# Formation of Comets

Jürgen Blum
Institute for Geophysics and Extraterrestrial Physics
Technische Universität Braunschweig
Mendelssohnstraße 3, 38106 Braunschweig, Germany
<EMAIL_ADDRESS>
&Dorothea Bischoff
Institute for Geophysics and Extraterrestrial Physics
Technische Universität Braunschweig
Mendelssohnstraße 3, 38106 Braunschweig, Germany
&Bastian Gundlach
Institute for Geophysics and Extraterrestrial Physics
Technische Universität Braunschweig
Mendelssohnstraße 3, 38106 Braunschweig, Germany

###### Abstract

Questions regarding how primordial or pristine the comets of the solar system
are have been an ongoing controversy. In this review, we describe comets’
physical evolution from dust and ice grains in the solar nebula to the
contemporary small bodies in the outer solar system. This includes the phases
of dust agglomeration, the formation of planetesimals, their thermal evolution
and the outcomes of collisional processes. We use empirical evidence about
comets, in particular from the Rosetta Mission to comet
67P/Churyumov–Gerasimenko, to draw conclusions about the possible thermal and
collisional evolution of comets.

_K_ eywords comets; formation of planetesimals; evolution of planetesimals

##  1 Introduction

Comets are believed to be the most pristine objects of our solar system. They
consist of several ices, mainly water ice but also super-volatiles such as CO
or CO2 ice, as well as refractory materials such as minerals, organics and
salts. This composition obviously results in cometary gas and dust if the
insolation is intense enough. In principle, a comet becomes dust-active if the
outgassing rate is large enough to release dust particles against holding
forces such as gravity and cohesion [1]. However, the exact physical mechanism
of the ejection of dust is not yet well understood. Additionally, several
aspects of the formation and evolutionary pathways of comets are still under
debate. In this work, we provide a detailed overview of how icy planetesimals
may have formed in the protoplanetary disc (PPD) and may have evolved into
present-day bodies of the solar system, including comets. In Figure 1, we
provide a graphical overview of the formation and evolutionary stages from
protoplanetary dust to the contemporary small bodies in the solar system; we
explain the stages in detail in the following sections. A more detailed
version of Figure 1 can be found at https://www.tu-
braunschweig.de/fileadmin/Redaktionsgruppen/Institute_Fakultaet_5/IGEP/AG_Blum/Comet_Formation.pdf
(accessed on 5 May 2022) and in the Supplementary Materials. In Section 2, the
coagulation processes of the dust and ice particles are summarised, beginning
with an overview of protoplanetary discs. In this work, we use the
nomenclature proposed by Güttler et al. 2019 [2]. When referring to particles,
their sizes are not further constrained. However, (dust or ice) grains are
restricted to the (sub-)micrometre size range and are assumed to be
homogeneously composed of one material only. Agglomerates consist of grains
and can be heterogeneous in composition. The hit-and-stick growth of particles
stops at growth barriers where pebbles, millimetre- to decimetre-sized porous
agglomerates, are formed. Section 3 discusses the formation of planetesimals
from pebbles via streaming instability and subsequent gravitational collapse.
The required properties of the particles and the protoplanetary disc, as well
as other scenarios, are briefly discussed. The different evolutionary
processes that can alter the formed planetesimals are then presented in
Section 4. The formation processes in combination with evolutionary
alterations result in three different categories of evolved planetesimals: icy
pebble piles, icy rubble/pebble piles and non-icy rubble piles, which can be
further subdivided depending on the evolutionary processes. In Section 5, we
discuss the properties of possible contemporary end products of the evolution
and compare them to observations of comets in the solar system to connect them
to the formation and evolution pathways. Finally, we summarise the paper and
discuss open questions in Section 6.

It must be emphasised that we only provide one plausible, but not the only
possible scenario for the formation of planetesimals and evolution into
comets. This model heavily relies on the existence of pebbles, for which only
indirect evidence exists [3].  Alternative planetesimal-formation models exist
and are discussed in detail by Weissman et al. 2020 [4].

Figure 1: This overview is a graphical representation of the formation and
evolution of planetesimals beyond the H2O snowline. The blue and green
backgrounds denote objects and processes, respectively. Each step is explained
and discussed in the paper. A detailed version can be found at https://www.tu-
braunschweig.de/fileadmin/Redaktionsgruppen/Institute_Fakultaet_5/IGEP/AG_Blum/Comet_Formation_detailed.pdf
(accessed on 5 May 2022) and in the Supplementary Materials.

