feature,
driven by the C-H $\pi$-bond. Centered in the NIR, the shape and width of this
feature depend on the amount of dehydrogenation of the organic, how disordered
the molecular structure is, and the level of non-organic contaminant in the
molecular chains, in particular (_Seccull et al._ , 2021). This feature is
common to many organic materials that are considered suitable astrophysical
analogs; compare the chemically simple polycyclic aromatic hydrocarbons (e.g.,
_Izawa et al._ , 2014) to the highly disordered laboratory materials called
tholins (e.g.. _Roush and Dalton_ , 2004), both of which show this deep
optical gap. If attribution to organic materials is correct, the red colors of
TNOs imply that simple organics such as methane were abundant for enough time
in the early solar system that red dehydrogenated crusts could develop
(_Brunetto et al._ , 2006) before those volatile ices were depleted.

The spectrum of Arrokoth reveals a mostly featureless spectrum typical of most
TNOs, except for two weak features at 1.8 and $2.2\mbox{ $\mu$m}$. The
absorption at $2.2\mbox{ $\mu$m}$ has been attributed to methanol ice (_Grundy
et al._ , 2020). It has been suggested that the $1.8\mbox{ $\mu$m}$ feature
can be driven by the presence of sulfur in the organic residue (_Mahjoub et
al._ , 2021). Irradiation experiments on laboratory ice mixtures containing
methane, ammonia, hydrogen sulfide, and water result in a red material bearing
an absorption at $1.8\mbox{ $\mu$m}$ that is absent in mixtures with no sulfur
(_Mahjoub et al._ , 2021). Such a feature has not been detected on any other
TNO, possibly as a result of the low available signal-to-noise ratio of even
the best spectra of small TNOs. It may be that the feature is unique to the
so-called cold-classical TNOs (see Section 2.1) which are the only TNO
population presumed to have formed in-situ. The search for sulfur in the comae
of JFCs has taken on new importance, as the presence or absence of sulfur-
bearing materials in JFCs would provide significant insights regarding the
compositional variations in the protoplanetesimal disk. The recent strong
detection of atomic sulfur at 1425 Å in the JFC 46P/Wirtanen rivals that of
atomic hydrogen (_Noonan et al._ , 2021), and is consistent with emission
directly from the nucleus or from grains very near the surface, similar to
atomic sulfur and other sulfur-bearing species in 67P/Churyumov–Gerasimenko
(_Calmonte et al._ , 2016). Additional searches are underway for other sulfur-
bearing species in JFCs to test models of cometary ices and their subsequent
processing history (_Presler-Marshall et al._ , 2020; _Saki et al._ , 2020;
_Altwegg et al._ , 2022).

No discussion about TNO compositions would be complete without the mention of
silicate materials. Two TNOs, the $\approx 700$ and 300-km diameter Plutinos
(208996) 2003 AZ84 (_Fornasier et al._ , 2009) and (120216) 2004 EW95
(_Seccull et al._ , 2018), exhibit spectra that appear similar to C-type
asteroids, with absorption features consistent with hydrated silicates. These
two bodies are not icy, lacking even the absorptions due to water ice at 1.5
and $2.0\mbox{ $\mu$m}$ seen in the Haumea family (_Brown et al._ , 1999).
Frustratingly, silicate materials have avoided spectroscopic detection for icy
TNOs. Their presence was first inferred by the need for silicate materials to
account for the densities of the largest TNOs. Of the eleven TNOs with
diameters $d>600$ km and measured densities $\rho$, all but one, 55637 (2002
UX25), have $\rho>$ 1 g cm-3 (_Brown_ , 2013; _Brown and Butler_ , 2017) [see
_Bierson and Nimmo_ (2019) and _Grundy et al._ (2019a) for densities of other
TNOs]. The largest density is $2.43\pm 0.05$ g cm-3 for Eris/Dysnomia, the
most massive TNO system known (_Holler et al._ , 2021). The presence of
silicates has also been inferred from spectroscopic modeling, either of
individual spectra (see _Barucci et al._ 2011, for example), or of the
continuum of TNO optical and NIR colors (e.g. _Fraser and Brown_ , 2012).
Recent modeling of spectrophotometry spanning $\sim 0.5-4.5\mbox{ $\mu$m}$
implies the presence of silicate-rich surfaces amongst some of the brighter
TNOs (_Fernández-Valenzuela et al._ , 2021). These results demonstrate that
silicates _do_ exist in icy TNOs (of course they do!), but simply are masked
by the presence of other materials. It is likely that characterization of
silicates in TNOs will have to await observations at longer wavelengths
($\lambda\gtrsim 3\mbox{ $\mu$m}$; _Parker et al._ 2016). Spectral
observations from JWST are likely to be quite important in this regard (see
Section 5).

Beyond spectral studies, many insights regarding the compositions of TNOs have
come from broadband photometric techniques. We review those here.

Significant effort has been devoted to developing a taxonomic system for TNOs,
as even the simple act of determining the number of classes is likely to
influence our interpretation of the early solar system. It is generally
thought that the varied classes of TNOs reflect the compositional structure of
the regions of the protoplanetary disk from which TNOs originated. Proposed
mechanisms for compositional differences of planetesimals include ice lines
(_Dalle Ore et al._ , 2015) and post-formation volatile loss (_Wong and Brown_
, 2016; _Brown et al._ , 2011), which would lead to variable composition with
distance from the Sun, prior to disk dispersal by the migrating gas giants. It
is important to highlight that to date, TNO compositional measurements are all
measured from reflected light, and are typically assumed to be indicative of
primitive nucleus values.

Efforts to determine the number of TNO classes have been frustrated by their
nearly featureless spectra. TNO reflectance spectra (e.g. _Fornasier et al._ ,
2009; _Guilbert et al._ , 2009; _Barkume et al._ , 2008; _Barucci et al._ ,
2011), like those of most icy bodies, including the Jupiter Trojans, Centaurs,
and JFCs (_Emery et al._ , 2011; _Cruikshank et al._ , 1998; _Barucci et al._
, 2002) can be broadly described as linear in the optical and near-infrared
(NIR), with a different spectral slope in each region, and a smooth roll-over
or transition between the two slopes, very roughly centered at $\sim$0.9 $\mu
m$, and sometimes an absorption band of water ice at 1.5 $\mu m$ and other
ices in the infrared (see Sec. 3.1). A few examples are presented in Figure 8.
By comparison, asteroids generally exhibit distinct features between classes
that aid taxonomic interpretation (_DeMeo et al._ , 2009); such features are
generally unavailable for the classification of TNOs. Those few materials that
have been confidently detected from the spectra of TNOs, such as water ice, do
not seem to belong uniquely to certain TNO taxa. Rather, taxonomic systems
have been largely generated from the variations in optical and NIR colors seen
from object to object.

Figure 8: Select TNO and Centaur reflectance spectra. Top: spectra of (from
top to bottom) the inactive Centaur 5145 Pholus (_Cruikshank et al._ , 1998),
TNOs (44594) 1999 OX3 (_Seccull et al._ , 2018), (145452) 2005 RN43 (_Alvarez-
Candal et al._ , 2008; _Guilbert et al._ , 2009), and (73480) 2002 PN34 (black
_DeMeo et al._ 2010; gray _Brown et al._ 2012), and the active Centaur 60558
Echeclus, also known as comet 174P (_Seccull et al._ , 2018). Spectra were
normalized to unity at $0.65\mbox{ $\mu$m}$ and offset vertically in steps of
0.45. The NIR spectrum of 2005 RN43 has been renormalized to the optical
spectrum using its observed (V-R) color. The dashed curve is a spectral model
of Pholus, which includes contributions from olivine, tholin, water ice, and
methanol. Bottom: Spectra of the dwarf planets Orcus (top; _DeMeo et al._ ,
2010), Eris (middle; _Alvarez-Candal et al._ , 2011) and Pluto (bottom;
_Merlin et al._ , 2010). The spectra were normalized to unity at $1.5\mbox{
$\mu$m}$, and those of Orcus and Eris have been offset by 0.8 and 1.0
vertically. In both panels, regions affected by telluric lines or instrumental
artifacts have been removed, and data have been rebinned for clarity.  This
figure omits notable objects for which the published spectra were not
available to the authors, including that of the methane rich Quaoar _Jewitt_
(2004), and the water-ice rich Haumea _Trujillo et al._ (2007).

Centaurs and most dynamically excited TNOs exhibit a bifurcated optical color
distribution (_Tegler and Romanishin_ , 1998; _Peixinho et al._ , 2012;
_Tegler et al._ , 2016; _Fraser and Brown_ , 2012; _Peixinho et al._ , 2015;
_Lacerda et al._ , 2014; _Marsset et al._ , 2019). The bimodal color
distribution has provided a functional taxonomy of two populations for small
TNOs, now colloquially referred to as Red and Very Red. In this basic system,
Pluto is a Red member, and Arrokoth belongs to the Very Red population of TNOs
(_Grundy et al._ , 2020). Intrinsically, Red class TNOs outnumber the Very Red
objects by at least 4-to-1 (_Wong and Brown_ , 2017; _Schwamb et al._ , 2019).
This ratio has been used to infer that the purported compositional line that
divides the proto-Red and proto-Very Red populations fell between 30 and 40 au
(_Nesvorný et al._ , 2020; _Buchanan et al._ , 2022).