##  2 From Dust To Pebbles

###  2.1 Protoplanetary discs

Directly connected to the formation of a star from the gravitational collapse
of a molecular cloud is the formation of a protostellar disc, which then
evolves into a PPD within $\sim$$10^{4}$ years [5, 6]. This process is
initially connected to high temperatures, but while material from the disc
gets accreted by the star, temperature and mass decrease. This transition from
a protostellar to a protoplanetary disc lasts about $\sim$$0.5$ Myrs for a
solar-type star and is determined by the complete dispersion of the envelope,
resulting in a disc mass of a few percent of the mass of the central star [7].
The following evolution of the disc is dominated by the ongoing accretion of
material onto the star, photoevaporation, dust agglomeration and dynamical
interactions with the stellar or galactic environment. Properties of
protoplanetary discs are traditionally observed by optical or near-IR methods.
With the Atacama Large Millimeter/submillimeter Array (ALMA), a new era of
observation of protoplanetary discs has started. ALMA has shown, due to its
high angular resolution and sensitivity, detailed substructures of PPDs,
namely spirals, gaps, axisymmetric rings and inner cavities [8, 9, 10], which
were unexpected from the traditional view of PPDs [11]. Several ideas have
been proposed to explain these structures, e.g., interaction with planetary
bodies, which are beyond the scope of this review. Protoplanetary disc masses
can be constrained by ALMA measurements using different methods. For example,
the mass of solids in millimetre-sized dust grains can be estimated from the
millimetre flux density combined with assumptions about the optical depth,
dust opacity and disc temperature (e.g., [12, 13, 14, 15, 16, 17]). Another
method uses the amplitude and wavelength of gravitational instability wiggles
[18]. The total dust masses and typical PPD sizes seem to correlate, as low-
mass discs are generally smaller than massive discs [19, 8, 20].

When the temperatures inside the PPD have sufficiently dropped, submicrometre-
to micrometre-sized solid particles start to condense. The condensation
sequence depends on the local temperature and pressure in the disc (see [21]
for a list of condensation temperatures for several elements). Complex 2D
models describe the chemical evolution of PPDs and the different material
compositions in different regions of the disc (e.g., [22] and references
therein). For example, forsterite, enstatite, olivine, pyroxene and quartz are
important minerals, whose abundances can be compared to meteoritic and
cometary dust compositions (e.g., Figure 11 in [23]).

For water ice, the critical temperature of condensation is between
$145\,\mathrm{K}$ [24] and $170\,\mathrm{K}$ [25], depending on the assumed
local pressure. However, the locations of the snowlines of various ice species
can vary due to several processes in the disc [26, 27, 28]. It has also been
argued that the condensation of volatile gases onto refractory grains at the
position of the respective snowlines can be a possible growth mechanism for
solid bodies [29]. The processes acting on dust and gas in PPDs are key
elements to understand planetesimal formation. While gasses (mostly H2 and He)
dominate the mass of the PPD, the dust is essential for the formation of the
first larger solid bodies. The effects behind dust growth will be presented in
the following.

The orbital gas velocity in PPDs is reduced below the Keplerian speed because
the negative radial gas-pressure gradient counteracts the gravitational pull
of the star. Because solid material is not pressure-supported, dust particles
should orbit the central star with Keplerian velocity. However, as they
experience a headwind due to the slower-rotating gas, a drag force acts on the
particles. This drag can be described by the Epstein drag law for particles
that are smaller than the mean free path of the gas. For particle size
exceeding the mean free path of the gas, the Stokes regime becomes relevant
for the gas drag. The gas drag acting on dust particles is best described by
the stopping time, which can be written as

$\tau_{f}=\begin{cases}\frac{R\,\rho_{p}}{c_{s}\,\rho_{g}}&\text{in the
Epstein regime},\\\
\frac{4\,\rho_{p}\,R^{2}}{9\,c_{s}\,\rho_{g}\lambda}&\text{in the Stokes
regime.}\end{cases}$ (1)

Here, $R$, $\rho_{p}$, $c_{s}$, $\rho_{g}$ and $\lambda$ are the particle
radius, particle density, gas sound speed, gas density and mean free path,
respectively. The Stokes number as a common measure of particle sizes in PPDs
is defined as

$St=\Omega\,\tau_{f}\,$ (2)

with the Keplerian frequency $\Omega$. Particles with the same Stokes number
behave aerodynamically similar. For a given PPD model and a fixed heliocentric
distance, the Stokes number corresponds to a specific value of $R\,\rho_{p}$
or $R^{2}\,\rho_{p}$, depending on the flow regime (see Equation (1)). Thus,
for a fixed value of the mass density of the dust particle, the Stokes number
represents the particle size. Hence, particles with different sizes (or Stokes
numbers) obtain different speeds at the same heliocentric distance, which
leads to relative velocities among the solid particles and, consequently, to
collisions.

The frictional interaction of gas and dust and the subsequent sub-Keplerian
speed of the dust particles result in an inward drift of the dust, with radial
velocities depending on Stokes number (i.e., particle size). Very small and
very large objects possess radial velocities that are very small; the maximum
radial speed is reached for dust particles with $St=1$. In general, dust
drifts towards higher gas pressures, which also applies for vertical settling
towards the disc midplane or local pressure bumps.

Turbulent gas motion influences the dust motion as well. Quantitatively, the
turbulence of a disc can be described by the turbulent strength parameter
$\alpha$. Qualitatively, gas turbulence can lead to collisions among the dust
particles as well as to particle transport. Thus, thermally processed
particles from the inner disc might be transported in- or outward due to
turbulence, which leads to radial mixing of the dust species formed at
different temperatures.

For very small, i.e., sub-micrometre to micrometre-sized, grains, Brownian
motion may also be responsible for very-low-speed collisions. Due to the
Maxwell–Boltzmann distribution of the mean thermal kinetic energy of the
grains, equal-sized particles can also collide due to Brownian motion [30].

###  2.2 A Growth Scenario from Grains to Pebbles

When dust or ice particles collide, the outcome depends on material
properties, particle size and collision velocity [31, 32, 33, 34, 35, 36, 37,
38]. The relative velocities between the grains, the number of particles of a
given size and the collisional cross-sections determine the number of
collisions per unit time. The collision velocities result from the processes
that induce the relative motion between dust and gas (see Section 2.1). For
radial, azimuthal and vertical drift, the velocity between dust and gas
depends on particle size; hence, only particles of different sizes collide,
because particles of equal size move with the same speed. However, equally
sized particles can collide in case of stochastic motion, as induced by
Brownian motion or gas turbulence.

When particles of comparable size collide, the outcome can be sticking,
bouncing, abrasion or fragmentation. Sticking always occurs when the collision
energy is small compared to the van der Waals binding energy of the formed
contact [32]. In collisions at higher impact energies, the outcome is
determined by the degree of inelasticity, which can be a function of
temperature [39, 40].

The hit-and-stick process can be accompanied by deformation and compaction
[37]. However, in the ultra-low velocity regime, compaction does not occur,
and the growing agglomerates develop a fractal structure [32, 41, 42, 43, 44],
with a fractal dimension of $D_{f}\lesssim 1.9$ [32, 42, 45, 35]. For higher
collision speeds, the fractal dimension may increase to $D_{f}\thickapprox
2.5$ [35] or even to the limit of $D_{f}\thickapprox 3.0$. High-speed
collisions can lead to fragmentation of the agglomerates [46, 47, 48, 49, 50].
The mass ratio of the largest fragment to the initial mass decreases with
increasing collision speed [50]. In the transition regime between sticking and
fragmentation of similar-sized aggregates, bouncing occurs [46, 51, 52, 53,
54, 55]. Bouncing collisions are inelastic and result in compaction.
Successive bouncing events result in a volume-filling factor of the packing of
$\sim$$0.36$ [56]. We refer to these particles as porous agglomerates.

When a small aggregate (projectile) hits a larger one (target), along with the
outcomes mentioned above, mass transfer, cratering and erosion are also
possible. Mass can be transferred from the projectile to the target, while the
projectile fragments [57, 58, 59, 37, 60, 47, 61, 62, 50]. The mass-transfer
efficiency reaches from a few percent to roughly $50$ percent of the
projectile’s mass, and the mass-transfer process leads to compaction of the
target, with typical volume-filling factors of $0.3$ to $0.4$ [60, 61]. For
smaller size ratios between projectile and target, cratering occurs instead of
net mass transfer. In this case, more mass is lost in the form of ejecta than
transferred to the target [63, 64]. The relative mass loss of the target
agglomerate mainly depends on the impact energy [50] and material strength,
and can be up to $35$ times the projectile mass [63, 64]. For very small
projectile-to-target size ratios, erosion (mass loss without a visible crater)
has been experimentally observed for silica dust [48, 38] and water ice [40],
and has also been numerically studied [65, 66]. The efficiency of erosion
depends on the impact velocity and the projectile mass [38].

In general, all mentioned processes depend on material and disc properties,
e.g., monomer-grain material and size distribution, PPD model, turbulence
strength and distance to the central star. Different materials can differ
significantly in properties, such as sticking threshold or tensile strength,
as shown, e.g., for organic materials [67]. This was also observed for
collisions of “interstellar organic matter analogues”, which showed enhanced
stickiness around $250\,\mathrm{K}$, but less sticking for lower or higher
temperatures [68, 69]. For $\mathrm{CO_{2}}$, the sticking threshold seems to
be comparable to that of silica [70]. Recently, Arakawa et al. 2021 [71]
reconciled the different experimental results on the sticking–bouncing
threshold for water ice, carbon-dioxide ice and silica particles. Besides the
surface energy (closely related to the tensile strength) of the material, the
visco–elastic dissipation of energy is the essential material property, and is
much larger for water ice at low temperature than for the other two materials.
Hence, water ice sticks at higher velocities than carbon dioxide or silica
particles of the same size, in agreement with laboratory results [40].