The Red/Very Red taxonomy only considers optical spectral slope or color, and
does not make use of any other wavelengths. Longward of $\sim 0.9\mbox{
$\mu$m}$, TNOs tend to exhibit NIR colors that are correlated with optical
spectral slope (e.g. _Fraser and Brown_ , 2012). Attempts have been made to
use the optical-NIR color space to create more complex taxonomies. Early
efforts applied principal component analysis to a sample of BVRIJ colors and
found 4 classes (e.g. _Barucci et al._ , 2005). This 4-taxon system is
presented in Figure 9, and essentially divides the Red and Very Red classes
into two subpopulations based on their IR behavior. For example, the IR and RR
classes are Very Red, with the RR exhibiting red spectral slopes across the
BVRIJ range, and the IR exhibiting bluer NIR spectral slopes than found in the
optical. Generally, the number of taxa found would increase with the number of
filters or the complexity of the analysis (_Dalle Ore et al._ , 2013). A
recent effort to include visible albedo in the analysis expands the number of
taxa to as many as 6, with an additional 4 taxa each containing a single dwarf
planet (Pluto, Eris, Makemake, and Quaoar). Alternative analyses have
concluded that the optical-NIR color distribution should not be further
subdivided. Rather, excited TNOs exhibit only 2 separate taxa, with each
exhibiting a continuum of colors through the optical and NIR color spaces
(_Fraser and Brown_ , 2012; _Schwamb et al._ , 2019).

Figure 9:  Colors of TNOs and Centaurs from _Hainaut et al._ (2012, H12),
_Fernández-Valenzuela et al._ (2021, F21), and _Buchanan et al._ (2022, B22).
The colors of the 4-taxon system of _Barucci et al._ (2005) are shown by the
rectangles _Hasegawa et al._ (2021). Estimates of (B-R) of the _Buchanan et
al._ (2022) measurements were done by determining the range of linear spectral
slopes that match the reported (g-r) colors, and projecting those slopes onto
(B-R). (R-J) was estimated from (r-J) in a similar fashion.

For completeness, we point out the so-called cold classical TNOs, which stand
out in many ways, including their tight orbital distribution (see Section 1.1)
and high binary fraction (_Noll et al._ , 2008, 2020). They are found in a
tight annulus between $42<a<48$ with inclinations $i\lesssim 5^{o}$.
Considering their red optical colors (_Gulbis et al._ , 2006), cold classicals
mainly appear to belong to the Very Red taxon. Unlike most dynamically excited
Very Red objects, however, cold classicals appear to exhibit NIR colors that
tend to values closer to solar (_Pike et al._ , 2017) and have higher than
usual visual albedos (_Brucker et al._ , 2009), suggesting cold classical
objects may occupy a third taxon. Due to their stable orbits, however, they do
not act as a significant source of Centaurs or JFCs.

Unsurprisingly, the Centaurs tend to exhibit similar optical-NIR color
distributions as the TNOs that feed the Centaur population. A detailed
comparison is limited by biases, both observational, such as inconsistent
target selection in color surveys (_Schwamb et al._ , 2019), and physical,
such as that colors seem to vary with size (_Benecchi et al._ , 2019), and
surface alteration processes (_Seccull et al._ , 2019), all of which will
likely affect the TNO and Centaur color distributions differently.

JFCs do not exhibit any of the color structure shown by TNOs and Centaurs.
Instead, they consist entirely of objects with surfaces only slightly redder
than solar (e.g. _Jewitt_ , 2015). As the JFCs are predominantly directly fed
from the excited TNO populations, the gray surfaces of the JFCs must be the
result of alterations to their surfaces as objects migrate closer to the Sun.
Cometary activity seems a likely culprit. Indeed, those Centaurs which have
been found to be active all have surface colors that are closer to solar than
the average TNO, with none of the Centaurs with Very Red colors exhibiting
detectable levels of activity. This implicates activity as a main driver for
surface color alteration, possibly through deposition of gray dust (e.g.
_Seccull et al._ , 2018). Other alteration mechanisms might be at work, such
as the thermal destruction of reddening agents.

###  3.2 Coma Compositions of Centaurs

At least 10–15% of known Centaurs exhibit dust comae and are deemed active
(_Jewitt_ , 2009; _Bauer et al._ , 2013). Such comae are composed primarily of
dust grains with expansion velocities of 0.3 km s-1 or less and production
rates ranging from $\sim$ 1–1,000 kg s-1 (Table 2) (_Whitney_ , 1955; _Hughes_
, 1991; _Trigo-Rodríguez et al._ , 2010; _Kulyk et al._ , 2016). Identifying
the volatile components and ascertaining which are produced in high enough
amounts is an important first step in constraining models of Centaur activity
and solar system formation and evolution.

A summary of volatile production rates in Centaurs is provided in Table 2.
There are so few detections and significant limits that their production rates
(in molecules s-1 and kg s-1) can be listed succinctly in this table.
Representative dust mass loss rates are also included in the table, with 29P
leading the pack with the highest values, although low rates are sometimes
seen in this Centaur.

Table 2: Measured and derived properties of dust and gas in Centaurs

Comet | Volatile | r (au) | Production rate | Mass loss rate a | Reference
---|---|---|---|---|---
|  |  | 1027 mol/s | (kg/s) |
29P | Dust | 5.8 - 6.3 | – | 30 – 4700 | [1,2,3,4,5]
| CO | 5.7 - 6.3 | 10 - 70 | 460 – 3200 | [6,7,8,9,10,11]
| H2O | 6.2-6.3 | 4.1 - 6.8 | 120 - 188 | [5, 8]
| CO2 | 6.2 | 0.5 $\pm$ 0.3 | 36 $\pm$ 22 | [12]
| N2 (N${}_{2}^{+}$) b | 6.3 | 0.4 $\pm$ 0.2 | 17 $\pm$ 8 | [10, 11, 13]
| O2 c | 6.3 |  $\sim$0.24 |  $\sim$13 | [11]
| HCN | 6.3 | 0.048 $\pm$ 0.011 | 1.8 $\pm$ 0.4 | [5]
| CN | 5.8 | 0.008 $\pm$ 0.003 | 0.3 $\pm$ 0.1 | [14]
| NH3 | 6.3 |  $<$4.5 |  $<$128 | [9]
| CH3OH | 6.3 |  $<$0.55 |  $<$29 | [9]
| CH4 | 6.3 |  $<$1.3 |  $<$34 | [9]
| H2CO | 6.3 |  $<$0.1 |  $<$5 | [9]
Chiron | Dust | 9 - 18 | - | 1 - 45 | [15, 16, 17]
| CO | 8.5 | 13 $\pm$ 3 | 605 $\pm$ 151 | [18]
| CN | 11.3 | 0.037 $\pm$ 0.011 | 1.4 $\pm$ 0.3 | [19]
Echeclus | Dust | 13.1 | - | 10 - 700 | [20, 21]
| CO | 6.1 | 0.8 $\pm$ 0.3 | 300 $\pm$ 130 | [22]
| CN | 12.9 |  $<$0.04 | $<2$ | [23]
P/2019 LD2 | Dust | 4.5 | - | 40 - 60 | [24]
| CO | 4.58 |  $<$4.4 |  $<$200 | [25]
| CN | 4.5 |  $<$0.0014 |  $<$ 0.1 | [23]

[1] _Fulle_ (1992), [2] _Ivanova et al._ (2011), [3] _Hosek et al._ (2013) [4]
_Schambeau et al._ (2021) [5] _Bockelée-Morvan et al._ (2022), [6] _Senay and
Jewitt_ (1994) [7] _Festou et al._ (2001), [8]_Ootsubo et al._ (2012), [9]
_Paganini et al._ (2013) [10] _Womack et al._ (2017), [11] _Wierzchos and
Womack_ (2020), [12] Harrington Pinto et al., under review, [13] _Ivanova et
al._ (2016), [14] _Cochran and Cochran_ (1991), [15] _Luu and Jewitt_ (1990),
[16] _Romon-Martin et al._ (2003), [17] _Fornasier et al._ (2013), [18]
_Womack and Stern_ (1999), [19] _Bus et al._ (1991), [20] _Rousselot et al._
(2016), [21] _Bauer et al._ (2008), [22] _Wierzchos et al._ (2017), [23]
_Rousselot_ (2008), [24] _Licandro et al._ (2021), [25] _Kareta et al._
(2021),

a Gaseous mass loss rates were calculated using production rates and
appropriate atomic mass units.
b N2 production rate is derived from CO+, N${}_{2}^{+}$ and CO measurements,
see _Womack et al._ (2017).
c O2 production rate is inferred by scaling the mixing ratio of O2 and H2O in
67P (a JFC) to the water production rate measured in 29P by AKARI, see
_Wierzchos and Womack_ (2020) for details.