Several barriers prevent the further collisional growth of dust agglomerates
to kilometre-sized planetesimals. The most important ones will be briefly
described below.

First, drift of particles into the central star, caused by the friction
between dust and gas, is a limiting factor. The drift efficiency depends on
particle and disc properties, with a drift time scale of

$t_{d}=a/v_{d}=a/(2\,\mathrm{St}\,v_{\mathrm{max}}).$ (3)

Here, $a$, $v_{d}$, $\mathrm{St}$ and $v_{\mathrm{max}}$ are the heliocentric
distance, radial drift velocity, Stokes number of the dust particle and
maximum deviation of the orbital gas velocity from Keplerian velocity,
respectively. Equation (3) is valid for $\mathrm{St}\leq 1$, and typical
values for $v_{\mathrm{max}}$ are $50\,\mathrm{m/s}$ [31]). This barrier
provides a critical time constraint for the formation of planetesimals. The
maximum radial drift velocity of $2\,v_{\mathrm{max}}$ is reached for bodies
with $\mathrm{St}=1$, which means such particles possess drift timescales on
the order of $t_{d}\approx 100\,\mathrm{yr}$ for $a=1\,\mathrm{au}$. This
timescale is usually much shorter than the collisional growth time beyond
$\mathrm{St}=1$.

Second, the so-called bouncing barrier stops growth when the sticking–bouncing
threshold is reached and the colliding aggregates bounce off. Due to the
inelasticity of the bouncing process, compaction of the aggregates occurs [56,
72, 73]. The bouncing barrier is reached at aggregate sizes of millimetres to
centimetres, depending on the particle and disc properties [72, 73]. The
resulting agglomerates have been termed “pebbles”. The largest pebbles are
achieved in the minimum mass solar nebula model [72]. For increasing
heliocentric distance or increasing dust-to-ice ratio, the maximum pebble size
decreases and the pebbles become more porous [73]. Millimetre- to centimetre-
sized solid particles have been observed in PPDs [74, 75, 76, 77, 78, 79, 80,
81, 82, 83].

Third, even if the bouncing barrier can be overcome, further growth is halted
because collisions result in destruction of the aggregates. Fragmentation
typically happens at collision speeds of $\gtrsim$1 m/s [34].

Fourth, recently, the erosion barrier was experimentally discovered [38].
Erosion is present when dust grains, or small aggregates thereof, impinge
larger dust aggregates at high speeds. In this case, impacts liberate other
grains from the aggregate surfaces so that the mass of the aggregates is
slightly reduced. Numerical simulations have shown that this erosion is a
runaway effect even if all other other collisions are assumed to result in
sticking. Due to the erosion barrier, maximum aggregate sizes are on the order
of $0.1\,\mathrm{m}$ [38].

Particles in the weakly ionized disc can carry a nonzero negative charge,
which also influences the collisional behaviour. Due to the asymmetric
distribution of charges, a repulsive force acts between the particles,
hindering sticking [84, 85, 86]. This effect is called the electrostatic
barrier. It can already halt growth at sizes of fractal agglomerates [85].
When taking the photoelectric effect into account, a layer of uncharged dust
can build up, which might overcome the electrostatic barrier [87]. However, in
low turbulence regions of the disc, such as the dead zone, growth can be
effectively suppressed [88]. Numerical models have also shown that the charge
of the particles influences growth rate, size and compactness, as highly
charged particles grow to larger sizes and get more compact [89], which
influences the bouncing and fragmentation thresholds. This may lead to a
bridge between bouncing barrier and pebble sizes required for streaming
instability, as indicated by experimental and numerical work [90] and could
therefore also be beneficial for growth. However, the electrical charging of
particles and its influence on the growth process need to be studied further
to understand the whole picture.

To summarise, the formation of pebbles, millimetre- to centimetre-sized
agglomerates of microscopic dust and ice grains, can be understood with
current empirical knowledge about the collision behaviour of protoplanetary
dust. However, any further growth seems impeded by the presence of a number of
barriers, which — at the current stage of research — makes the direct growth
of planetesimals impossible. Thus, other processes that lead to the formation
of planetesimals are required. In the next Section, we show how this might be
possible.

##  3 Collapse of Pebble Clouds into Planetesimals

###  3.1 Pre-concentration of Pebbles

Regions of enhanced concentration of pebbles can be formed in eddies, vortices
and pressure bumps of turbulent PPDs [91]. Vortices and pressure bumps can be
caused by several phenomena, e.g., magneto-rotational instability [92],
baroclinic instabilities [93, 94], tidal forces of early formed planets and
gaps induced by them [95], the edges of the dead zone [96] and snow lines
(e.g., [97]). For example, in the transitional disc IRS 48, large-scale vortex
structures with a concentration of millimetre-sized pebbles were observed
[98].

Turbulent rotating structures can be described by their spatial dimension $l$,
their rotation velocity $v_{e}$ and their turnover time $t_{e}=l/v_{e}$. For
example, particles with stopping times of $\tau_{f}\thickapprox t_{e}$ are
efficiently concentrated in high-pressure regions between eddies, which
results in a narrow size range for such concentrated particles. Coriolis force
and shear are dominant on larger timescales. In such cases, particles with
$\tau_{f}\sim(2\Omega)^{-1}\ll t_{e}$ are efficiently trapped, independent of
the eddy turnover time. When also taking Keplerian shear into account, the
optimal stopping time is $\tau_{f}=\Omega^{-1}$. The radial drift speed can
then be deduced from the eddy velocity, and reads

$v_{r}=-\frac{2\Delta v}{St^{-1}+St}\,.$ (4)

Here, the local value of $\Delta v$ is important. For example, if $\Delta
v=0$, i.e., in pressure bumps, the particles are being concentrated [91].

###  3.2 Further Concentration of Pebbles by the Streaming Instability

Due to the concentration of particles as described above, the collective
surface-to-mass ratio of a pebble cloud is reduced and consequently also the
gas drag. If the local dust-to-gas mass ratio exceeds unity, streaming
instability is triggered and concentrates the pebbles further [99]. The
velocity of the pebble cloud reaches Keplerian velocity, and radial drift is
reduced. As a back-reaction by the pebble ensemble, the gas is forced to move
at Keplerian velocity. Individual pebbles or small pebble clusters on the same
orbit, which still move at reduced speed due to gas friction, are overtaken by
the pebble cloud. Inward-drifting pebbles are also incorporated into the
pebble ensemble when crossing the respective orbit. Thus, the mass of the
pebble cloud rapidly grows over a short timescale. An upper limit of the
growth timescale was found to be $\sim$$10^{5}$ years [100]. The length scale
of streaming instability is typically 5 percent of the gas scale height [101],
and a dust concentration of up to several thousands can be reached [102, 103].
The threshold when streaming instability is triggered can also be expressed by
the metallicity $Z=\sum_{peb}/\sum_{g}$, i.e., the surface density ratio of
pebbles and gas. For Stokes numbers $St\thickapprox 0.1$ (which corresponds to
pebble sizes of $\sim$0.1 $\,\mathrm{m}$ at $1\,\mathrm{AU}$ and
$\sim$$1\,\mathrm{mm}$ at $100\,\mathrm{AU}$), a minimum metallicity of
$Z_{\mathrm{min}}\thickapprox 0.015$ is required, and $Z_{\mathrm{min}}$
increases for larger and smaller Stokes numbers [99, 104]. As the solar
metallicity is $Z=0.0134$ [105], enhancement in $Z$ by partial dissipation of
nebula gas might be required (see discussion in [106]). However, recent
results show the possibility for particle clumping due to streaming
instability for smaller metallicities [107]. Substructures of the concentrated
regions have been observed in computer simulations [103]. The resilience of
streaming instability was investigated by Carrera et al. 2021 [108], who found
it to be very robust for centimetre-sized pebbles and in the case of only weak
pressure bumps.

Most studies assume monodispersed pebble sizes. However, this is certainly an
academic assumption. Recent works on streaming instability with polydispersed
pebble sizes show that the size–frequency distribution has an important
influence on, e.g., the parameters for instability and growth time scales
[109, 110, 111, 112, 113]. Additionally, including turbulence reduces the
growth rates compared to laminar discs [114] and increases the critical
metallicity, depending on Stokes number, needed to trigger streaming
instability [104].

###  3.3 Gravitational Collapse

If the mass concentration of the pebble cloud reaches the Roche density

$\rho_{R}=\frac{9\Omega^{2}}{4\pi G}$ (5)

with gravitational constant $G$, gravitational collapse occurs, as described
by Johansen et al. 2014 [91].