Despite decades of observations, very few volatiles have been detected on
Centaurs. This is largely due to their faintness and because most are
inactive. Their distant orbits combined with only rare episodes of comae or
outbursts make it difficult to discover when they are active and then carry
out observations. Challenges also arise from the fact that some of the
candidate species for driving activity, such as CO2, CH4, N2, and O2, are
rotationally symmetric and thus have no pure rotational transitions at mm-
wavelengths, which is how most cometary volatiles are observed. Furthermore,
telluric contamination is a substantial obstacle for detecting CO2 and CH4
emission via infrared rovibrational spectra, and thus observing these two
volatiles directly has been restricted to a few instruments above Earth’s
atmosphere, such as the Infrared Space Observatory, AKARI Space Observatory,
and in situ spacecraft mission measurements.

Highly volatile species, such as N2 and O2, may be abundant enough in nuclei
to play a role in Centaur activity, but thus far have not been detected.
N${}_{2}^{+}$, a probable ionization product of N2, has been detected in
optical spectra of 29P’s coma. N${}_{2}^{+}$ is also a frequent night sky
emission feature; however, a telluric source can be ruled out with longslit
spectra when N${}_{2}^{+}$ emission is visible only in the tailward direction
(e.g., _Ivanova et al._ (2019)). Analysis of 29P’s N${}_{2}^{+}$ and CO+
emission in such tailward spectra of 29P is consistent with an N2 production
rate of $\sim$ 17 kg s-1, which is much smaller than CO (_Wierzchos and
Womack_ , 2020). However, care should be used when interpreting either
N${}_{2}^{+}$ and CO+ spectra, because their line strengths in 29P’s coma
appear strongly correlated with solar wind particle velocities, possibly
indicating a charging mechanism of solar-wind proton impact onto CO and N2 in
the coma (_Cochran et al._ , 1991; _Ivanova et al._ , 2019). An O2 production
rate was estimated by using measurements of its abundance in the Rosina mass
spectroscopy of the JFC 67P, and then scaling it to the measured water
production rate (_Wierzchos and Womack_ , 2020). These values suggest that N2
and O2 are not produced in high enough amounts to drive much of the activity
of 29P.

HCN emission was detected at millimeter wavelengths in only one Centaur – 29P
in 2010 – but with relatively low production rates and with a spatial profile
that indicates it may have been released from icy grains and not directly
sublimating from the nucleus (_Bockelée-Morvan et al._ , 2022). Although seen
in TNO and Centaur reflectance spectra, methanol (CH3OH) emission has not yet
been detected in Centaur comae, with the strongest upper limit of 29 kg s-1
set for 29P (_Biver_ , 1997).

Evidence for water-ice grains has been observed in cometary comae (_Yang et
al._ , 2009; _A’Hearn_ , 2011; _Kelley et al._ , 2013; _Protopapa et al._ ,
2018); by extension, it is reasonable to search for them in Centaur comae.
Centaurs orbit at heliocentric distances too large for water ice on the
nucleus surface to sublimate efficiently, but water vapor may still be
detected in the coma due to water ice-rich grains that are carried off the
nucleus by other outgassing mechanisms and then sublimate once bathed in the
solar radiation field, as was reported for 29P for water (_Ootsubo et al._ ,
2012) and in the aforementioned HCN. Recently, the signature of water ice
grains was again reported during a significant outburst of 29P in September
2021 (_Kelley et al._ , 2021), and a water ice grain signature at the 1–10%
level was seen in the near-infrared spectrum of the Centaur C/2019 LD2 (Pan-
STARRS)’s coma at 4.6 au (_Kareta et al._ , 2021).

There are also occasional reports of CN, C2, and C3 detections or upper
limits. These are radicals and not capable of long-term storage in the
nucleus, and so are probably daughter products from another cometary volatile
and not directly responsible for driving activity (_Bus et al._ , 1991;
_Cochran et al._ , 1991; _Womack et al._ , 2017; _Ivanova et al._ , 2019;
_Kareta et al._ , 2021; _Licandro et al._ , 2021; _Bolin et al._ , 2021).

Although considered as a likely candidate for distant activity in Centaurs
because of its relatively high abundance in many comets and the good match of
CO2’s sublimation efficiency at Centaur distances, CO2 emission has been
searched for in Centaur comae, with no detections thus far. A significant
limit was obtained only for 29P with the AKARI space telescope (_Ootsubo et
al._ , 2012), implying a CO/CO2 ratio $>90$, much higher than what is seen in
other comets (Harrington Pinto et al., under review). The space-based
telescopes Spitzer and NEOWISE have been used to observe many Centaurs and
were set up to detect the combined emission of CO and CO2 in the same $\sim$
4.5 $\mu$m filter bandpass. Unfortunately, because the emission is combined,
individual CO2 or CO production rates cannot be derived from the data without
independent and simultaneous measurements of one of the molecules. Recently,
CO2 production rates were inferred for 29P using Spitzer and NEOWISE imaging
data in 2010 along with contemporaneously obtained CO millimeter-wavelength
spectra, which confirms that CO2 is produced in relatively small amounts in
the 29P coma, as low as approximately 1% of CO and 14% of H2O, (Harrington
Pinto et al., under review).

Consequently, CO is the most tractable volatile for direct measurement in
Centaur comae that may play a significant role in activity, and these
observations are possible using ground-based as well as space-based
instruments at millimeter and infrared wavelengths. Detection of CO emission
is reported for three Centaurs: 29P, 95P/Chiron, and 174P/Echeclus (_Senay and
Jewitt_ , 1994; _Womack and Stern_ , 1999; _Wierzchos et al._ , 2017;
_Bockelée-Morvan et al._ , 2022). On a related note, CO emission is also
detected in some long-period comets at “Centaur distances” from the Sun, such
as C/1995 O1 (Hale-Bopp) and C/2017 K2 (Pan-STARRS) (_Gunnarsson et al._ ,
2003; _Yang et al._ , 2021) and CO appears to play a large role in distant
comet activity (_Biver et al._ , 2002; _Womack et al._ , 2017).

The apparent absence, or at least very low abundance in the coma, of CO2
emission in 29P’s coma is instructive. If we assume that Centaurs and comets
formed in similar environments and should have similar chemical compositions
of their nuclei, then the available data on comets may be useful for
predicting what we should see in other Centaurs. In a study of 25 comets for
which CO and CO2 were simultaneously measured, the mixing ratio of CO and CO2
production rates showed a possible preference for CO2 in the comae of most
JFCs, but the opposite is true for some Oort Cloud comets and the lone Centaur
(29P), (see _A’Hearn et al._ , 2012, and Harrington Pinto et al., under
review) . However, if JFCs, active Centaurs, and long-period comets are
analyzed as an aggregate, the coma mixing ratio may be better explained as
following a heliocentric trend out to at least 6 au. CO2 is preferentially
detected in most comets (not just JFCs) within 3 au, and CO is dominant beyond
3 au, although selection effects cannot be ruled out since JFCs are typically
fainter than long-period comets and less likely to be seen at large distances.
However, if this trend continues for other active Centaurs, then CO emission
is likely to exceed CO2 emission in the comae of active Centaurs, as is the
case for 29P. This effect may be at least partly due to differences in the
degree of thermal processing of the nucleus, rather than compositional
differences (_A’Hearn et al._ , 2012; _Harrington Pinto and Womack_ , 2019).
Indeed, one of the problems remaining in cometary science is accurately
determining comet nucleus composition from coma abundances.

##  4 Activity and Physical Evolution: Comet Beginnings

###  4.1 Activity in Centaurs

The drivers of activity in Centaurs have implications for the nature and
evolution of ice in small bodies and the cause of all activity in icy bodies
at large heliocentric distances. Unfortunately, very little is known about the
dominant mechanisms. Active Centaurs frequently display two types of activity:
sustained comae and discrete outbursts. The first Centaur discovered,
95P/Chiron, undergoes periods of sustained activity as well as short-term
brightening periods. Arguably, the best-known active Centaur is 29P, an object
on a nearly circular orbit just beyond Jupiter’s distance that exhibits
continuous activity with occasional outbursts of 10–250 times in brightness
superimposed. Another well known active Centaur is 174P/Echeclus, which has
undergone several outbursts, including a large one in which the activity was
centered on an apparent fragment of the main nucleus, and a few longer-term
periods of activity with lower-level dust comae.

Vigorous water-ice sublimation in comets releases many minor species in
cometary comae, but Centaurs are too far from the Sun for water ice to
sublimate efficiently. Thermal equilibrium temperatures of Centaur nuclei are
most similar to the sublimation temperatures of CO2 and NH3 and hence they are
favored by some models of Centaur activity, e.g. for the Centaur C/2014 OG392
at $\sim$ 10 au (_Chandler et al._ , 2020). However, no emission from these
volatiles has yet been detected in a Centaur, and studies of 29P place
stringent limits on their mixing ratio relative to CO.