The cloud collapses into a gravitationally bound body. Whether the pebbles
survive the collapse depends on the mass of the pebble cloud. Pebbles can be
destroyed either during collisions in the free-fall phase or upon impact on
the surface of the forming planetesimal [50, 115]. Moreover, the hydrostatic
pressures inside the planetesimal can also destroy the pebbles [116]. Thus,
the integrity of the pebbles is only guaranteed for low-mass planetesimals.
Estimates on the strength of pebbles have shown that this criterion is
satisfied for planetesimals with radii $\lesssim 50\,\mathrm{km}$. Size
sorting during the collapse could lead to stratification of the pebble size
inside a planetesimal [117]. It has been argued that during the collapse, the
pebbles may capture smaller dust/ice particles, including those still in the
fractal growth stage [118]. If the pebbles survive the collapse intact, the
pore spaces between the pebbles may not be entirely empty.

The radii of planetesimals formed by streaming instability with gravitational
collapse are predicted to be between 50 and 1000 km, depending on the place of
birth in the PPD and the disc properties [119, 120, 121, 103, 122, 123, 124,
125]. With increasing disc mass, the formed planetesimal sizes increase [103].
The resulting mass–frequency distribution function of planetesimals can be
fitted with a power law with exponent $-1.6\pm 0.1$ [126, 127, 128], but it
was also found that an exponentially truncated power law with a low-mass slope
of $-1.3$ fits better [129]. Klahr and Schreiber 2020 [125] discuss that a
Gaussian distribution of the initial planetesimal size could provide a
reasonable fit. High variability of the resulting planetesimal size
distribution for simulations with slightly different initial conditions was
found by Rucska et al. 2020 [130].

However, due to restrictions of the numerical simulation resolution, the lower
threshold of the planetesimal size is unknown. With increasing numerical
resolution, ever smaller pebble clouds and their collapse can be resolved
[103]. Therefore, it is an open question as to which sizes of planetesimals
can be formed by streaming instability and the subsequent gravitational
collapse. Klahr and Schreiber 2020 [125] suggest that large planetesimals form
first and closer to the Sun, and the formation of smaller planetesimals is
possible further out in the PPD. Consequently, these objects would form later
in time.

It seems likely that pebble clouds can also collapse into binaries, which can
merge into contact binaries via a low-velocity impact [131, 132]. The
influence of the water-ice snowline opens the possibility for a bifurcation in
planetesimals with different properties inside and outside the snowline [133].

As stated above, planetesimals larger than $50\,\mathrm{km}$ in radius are
mechanically altered under their own weight. Pebbles are compacted and
destroyed through local hydrostatic pressure, depending on their radial
position inside and the total mass of the planetesimal. The loss of the pebble
structure is accompanied by an increase of the tensile strength from
$\sim$$1\,\mathrm{Pa}$ [134] to $\sim$1–10 $\,\mathrm{kPa}$ [44] due to
considerable increase in grain–grain contacts when the pebbles are compressed.
Thus, cometary activity by gas pressure cannot be explained without pebbles,
because pressures in excess of a few Pa cannot be reached in the cometary
subsurface regions [135]. Because we focus on comet formation in this review,
we further exclude planetesimals larger than $50\,\mathrm{km}$ in radius.

##  4 Evolution of Planetesimals towards Comets

In this Section, we discuss the main evolutionary processes acting on the bulk
of the planetesimal volume over a timespan of 4.6 Gyrs. This encompasses, on
the one hand, internal heating from radioactive decay of short-lived and long-
lived radionuclei, and, on the other hand, possible collisional encounters of
the planetesimal with other bodies in the outer regions of the solar system.

###  4.1 Radiogenic Heating

Due to the decay of radioactive isotopes, planetesimals can be heated in their
interior. This alters the body dramatically if critical temperatures are
reached. In this case, sublimation of volatiles depletes ices in the central
regions, where temperatures are typically higher than those closer to the
surface. Consequently, the advecting volatiles recondense in cooler regions
and thus accumulate in shells in the outer parts of the planetesimals. At
higher temperatures and pressures, some materials can also melt. Both melting
and vaporisation lead to differentiation of the objects. The efficiency of
radiogenic heating mainly depends on the size of the planetesimal, the thermal
conductivity of the material and on the amount and half-lives of the
radiogenic isotopes incorporated into the body.

The radioactive materials are divided into two groups, short-lived
radionuclides (SLNs) and long-lived radionuclides (LLNs). SLNs (see Section
4.1.1) possess half-lives typically on the order of one to a few million
years, which means that their heating effectively occurs only early in the
lifetime of the solar system in the PPD phase. Moreover, as SLNs decay
quickly, the formation time of the planetesimals also matters. In contrast,
LLNs decay over billions of years (see Section 4.1.2).

Along with thermal alteration due to radiogenic heating, solar illumination
can also increase the temperature, depending on long-term orbital dynamics. As
shown by modelling of Jupiter-family comets on their path inwards from the
scattered disc or the Kuiper Belt [136], this external thermal alteration can
penetrate deep into the body, so that hypervolatiles may be redistributed and
lost completely. Further, temperatures above 80 or even 110 K can be reached;
hence, super-volatiles and amorphous water ice can be affected, too.