As discussed in the previous section, CO is the only molecule detected in the
gaseous state in active Centaurs that is capable of driving activity. CO is
also abundant in a few Oort Cloud comets active beyond 5 au, but no CO
detections or significant limits exist for JFCs this far out (this may not
imply compositional differences between JFCs and Centaurs). There is evidence
for water ice grains in the comae for two Centaurs: 29P and P/2019 LD2
(ATLAS). These grains were most likely released from a surface component,
similar to what has been reported for some Centaur and TNO surfaces in Section
3.2.

Another model for Centaur activity invokes cosmogonically important volatiles
with lower sublimation temperatures, such as CO, which can survive in the
nucleus as ices just below the surface, and also be partially incorporated in
the gaseous state within amorphous ice and then released when this ice
undergoes the phase change to the crystalline state (_Prialnik et al._ , 1995;
_De Sanctis et al._ , 2000; _Prialnik et al._ , 2008; _Capria et al._ , 2009;
_Guilbert-Lepoutre_ , 2011). This phase change is optimized around $\sim$
120-140K (equivalent to Centaurs and comets at 5–10 au), but it can proceed at
farther distances (and colder temperatures) less efficiently.

The most popular model that explains the observations of Centaur (and distant
comet) comae is that of a nucleus with pockets of amorphous ice that undergoes
the crystallization process, which releases trapped volatiles. Another model
invokes isolated and insulated pockets of frozen CO or CO2 that sublimates
once the surface is disrupted enough to expose a relatively small and
previously protected frozen patch (e.g. _Prialnik et al._ , 2008). However,
given the very few measurements we have on Centaurs, more observations are
needed to settle between these two models.

Figure 10: Spectral line of CO J=2-1 rotational transition at 230 GHz for the
Centaur 29P/Schwassmann-Wachmann 1 obtained with the IRAM 30-m telescope in
January 2004. Superimposed is a model fit to the data, which includes a strong
blue-shifted peak of sunward emission from a very cold nucleus source, and a
smaller contribution from the nightside. From _Gunnarsson et al._ (2008)

.

Because of the lack of detections or low production rates and significant
limits for other volatiles in Centaurs, our main clues to outgassing must come
from CO in 29P. The spectral line profile of CO via its J=2-1 rotational
transition at 230 GHz is very narrow and slightly blueshifted, consistent with
sunward emission of CO from a very cold region and a secondary source more
distributed over the nucleus surface (Figure 10). This is also true for CO in
Chiron (_Womack and Stern_ , 1999) and Echeclus (_Wierzchos et al._ , 2017),
as well as other distantly active comets like Hale-Bopp (_Biver_ , 1997;
_Womack et al._ , 1997) and C/2017 K2 (Pan-STARRS) (_Yang et al._ , 2021). The
strikingly similar spectral shapes suggest there is a common outgassing
mechanism for CO in active Centaurs and distant Oort Cloud comets (_Womack and
Stern_ , 1999; _Biver et al._ , 2002; _Gunnarsson et al._ , 2003, 2008;
_Wierzchos et al._ , 2017; _Yang et al._ , 2021) originating from a very cold
($\sim$ 4K) gas, (e.g., _Paganini et al._ , 2013). Thus, it is reasonable to
plan for narrow emission from a very cold gas in the inner coma when searching
for CO in other active Centaurs.

Interestingly, Hale-Bopp, 29P, and Echeclus appear to have approximately the
same nucleus diameter and were all observed at 6 au, making an intercomparison
possible that minimizes size and heliocentric distance contributions
(_Wierzchos et al._ , 2017). Thus, 29P is an abundant producer of CO, even
sometimes outproducing Oort Cloud comet Hale-Bopp at the same distance. In
contrast, Echeclus and Chiron emitted CO very weakly, and it was only
marginally detected. Searches for CO in many other Centaurs did not yield
detections (_Drahus et al._ , 2017), but some, such as (10199) Chariklo,
342842 (2008 YB3), (8405) Asbolus, and 95626 (2002 GZ32) provide tight upper
limits that eliminate the possibility of significant outgassing activity from
CO at the time of observation (see Figure 11). We do not know whether Centaurs
like Chiron, Echeclus, and others that produce little to no CO formed in a
different environment, or whether they are devolatilized, or have not yet
started to become more active, partly due to spending more of their orbits
well beyond 6 au, when compared to 29P. The difference in CO output in 29P and
these other active Centaurs is particularly striking and may be useful to
constrain Centaur models. Further accurate measurements of nucleus diameters
and CO and CO2 production rates are needed to better understand how these
species contribute to activity and ultimately to determine the composition of
their nuclei.

Figure 11: Specific gas production rates, Q(CO)/D2, for Centaurs. The solid
line is a fit to data for Hale–Bopp provided for comparison. As the figure
shows, after normalized by surface area, 29P produces far more CO than other
Centaurs like Echeclus and Chiron, where CO was detected in lower amounts, and
other Centaurs for which strong upper limits were set. From _Wierzchos et al._
(2017).

Centaur activity also appears to be related to the residence time in its
orbital region, and a decrease in perihelion distance and/or semimajor axis
may occur before the observed onset of activity (_Fernández et al._ , 2018;
_Sarid et al._ , 2019; _Lilly et al._ , 2021). A Centaur’s perihelion distance
also apparently plays a large role in whether a Centaur will become active,
with lower values more likely to correlate with activity (_Jewitt_ , 2009).
_Rickman et al._ (1991) noted a similar trend for short-period comets whose
perihelion distances had recently decreased. Such comets had larger values for
their nongravitational parameters, suggesting that their mantles had been
removed, allowing more of their surfaces to be active. The ongoing CO
outgassing in Centaur 29P is recently proposed to be due to the nucleus
responding via the crystallization phase change of water due to the relatively
sudden, within $\approx 2000$ years, the median residence time of the Gateway
orbit (_Sarid et al._ , 2019)), change in its external thermal environment
produced by its dynamical migration from the Kuiper belt to the Gateway region
where it maintains a nearly constant thermal environment at a heliocentric
distance of $\approx 6$ au (Lisse et al. 2022, under review). Thus, orbital
history may play a large role in triggering the activity of Centaurs.

In addition to steady-state production that may produce a coma lasting weeks
or months, active Centaurs sometimes have discrete outbursts lasting a few
days to weeks. 29P is the best-known example whose outbursts have been
documented for more than a century, primarily with secular lightcurves of the
visible magnitudes and images which capture morphology in the coma, e.g.,
_Trigo-Rodríguez et al._ (2010); _Schambeau et al._ (2017, 2019). One of the
largest outbursts in decades began in September 2021, when 29P increased its
brightness by a factor of $\sim$ 250 during a series of four smaller outbursts
occurring over a few days. Such outbursts give an opportunity to test models
of chemical composition and physical mechanisms of ejection. Unlike 29P,
Chiron and Echeclus typically do not maintain long-term quiescent comae, but
both have exhibited outbursts or brightening episodes. In 2005 Echeclus
underwent a $\sim$ 7 magnitude outburst (from 21 to 14, corresponding to an
increase in brightness by a factor of $\sim$ 630) and was accompanied by a
large, detached coma $\sim$ 2 arcmin across, projected to be 1,000,000 km at
the Centaur’s distance and was visible for a few weeks (_Choi and Weissman_ ,
2006; _Tegler et al._ , 2006; _Rousselot_ , 2008). More details about its
observational timeline, orbital dynamics and measured characteristics during
outbursts are found in _Wierzchos et al._ (2017); _Seccull et al._ (2019);
_Kareta et al._ (2019).

29P’s long-term behavior of continuously having a dust and gas coma, regularly
punctuated by outbursts, is well-suited to dedicated observation over years,
and its lightcurve displays two types of outburst shapes: most have an
asymmetric sawtooth pattern, where the reflected light grows tremendously in a
few hours and then decays in days to weeks. These outbursts must have an
explosive trigger that releases a great deal of dust. Less frequently, the
visible lightcurves of smaller outbursts appear to grow and decay
symmetrically in time (cf. _Trigo-Rodríguez et al._ , 2010; _Wierzchos and
Womack_ , 2020; _Clements and Fernandez_ , 2021). In contrast to the larger
sawtooth shaped outbursts, the smaller symmetric outbursts may originate from
a source region that spans a larger surface area on the nucleus which releases
material over a longer period of time, perhaps a few days. Still another
mechanism contributing to the changing brightness of Chiron is the presence of
rings or ring arcs (also detected around Chariklo (_Braga-Ribas et al._ ,
2014)), which changes the Centaur’s apparent brightness as the aspect of the
rings varies from open to edge-on (_Sickafoose et al._ , 2020; _Fernández-
Valenzuela_ , 2022).

There are very little data about possible triggers for the outbursts in 29P.
However, outbursts of CO and dust were both recorded during simultaneous
observations of CO mm-wavelength spectral flux measurements and visible
magnitudes, providing an opportunity to test the hypothesis that a strong CO
outburst was needed to trigger the dust outbursts. Interestingly, the CO
production rate doubled, but did not trigger a noticeable rise in dust
production (_Wierzchos and Womack_ , 2020). Similarly, two dust outbursts
occurred without an accompanying increase in CO production. Two other dust
outbursts may show CO gas involvement. These odd results may be explained if
the CO is not always substantially incorporated with the dust component in the
nucleus, or if CO is primarily released through a porous material.

###  4.2 Morphological Evolution and TNO Binaries in Context

The prevalence of contact binaries found in the comet and TNO populations is
suggestive of a formation mechanism that preferentially forms contact binary
objects. Such a connection is not so obvious, however, without morphological
and evolutionary considerations. This short discussion highlights only a few
of the important processes one needs to consider when comparing the
morphologies of JFCs to their precursor TNO populations, and the challenges
faced when attempting to make inferences about their formation modes.

Most cometary nuclei imaged by spacecraft or radar have bilobed shapes; of the
seven, only 9P/Tempel 1 and 81P Wild are nearly spheroidal (see the chapters
by Pajola et al. and Knight et al. for further details). This suggests that
comets are born bilobed or morphologically evolve to become bilobed during
their lifetimes. Here we first consider the formation stage.

Formation of small planetesimals in the outer solar system favors binarity.
For example, the streaming instability model (_Youdin and Goodman_ , 2005, see
chapter by Simon et al.), where rotating clouds of pebbles collapse under
their own gravity, gives birth to binary systems with near–equal-sized
components, with properties that match observations (_Grundy et al._ , 2019a;
_Nesvorný et al._ , 2019a). The components of a newly formed close binary can
be brought into contact by gas drag (_Lyra and Umurhan_ , 2019), producing a
contact binary. The early-stage low-speed collisions between similar size
bodies can lead to mergers and bilobate shapes as well (_Jutzi and Asphaug_ ,
2015).

Contact binaries are ubiquitous in the Kuiper Belt. For example, the New
Horizons spacecraft revealed that Arrokoth is a contact binary, which likely
resulted from a low-speed merger of two flattened, spheroidal components
(_Stern et al._ , 2019). Additionally, light curve observations of TNOs
indicate that the contact binary fraction can be 30% or higher  (_Sheppard and
Jewitt_ , 2004; _Thirouin and Sheppard_ , 2018, 2019, 2022; _Noll et al._ ,
2020; _Showalter et al._ , 2021).

It is suggestive to draw connections between these observations and bilobed
comets. Note, however, that: (i) comets are much smaller than most known TNOs,
and (ii) Arrokoth, with its nearly-circular, nearly-ecliptic orbit 44 au from
the Sun, formed well beyond the original formation region of most comets, in a
sparsely populated region of the Kuiper Belt. As discussed in Section 2.1,
present-day comets presumably formed in a massive disk $\sim$20–30 au from the
Sun, became part of the scattering TNO population (at distances of $\sim$
50–1,000 au) for $\sim 4.5$ Gyr, then evolved onto inner solar system orbits.
The size and formation distance of TNOs affect their survival. Arrokoth is
thought to be a pristine planetesimal that formed and survived essentially
unchanged in the low-mass classical belt (_McKinnon et al._ , 2020). Small
comets, instead, are less likely to survive intact, their first obstacle being
the disruptive and shape-changing collisions during the massive disk stage
(_Benavidez et al._ , 2022).

The overall significance of collisions during the disk stage mainly depends on
the disk lifetime, $t_{\rm disk}$. If $t_{\rm disk}\gtrsim 10$ Myr, the great
majority of comet-sized bodies would be disrupted (_Morbidelli and Rickman_ ,
2015), and the size distribution of small bodies would approach the Dohnanyi
slope (_Dohnanyi_ , 1969; _O’Brien and Greenberg_ , 2003). This could explain
the size distribution break observed near $D=100$ km (_Bernstein et al._ ,
2004, 2006; _Fraser et al._ , 2014, and Section 4.3). Any traces of the
original surface morphology would be wiped out: most comets would be fragments
of larger bodies. If $t_{\rm disk}\ll 10$ Myr instead, 67P-sized comets would
avoid being catastrophically disrupted. Smaller impacts, however, could still
cause important shape changes (_Jutzi and Benz_ , 2017).

Catastrophic disruptions (_Schwartz et al._ , 2018) and sub-catastrophic
impacts on elongated and rotating bodies have been modeled to demonstrate the
formation of bilobate comets (_Jutzi and Benz_ , 2017). As the massive disk
was dispersed by Neptune, the collisional probabilities dropped, and the
collision speeds increased from hundreds of m/s to several km/s (_Nesvorný and
Vokrouhlický_ , 2019). It is likely in this situation that each catastrophic
disruption was followed by sub-catastrophic impacts, and each sub-catastrophic
impact – potentially capable of generating a bilobate shape – was followed by
shape-changing impacts. The observed comet shapes could be a complex end
product of this sequence.

As comets evolve into the inner solar system, they become affected by H2O
sublimation torques. Simulations suggest that 67P, and bilobed comets in
general, should often spin up past the breakup limit, fission, and reconfigure
(_Hirabayashi et al._ , 2016). Many new bilobate configurations can be
produced by this process. CO or CO2 sublimation-driven spin-up might be
capable of disrupting a typical JFC even before it reaches the inner solar
system (_Safrit et al._ , 2021). These results highlight the important
relationship between spin and morphology. Adding to that, a spinning bilobed
object also better resists reconfiguration into a more spheroidal body by
small impacts (Jutzi et al. 2017).

There are at least two basic possibilities: (1) small TNOs formed as contact
binaries and these shapes survived, even if with some modifications, such that
TNOs remained bilobed as they dynamically evolve into Centaurs/JFCs; or (2)
the bilobed shapes of JFCs have nothing to do with the formation of TNOs, but
instead were produced by other processes, such as impact disruption, activity
(_Safrit et al._ , 2021), rotational fission, etc., and could reflect the
reaccumulation of fragments. It may be hard to distinguish between these two
possibilities. One option would be to measure the shapes of a large sample of
small TNOs via occultations or lightcurve surveys, and, in the long run, via
spacecraft imaging. This would give us a rough sense of the fraction of
contact binaries in different TNO populations, including the cold classicals.
For example, option (1) could be ruled out if small cold classicals show a
very low contact binary fraction. This would indicate that small planetesimals
in the outer solar system did not form bilobed, therefore pointing toward
evolutionary processes as the primary cause. It is worth pointing out,
however, that the only small TNO we have flown past happens to be bilobed. We
could also expect some information from future surveys about the physical
properties of TNO contact binaries – for example, about the relative size of
individual components in each detected small contact binary – and compare that
with bilobed JFCs and Centaurs. A match would be expected if small TNOs formed
bilobed and the evolutionary processes have only a small effect on the overall
shape.

###  4.3 Size Distributions of TNOs, Centaurs, and JFCs

Here we consider the size-frequency distribution (SFD) of TNOs, Centaurs, and
JFCs. The SFD holds information about the formative, morphological, and
destructive processes that have altered the sizes of these bodies.

The SFD of Trans-Neptunian Objects is almost always estimated from reflectance
photometry of TNOs in well-characterized surveys. The cumulative distribution
of apparent magnitudes $m$, which we will call the luminosity function (LF),
is typically expressed as $\Sigma(<\\!m)\propto 10^{\alpha m}$. Here
$\Sigma(<\\!m)$ represents the surface density in TNOs per square degree on
the sky (usually on the ecliptic) of bodies with magnitudes less than
(brighter than) $m$, and $\alpha$ is the slope of the distribution on a plot
of $\log_{10}{\Sigma}$ vs. $m$. If the TNOs follow a power-law differential
size distribution of the form $dN/dD\propto D^{-q}$, where $D$ is the diameter
of the TNO, and we assume constant albedos, then the _differential_ SFD slope,
$q$, and $\alpha$ are related by $q=5\alpha+1$. The cumulative size
distribution is given by $N(>D)\propto D^{-\gamma}$, where
$\gamma=5\alpha=q-1$ (e.g., _Gladman et al._ (2001)). Correctly converting
from a magnitude distribution to an SFD relies on a number of assumptions,
including (1) the albedo and size distributions are constant and do not depend
on heliocentric distance, (2) shape/lightcurve effects are not important, and
(3) observational biases such as the limiting magnitude of the survey are
accounted for. With these limitations in mind, surveys revealed a steep LF in
the outer solar system for objects brighter than $m_{r}\sim 25$, with slope
$\alpha\sim 0.7$ or $q\sim 4.5$ (_Jewitt et al._ , 1998; _Gladman et al._ ,
1998; _Trujillo et al._ , 2001; _Fraser et al._ , 2008), significantly steeper
than the value of $q$ between 3 and 4 expected for a population in steady-
state collisional cascade (_Dohnanyi_ , 1969; _Matthews et al._ , 2014;
_O’Brien and Greenberg_ , 2003). Deep “pencil-beam” surveys revealed a
shallower LF with slope $\alpha\sim 0.2$ at fainter magnitudes, with a
transition between the bright and faint slopes at a brightness $m_{R}\sim 26$
(_Bernstein et al._ , 2004, 2006; _Fuentes et al._ , 2009; _Fraser and
Kavelaars_ , 2009). This transition is referred to as the “knee” or break
magnitude in the LF.