####  4.1.1 Short-lived Radionuclides

The effect of SLNs is dominated by two nuclei, namely ${}^{26}\mathrm{Al}$ and
${}^{60}\mathrm{Fe}$. It seems that the distribution of ${}^{26}\mathrm{Al}$
was homogeneous in the solar nebula with a ratio of
${}^{26}\mathrm{Al}(t=0)/^{27}\mathrm{Al}=5\times 10^{-5}$ [137], with $t=0$
denoting the time of the formation of calcium–aluminium-rich inclusions
(CAIs). Due to their short half-lives, SLNs can heat bodies to high
temperatures. Even the melting point of water ice can be reached in
planetesimal-sized objects [138]. In the last two decades, more and more
complex studies have been performed to understand the influence of radiogenic
heating on the evolution of planetesimals [139, 140, 141, 142, 143, 144, 145,
146, 147, 133]. Most of these studies neglected LLN and did not consider
pebble-structured objects. The sizes of bodies investigated in their thermal
evolution vary from a few kilometres to several $100\,\mathrm{km}$ in radius.
In addition, formation time has a significant influence on the evolution of
the objects; for example, Lichtenberg et al. 2021 [133] focused on early
formed bodies with formation times $<3\,\mathrm{Myrs}$ and found mean
temperatures of $\sim$$150\,\mathrm{K}$, even for bodies as small as
$1\,\mathrm{km}$ in radius. Mousis et al. 2017 [146] found for planetesimals
with radii of $1.3\,\mathrm{km}$ and $35\,\mathrm{km}$ that they need to be
formed later than $2.5\,\mathrm{Myrs}$ and $5.5\,\mathrm{Myrs}$ after CAI,
respectively, to prevent amorphous water ice from crystallising. Golabek and
Jutzi 2021 [147] include, along with radiogenic heating, heating by
collisions, and provide estimates for the maximum radius and formation time of
planetesimals to avoid heating above $40\,\mathrm{K}$ in the interior. The
maximum radius can be up to $40\,\mathrm{km}$ for a formation later than
$5\,\mathrm{Myrs}$ after CAI, and even $100\,\mathrm{km}$, including
catastrophic collisions for a critical temperature of $80\,\mathrm{K}$ (see
Figure 9 in Golabek and Jutzi 2021 [147]).

However, the thermal conductivity of the body, which is linked to the internal
structure and composition, is of major importance for modelling radiogenic
heating. In cases of high thermal conductivity, the heat can be transported
efficiently to the surface, where it can be radiated away, resulting in lower
peak temperatures, whereas low thermal conductivities impede energy transport
from the interior towards the outer regions. Consequently, the peak central
temperature can be very high.

It is the pebble-pile structure that makes planetesimals formed by gentle
gravitational collapse so interesting for the study of their thermal
evolution, because (i) pebbles possess low thermal conductivity due to their
porous structure, (ii) the thermal contact between pebbles is minimal, and
(iii) radiative heat transport is very inefficient at low temperatures. The
heat-transport model of Gundlach et al. 2012 [148] shows that at low
temperatures and for pebbles with radii of $5\,\mathrm{mm}$, the thermal
conductivity is less than $10^{-3}\,\mathrm{W\,m^{-1}\,K^{-1}}$ (see also
Figure 1 in [149]) and, thus, is more than three orders of magnitude lower
than that of solid (i.e., non-porous, non-hierarchical) materials with the
same bulk composition.

The study by Malamud et al. 2022 [150] has for the first time included the
pebble structure of small planetesimals (see Section 3.3) in their analysis of
radiogenic heating by SLNs and LLNs. They found that even for planetesimals as
small as $0.5$ to $20\,\mathrm{km}$ in radius, the influence of radioactive
heating can be significant. Only bodies up to $2\,\mathrm{km}$ in radius with
a late formation time of $>$5$\,\mathrm{Myrs}$ after CAI obtain a peak
temperature below $70\,\mathrm{K}$. Higher temperatures force the
(super-)volatiles to diffuse outwards and to condense in regions where the
temperatures are below the condensation temperature. Differentiation of the
ices, with a depleted interior and an enriched outer layer, is the result of
this process. However, the near-surface regions are unaltered because outward
diffusion stops below the surface. This differentiation of the volatiles is
visualised in Figure 1 with red (pebbles depleted in ices) and white (ice-
enriched shell) colours. When water ice is redistributed within the
planetesimal, no hyper- or super-volatiles can remain in the water-ice
depleted interior. Reaching the melting point of water ice was observed in the
model when planetesimal radii are $5\,\mathrm{km}$ or larger; these
planetesimals were formed rapidly after CAI and have large mineral abundance.