As surveys and observational techniques improved, more of the discovered
objects were tracked over time, allowing accurate distance measurements and
even dynamical classification of the survey discoveries. We highlight the
Canada-France-Ecliptic Plane Survey, which arguably was the first survey to
provide 100% tracking for all survey discoveries (_Petit et al._ , 2011). This
improvement enabled the first direct measurements of the differential absolute
luminosity function (ALF), $\Sigma\left(H\right)$, where $H=m-2.5\log(\Delta
r)-f(\alpha_{p})$. Here $m$ is the apparent magnitude of a TNO (often in $R$
band), $r$ and $\Delta$ are the TNO’s heliocentric and geocentric distances,
$\alpha_{p}$ is the phase angle, or observer-Sun-TNO angle, in degrees, and
$f$ is a function that describes the decrease in reflectance of a TNO with
increasing $\alpha_{p}$. For the low phase angles for TNOs accessible from the
Earth, $f$ is usually linearly approximated as $f=0.15~{}\alpha_{p}$, where
$\alpha_{p}$ is measured in degrees (see _Alvarez-Candal et al._ , 2016, for
further details). The ability to measure the ALF provided higher fidelity
towards inferring the true underlying SFD.

The shape of the ALF has been characterized by power-law slopes of the form
$\Sigma(H)=10^{\alpha_{H}(H-H_{o})}$, and is known to exhibit three distinct
regions. This functional form has been chosen as a matter of convenience, as
it not only trivially translates to the power-law SFD discussed above, but
also provides a statistically sufficient description of the observations
(_Fraser et al._ , 2014). Formative and collisional processes do not
necessarily favor the production of power-law SFDs (_Li et al._ , 2019, see
chapter by Simon et al.).

The slopes of the ALF of the dynamically excited populations of TNOs are well
described by

$\alpha_{H}\sim\begin{cases}0.2,\text{ for }H_{r}\lesssim 4\\\ 0.87,\text{ for
}4\lesssim H_{r}\lesssim 8\\\ 0.2,\text{ for }H_{r}>8.\end{cases}$ (1)

We show a depiction of this shape in Figure 12. This ALF translates to a size
distribution that is shallow for the largest TNOs ($500\lesssim D\lesssim
2100$ km), with SFD slope $q\sim 2$ for $D\gtrsim 800$ km for a 6% albedo
(_Brown_ , 2008; _Fraser et al._ , 2014; _Nesvorný et al._ , 2017; _Abedin and
Kavelaars_ , 2022).  This part of the size distribution is colloquially
referred to as the _foot_ of the SFD (_Fraser et al._ , 2012). The SFD has a
steep slope $q\sim 5.25$ for objects with $100\lesssim D\lesssim 600$ km and
then becomes shallow again, with $q\sim 2$, for sizes smaller than the knee,
$D\lesssim 100$ km (_Fraser et al._ , 2014). Direct survey constraints on the
SFD much below the knee (e.g., to sizes $D\ll 100$ km) are difficult to gather
due to the faintness of such small objects in reflected light.

Figure 12: A depiction of the measured differential absolute luminosity
function of the dynamically excited TNOs. Each section of the ALF is
approximated by the functional form $\Sigma(H)\propto 10^{\alpha(H-Ho)}$.
Slopes and transition magnitudes are taken from _Fraser et al._ (2014). Object
diameters are shown across the top, and assume a geometric albedo of 6%.

Two separate scenarios for the creation of the SFD of the hot population have
been postulated. Historically, the break at $H_{r}\approx 8$ has been
associated with the size above which catastrophic collisions rarely occur.
That is, since the epoch of formation, collisions have been largely disruptive
due to the high relative velocities between TNOs (e.g., _Dell’Oro et al._ ,
2013). Also, for most of the solar system’s planetesimal populations,
including TNOs, smaller bodies are more numerous, and also easier to disrupt
down to sub-km sizes (_Benz and Asphaug_ , 1999). The net result is that
smaller bodies are more likely to be collisionally disrupted than are
relatively larger bodies (_Bottke et al._ , 2005). It follows that most of the
largest bodies may have avoided disruption. The steep slope for large objects
then is a result of their formation process, originally thought to occur by
hierarchical accretion, and the break diameter reflects the size below which,
on average, all objects have been collisionally disrupted. Numerical
simulations bear out this idea (e.g., _Kenyon et al._ , 2008; _Benavidez and
Campo Bagatin_ , 2009), though recently, this interpretation has fallen out of
favor. It is now thought that the observed break diameter is primordial, not
collisional, in origin. If the break were collisional, the significant
population of binary systems seen in the Kuiper Belt could not have survived
(_Parker and Kavelaars_ , 2010; _Nesvorný and Vokrouhlický_ , 2019).

The alternative idea to the collisional disruption scenario is the so-called
born-big scenario, first put forth to explain the size distribution of the
main-belt asteroids (_Morbidelli et al._ , 2009a), which has also been invoked
to explain the break in the SFD of the Neptune Trojans (_Sheppard and
Trujillo_ , 2010). In this scenario, planetesimals form with a preferred size,
$D\sim 200$ km, in a formation process that is much more rapid than can be
achieved through hierarchical accretion. One possible mechanism rests with the
streaming instability discussed in Section 4.2. In this scenario, the break
diameter reflects the preferred formation size, and the steep SFD at larger
sizes reflects subsequent growth through classical hierarchical accretion.
Notably, this scenario is broadly compatible with the observed properties of
TNO binaries, including the frequency (_Nesvorný et al._ , 2011; _Robinson et
al._ , 2020), orbital distribution (_Grundy et al._ , 2019b; _Nesvorný_ ,
2021), and diameters of TNOs themselves (_Li et al._ , 2019).

In either scenario, the _foot_ of the SFD remains unexplained. This structure
seems similar to expectations from models of runaway growth (_Lithwick_ ,
2014), though that has not been confirmed. It may also be that the foot is
merely a signature of the largest objects that can form through the streaming
instability.

Extension of the SFD to smaller diameters comes from interpretation of the
Pluto, Charon, and Arrokoth cratering records. At diameters $D\gtrsim$ 1–2 km,
the data are consistent with a slope $q\approx 3$ from the knee down to these
sizes. For $D\lesssim$ 1–2 km, the SFD appears to break again at the “elbow”
to an even shallower slope, $q=1.7\pm 0.3$, betraying a relative dearth of
small TNOs with $0.1<D<1$ km, compared with an extrapolation from larger
bodies (_Greenstreet et al._ , 2015, 2016; _Singer et al._ , 2019; _Parker_ ,
2021; _Robbins and Singer_ , 2021; _Singer et al._ , 2021). A robust
explanation of the change in the slope of the SFD near 1 km remains
unavailable.

There is some hint of a so-called _divot_ in the size distribution, just
smaller than the knee diameter. The divot is a purported sudden downward
deviation in the SFD, with fewer objects at sizes just below the break than
above it (_Shankman et al._ , 2013; _Lawler et al._ , 2018b). Such a feature
can result from a population of planetesimals that already has an SFD
reminiscent of that observed (a steep slope followed by a break) that
undergoes a sudden increase in velocity dispersion, such as that experienced
during the onset of planet migration (_Fraser_ , 2009). When the velocity
dispersion rises, objects suddenly have enough kinetic energy to disrupt
larger bodies than those they could shatter previously. Due to the transition
from a steep to shallow distribution at the break, objects larger than the
break see a relative increase in disruption rate than do objects smaller than
the break, with the largest relative increase occurring for bodies of size
just small enough to be disrupted by objects equal to the break radius. The
result is preferential destruction of bodies $\sim 10\times$ larger than the
initial break radius. While the presence of a divot is not statistically
required to match the observed ALF, its presence is compatible with
observations, and, notably, is compatible with expectations of the formative
and dynamical history of TNOs (_Fraser_ , 2009).

For completeness, we point out that the cold population appears to exhibit a
different SFD than do the dynamically excited populations. _Fraser et al._
(2014) found that the largest cold classical objects have $D\sim 400$ km and
fall on the steep part of the SFD, with a slope $q\sim 8$444In terms of
absolute magnitude, the brightest cold classical TNO is 79360 Sila-Nunam (1997
CS29), which has $H=5.29$. Sila-Nunam is a roughly equal-mass binary in which
each component has $D\approx 250$ km (_Grundy et al._ , 2012).. Contrast this
to the hot population SFD: the cold-classical SFD is missing the foot, and is
much steeper brightward of the knee. This implies a significant difference in
formation histories between those TNOs that appear to have formed in-situ, and
those that were scattered outwards during Neptune’s migration. The highest
fidelity measure of the cold-classical SFD (_Kavelaars et al._ , 2021)
demonstrates that this population is not well described by a broken power-law
as in Eq. (1), but rather is better fit by a modified exponential function,
$N(<H)=10^{\alpha_{S}I(H-Ho)}\times\exp^{10^{\beta_{S}I(H-Ho)}}$, similar to
the SFD produced in some simulations of formation via the streaming
instability (_Li et al._ , 2019). For the hot populations, it is likely that
future observations will clarify whether power laws are reasonable
descriptions of the SFD of the hot population.

We also point out a tension in the populations of small, excited TNOs inferred
from the ALF and the Pluto/Charon cratering record with that inferred from
three serendipitous stellar occultations. Taken at face value, the
occultations imply the existence of a population of small, $D\sim 1$ km
excited bodies that is more than an order of magnitude larger than implied
from the former techniques (_Schlichting et al._ , 2012; _Arimatsu et al._ ,
2019; _Parker_ , 2021). A solution to this tension may be the presence of a
very large population of small TNOs beyond $\approx$ 50 au (_Shannon et al._ ,
2021). It may also be the case that there is a population of small objects
with extremely low albedos that have caused them to avoid optical detection.
It may also be that some occultation events are not true detections, but
rather are the result of unknown instrumental artifacts.

Centaurs and Jupiter-family comets provide another opportunity to probe the
small-end size distribution of their parent population in the Kuiper Belt.
However, there are challenges to interpreting observations of both Centaurs
and JFCs. The first arises from the lack of dedicated, well-characterized
surveys, particularly for Centaurs. This is primarily due to the Centaurs’
small numbers, a result of their short dynamical lifetimes on planet-crossing
orbits, and their wide range of ecliptic latitudes owing to their dynamically
hot inclination distribution. Centaurs are thus much less dense on the sky
than TNOs. Most observational surveys are focused on detecting either the
close Near Earth Asteroid population or the more distant TNO populations, so
the biases in the observed Centaur population are typically not well
understood (see, e.g., discussion in _Peixinho et al._ 2020). Another
complication is that JFCs and some Centaurs are active. For such bodies, their
observed magnitudes contain contributions from (and often are dominated by)
the coma, rather than just the nucleus. Astronomers have tried to minimize
coma signal by taking observations when the comets are at aphelion and thus
less active or inactive; however, there is always the possibility of
unresolved coma that nonetheless affects the photometry (_Hui and Li_ , 2018).

With these limitations in mind, does the TNO size distribution match the JFC
and Centaur size distributions? _Lamy et al._ (2004) review data on 65
ecliptic comets with effective diameters between 0.4 and 30 km, and infer a
cumulative size distribution for $D\gtrsim 3$ km with $N(>D)\propto
D^{-\gamma}$, where $\gamma=1.9\pm 0.3$, corresponding to $q\approx$2.6–3.2
for the differential size distribution and $\alpha\approx$ 0.3–0.4 for the
luminosity function. _Lamy et al._ (2004) attribute the shallower size
distribution seen for comets with $D\lesssim$ 3 km to observational
incompleteness and mass loss due to activity. _Meech et al._ (2004), on the
other hand, find that the flatter slope for small comets is not explained by
observational bias.

_Snodgrass et al._ (2011) performed Monte Carlo simulations of the JFC size
distribution, accounting for uncertainties in photometry and the albedo, phase
function, and shape of the nucleus. They inferred $\gamma=1.92\pm 0.20$ for
nuclei with $D>2.5$ km, consistent with _Lamy et al._ (2004).

The largest survey to date of Jupiter-family comets was carried out by
_Fernández et al._ (2013), who observed 89 JFCs with Spitzer and included nine
other JFCs from the literature. They infer $\gamma\approx 1.9\pm 0.2$ for
$D>3$ km, but note that, surprisingly, JFCs with $D>6$ km and $q<2$ au are
still being found. _Fernández et al._ (2013) agree with _Meech et al._ (2004)
that the rarity of small comets is real.555Since the year 2000, the number of
known Near-Earth Asteroids (defined as inactive bodies with $q<1.3$ au) has
increased by a factor of $\approx 30$, while the number of Near-Earth Comets
has less than doubled. These numbers are tabulated by the Center for Near
Earth Object Studies at https://cneos.jpl.nasa.gov/stats/totals.html. Although
biases in the discovery of asteroids and comets differ, the different
discovery rates support the idea that small JFCs are intrinsically rare.
_Jewitt_ (2021) explains the scarcity of small short-period comets as the
result of sublimation torques, which he estimates can spin up comets with
perihelion distances between 1 and 2 au to rotational disruption in
$25(D/1\,{\rm km})^{2}$ years, i.e., only a few orbits. The inferred SFD
slopes for JFCs agree with those commonly adopted for the excited TNO parent
populations, but the SFD of the Jupiter Trojans is more commonly used as a
proxy for the TNO SFD for comet-sized bodies, as more Trojans are known than
JFCs, and Trojans are inactive  (_Jewitt et al._ , 2000; _Yoshida et al._ ,
2019, 2020).

Using data from the Deep Ecliptic Survey, _Adams et al._ (2014) found
$\alpha=0.42\pm 0.02$ (i.e., $\gamma=2.1\pm 0.1$) for seven Centaurs with
absolute magnitudes between 7.5 and 11, corresponding to 30 km $\lesssim
D\lesssim 170$ km for an assumed albedo of 0.06. OSSOS discovered 15 Centaurs
with $a<30$ au, $q>7.5$ au, and $H_{r}<13.7$ (i.e., $D>10$ km for an albedo of
0.06). _Nesvorný et al._ (2019b) found that his planetary instability models
predicted $11\pm 4$ such Centaurs if he assumed $\gamma=2.1$, similar to the
slope inferred for small Trojans (_Wong and Brown_ , 2015). In general, the
debiased SFDs of the JFCs and Centaurs are consistent with those measured for
the TNO populations that feed the JFCs, but a detailed comparison cannot yet
be made. We discuss this in Section 5.

##  5 Outstanding Questions and Future Prospects

In this section, we highlight three outstanding questions regarding TNOs and
their link to cometary populations. We point out the anticipated contributions
of certain new and upcoming telescope facilities that should provide
significant leaps forward in our understanding of these questions. This list
should in no way be considered impartial or complete, but rather reflects
problems that the authors find particularly pertinent.

The first outstanding problem we wish to highlight regards the compositions of
TNOs, and by extension the Centaurs and JFCs that are fed from the Kuiper
Belt. As expressed in Section 3.1, despite more than 25 years of observations
by the astronomical community, very little is known about the surfaces or
internal compositions of TNOs. We are still ignorant of the nature of the
reddening agent responsible for the colors of these icy bodies. Moreover,
beyond a couple of exceptions, no detection has been made of signatures of the
silicate materials that must be present on and inside TNOs.

Figure 13: Spectra of various laboratory materials through the optical and NIR
spectral range, reproduced from _Fernández-Valenzuela et al._ (2021).
Photometric bands of the Johnson-Cousins system which are accessible from
ground-based facilities, as well as the Spitzer-IRAC 3.6 and $4.5\mbox{
$\mu$m}$ bands, are shown.

The main reason for this sad state of affairs is the lack of identifying
absorption features in the optical and NIR atmospheric transmission regions.
It seems that whatever materials are present on the surfaces of TNOs, they
mutually mask any features that fall in this wavelength range. See, for
example, the spectral model of the Centaur Pholus in Figure 8, where tholin
and olivine mask the strong absorption features each would exhibit on their
own.

Longer wavelengths hold the potential to reveal some strong absorption
features. For example, many of the ice species known or suspected to exist on
TNOs exhibit deep and broad absorption features in the
$2.5\lesssim\lambda\lesssim 4.5\mbox{ $\mu$m}$ range (see Figure 13). This
spectral region is very difficult to observe for these faint bodies with
current technology, especially ground-based because of contamination from the
Earth’s atmosphere. It is for this reason that JWST holds the massive
potential to revolutionize our knowledge of the compositions of TNOs.

Most insight into the compositions of TNOs will come from spectral
observations with the JWST-NIRSpec instrument, which will provide
unprecedented sensitivity across a critical wavelength range out to 5 $\mu$m.
In Figure 14 we reproduce a figure from _Parker et al._ (2016), which presents
three different spectral models, all of which are broadly compatible with the
spectrum of the distant dwarf planet (90377) Sedna. Each model is wildly
different in their compositional makeup, but are nearly indistinguishable in
reflectance spectra at wavelengths $\lambda\lesssim 2.5\mbox{ $\mu$m}$. At
longer wavelengths, spectra from NIRSpec will be particularly useful in
diagnosing a surface as organic-rich or organic-poor, as the C-H and C-N
vibrational fundamental and overtone bands fall in this range (see _Roush and
Dalton_ , 2004; _Izawa et al._ , 2014, for recent discussions). Icy species,
including H2O, CH3OH, CH4, N2, CO, and CO2, also exhibit absorption features
in this range that should be readily apparent in high-quality NIRSpec
observations (see Figure 13 of this chapter, and Figure 4 of _Fernández-
Valenzuela et al._ , 2021).

Figure 14: Spectral models of the TNO (90377) Sedna, using the silicate
pyroxene, the organic material Titan tholin, CH4, and amorphous carbon, and N2
and H2O ices. Reproduced from _Parker et al._ (2016).

Longer wavelength spectra in the mid-infrared range $5<\lambda<28\mbox{
$\mu$m}$ will come from the JWST-MIRI instrument, where fine-grained silicate
materials exhibit emission features (_Martin et al._ , 2022). While objects in
the Kuiper Belt are too distant, and therefore too faint, for observations
with MIRI, many Centaurs should be bright enough. Spitzer observed 20 Centaurs
in the mid-infrared (_Lisse et al._ , 2020), but obtained spectral data over
the range 7.5–38 $\mu$m for only one, (8405) Asbolus (_Barucci et al._ ,
2008). That spectrum, which suggests the presence of fine-grained silicates on
the Centaur’s surface, is broadly similar to the spectra of three Jupiter
Trojans observed by Spitzer (_Dotto et al._ , 2008).

Unfortunately, the low signal-to-noise of Spitzer’s spectrum of Asbolus makes
it impossible to infer the nature of its putative silicates.  The MIRI spectra
should be of sufficient quality to not only definitively identify silicate
emissions on many Centaurs, but also to identify specific properties of the
silicates, such as whether those silicates are amorphous or crystalline in
nature.

With regard to the volatile component, the JWST NIRSpec-IFU spectrograph is
likely to either detect CO2 emission in active Centaurs, or set strong upper
limits, possibly up to two orders of magnitude less than the limit of
$3.5\times 10^{26}$ for 29P achieved by AKARI (_Ootsubo et al._ , 2012) [A.
McKay, personal communication]. In addition, CO and H2O emission will also be
reachable with the instrument (see Figure 15). As discussed in Section 4.1,
CO2 is reduced with respect to CO in the comae of objects beyond 3 au, a trend
that increases with heliocentric distance (Harrington Pinto et al., under
review). Thus, if other Centaurs are like 29P, then their comae may be also
remarkably depleted in CO2. JWST will be capable of detecting the 1.5, 2.0 and
3.0 $\mu$m bands of water, with the 3-$\mu$m band being the one most likely to
be detected in the comae of active Centaurs, and the 2-$\mu$m band being the
next likely.

Figure 15: Predicted JWST NIRSpec model gas emissions for an active Centaur
with a similar coma compositional profile as 29P (A. McKay, personal
communication). The model was calculated using the NASA Planetary Spectrum
Generator (https://psg.gsfc.nasa.gov/ _Villanueva et al._ (2018)) assuming
AKARI production rates for CO and H2O from (_Ootsubo et al._ , 2012) and
inferred Q(CO2) from Harrington Pinto et al. (under review).

An important, unanswered question about Centaur gaseous comae is whether
comparing the CO, CO2, and H2O mixing ratios in cometary and Centaur comae is
indeed a good match to compositional models of nuclei, or instead is more
influenced by outgassing behavior at different heliocentric distances, due to
differences in sublimation of the two species. This is a significant
opportunity for the modeling community.

The second outstanding problem we wish to highlight is the discrepancy between
the SFD of the JFCs and that predicted from our knowledge of the source
populations feeding the JFCs (see Sections 2.1 and 2.2). While the slopes of
the SFDs between the two populations seem to align (Section 4.3), there still
appears disagreement between the availability of the source populations, and
the observed density of JFCs. This problem was highlighted by _Volk and
Malhotra_ (2008), who found that TNOs following the _Bernstein et al._ (2004,
2006) SFD for faint TNOs could produce only $\approx$ 1% of the observed JFCs.
While modern models of the supply of JFCs from the TNOs match the orbital
distributions of the comets well (e.g. _Di Sisto et al._ , 2009; _Brasser and
Morbidelli_ , 2013; _Nesvorný et al._ , 2017), the problem of directly,
quantitatively linking the TNO and JFC population remains frustrated by
several factors: the imprecise measurement of the SFDs of the scattered disk
objects and other TNO populations, especially down to comet-sized objects; the
unknown ratio of active to inactive JFCs, i.e., the fading problem discussed
in Section 4.3; and the incomplete knowledge of the orbital structure of the
most distant TNO populations and the interplay between the scattering and
detached populations (discussed in Section 2.3).

The Vera C. Rubin Telescope’s Legacy Survey of Space and Time (LSST) will
provide many key insights towards resolving this problem. One of the major
advances from LSST will be a much improved census of the solar system’s small
bodies, down to a brightness threshold of $r\sim 24.5$, with well-understood
observational biases. LSST will increase the inventory of known TNOs with
well-determined orbits by at least an order of magnitude, detect large numbers
of comet-sized ($d\lesssim 10$ km) Centaurs, and increase the observed JFC
population (_LSST Science Collaboration et al._ , 2009). These observations
will yield important new constraints on the detailed orbital distributions of
all three populations. LSST will also provide 10 years of monitoring for each
discovered JFC and Centaur, on a 4–8 day cadence. This monitoring will be
fundamental in detecting the onset and turnoff of activity as comets move
between aphelion and perihelion, and measuring the vigor of the activity. It
will also yield improved insights into the beginning stages of activity in the
Centaur region. Importantly, the monitoring will enable a robust derivation of
the SFD of JFCs when they are inactive, which is what is required to make a
robust comparison with the Centaur and TNO populations.

A final issue is the possible presence of bodies more massive than Pluto and
Eris (0.002–0.003$M_{\oplus}$) in the distant Kuiper Belt. Even with its
sublunar mass, Pluto can destabilize bodies in the 3:2 MMR (_Nesvorný et al._
, 2000). _Gladman and Chan_ (2006) investigated how an Earth-mass body, ten
Mars-mass bodies (each $\approx 0.1M_{\oplus}$), or both would raise the
inclinations and perihelion distances of some objects in the primordial Kuiper
Belt and produce detached bodies like Sedna. _Lykawka and Mukai_ (2008)
proposed that a planet with mass $\approx 0.5M_{\oplus}$ excited the early
Kuiper Belt and evolved into a stable orbit with $a>100$ au, $q>80$ au, and an
inclination between 20 and 40∘. _Trujillo and Sheppard_ (2014) discovered a
TNO, 2012 VP113, with $a\approx 266$ au and a perihelion distance even larger
than Sedna’s, $q=80$ au. They noted that the twelve TNOs with $a>150$ au and
$q>30$ au appeared to cluster in argument of perihelion, and proposed that a
2–15M⊕ body could produce the clustering. This idea is now known as the
“Planet Nine” hypothesis (_Batygin et al._ , 2019; _Brown and Batygin_ , 2021)
and invokes a 5–-10$M_{\oplus}$ body with a perihelion distance $\approx 300$
au to shape the orbits of TNOs with $a>250$ au. Such a planet would even
affect the orbital distributions of JFCs and HTCs (_Nesvorný et al._ , 2017).
Well-characterized TNO surveys (_Shankman et al._ , 2017; _Kavelaars et al._ ,
2020; _Napier et al._ , 2021) find that the orbital distribution of “extreme”
TNOs does not require the existence of Planet Nine, but neither can it (or
less massive perturbers) be ruled out. Assuming an albedo between 0.20 and
0.75, _Brown and Batygin_ (2021) predict that Planet Nine’s most likely R
magnitude is $\approx 20$, but it could be as faint as magnitude 25. Searches
in the far-IR with archival IRAS and Akari data have also been carried out
recently (_Rowan-Robinson_ , 2022; _Sedgwick and Serjeant_ , 2022).
Observations in the next decade with the Vera Rubin Observatory and other
large telescopes such as Subaru, the VLT, and Gemini should clarify the
orbital distribution of distant TNOs and may finally detect the long-
speculated trans-Neptunian planet.

Acknowledgments

KV acknowledges support from NSF (grant AST-1824869) and NASA (grants
80NSSC19K0785,
80NSSC21K0376 and 80NSSC22K0512). LD thanks the Cassini Data Analysis Program
for support. DN would like to acknowledge support from the Emerging Worlds
program. This material is based in part on work done by MW while serving at
the National Science Foundation. We’d especially like to thank Rosita
Kokotanekova and Alan Fitzsimmons for their verbal contributions to this
chapter. We thank Adam McKay and Gareth Williams for useful discussions. We