The evolved planetesimals after the phase of radiogenic heating by SLNs can be
divided into undifferentiated and differentiated objects. Small planetesimals
that avoided excessive heating remain undifferentiated and are therefore
considered pristine (Type A). The differentiated planetesimals (Type B) are
split into subgroups. The first stage of differentiation is the redistribution
of super-volatiles, as observed in the simulations of Malamud et al. 2022
[150]. The most crucial differentiation occurs when melting temperatures and
pressures (e.g., of water) are reached. In this case, aqueous alteration
starts and pebble structures are destroyed, which also decreases porosity. In
general, radiogenic heating by SLNs seems to be an important evolutionary
process for most planetesimals, except for the smallest ones, which were
formed late after CAI. Within the timescale of the first radiogenic heating
phase of up to $10\,\mathrm{Myrs}$ after CAI, the influence of collisions can
often be neglected.

####  4.1.2 Long-lived Radionuclides

In contrast to the heating by SLNs, LLNs decay over a much longer period of
time. Relevant LLNs for planetesimals are ${}^{235}\mathrm{U}$,
${}^{238}\mathrm{U}$, ${}^{40}\mathrm{K}$ and ${}^{232}\mathrm{Th}$, and these
materials are important for larger objects and for long time scales. Their
influence was first analysed by Whipple 1965 [151] and Prialnik et al. 1987
[152]. Both publications found that LLNs can increase the central temperature
by a few $10\,\mathrm{K}$. The second phase of radiogenic heating is
accompanied by collisional evolution (see Section 4.2).

###  4.2 Collisional Evolution

Besides internal heating, collisions among planetesimals can have a
significant influence on their evolution. Collisions can occur over the whole
time-range after formation until today. However, collision probability evolves
over time and depends on the planetesimal size and orbit. Hence, bodies with
different sizes and thermal evolutions may collide with one another. The
outcome of these collisions depends on the physical properties of the
planetesimals, the collision angle, the impact velocity and the size of the
colliding bodies. In this review, we only consider collisions that have
potentially global impact on the planetesimals, and define three possible
collisional types, defined below.

  1. 1.

First, a collision can be _sub-catastrophic_ if the largest fragment possesses
at least half of the initial mass of the larger bodies. We assume that in this
case, the mechanical bulk properties of the planetesimals are essentially
conserved.

  2. 2.

Second, if the fragments are smaller, the collision is considered
_catastrophic_. However, if the energy input into the colliding bodies was not
sufficient to destroy the pebble structure, the fragments are still composed
of pebbles, but the original bulk properties might have changed.

  3. 3.

Third, the collisions can be _super-catastrophic_ , in which case the pebble
structure and the pebbles themselves are destroyed by the collision event.

Several researchers have performed simulations of the collisions of
planetesimals for different sizes and impact velocities. Abedin et al. 2021
[153] investigated the collision probabilities in the trans-Neptunian region
of today and found a wide range of possible radii and velocities of colliding
bodies, but favouring low relative speeds ($<1\,\mathrm{km/s}$) and the main
classical belt ($30\,\mathrm{AU}<R_{h}<50\,\mathrm{AU}$) as the collision
site. The scattered and detached populations of the trans-Neptunian region
show the smallest collision probability. The physical parameters are connected
to those introduced in Section 2 of the dust and ice particles, and the
pebbles thereof, and supported by experimental work. However, for
planetesimal-sized objects, experimental results need to be extrapolated from
laboratory scales. In addition, the impact angle can have an important
influence on the induced heating [154]. However, impact heating is most
relevant for impact velocities of several kilometres per second and can cause
melting of the material. It is interesting to note that porous bodies are
heated more efficiently by collisions [155] than solid objects. The numerical
study of Charnoz et al. 2007 [156] found that the formation of the Kuiper
belt, the scattered disc and the Oort cloud can be explained by dynamical
depletion of those regions or low-efficiency implantation of bodies, in both
cases accompanied by little collisional activity.

In the following subsections, we briefly review the previous work of sub-
catastrophic, catastrophic and super-catastrophic collisions in the framework
of comet formation.

####  4.2.1 Sub-Catastrophic Collisions

We term the cases in which the largest fragment after a collision has at least
half of the initial mass of the larger of the two colliding bodies as sub-
catastrophic collisions. These include cratering, erosion and collisions
resulting in mass growth, such as merging and mass transfer. Golabek and Jutzi
2021 [147] studied the combined effect of radiogenic heating and collisions
and found that only the unbound material is heated significantly, whereas the
material that remains bound is hardly effected. A study of Jutzi and Asphaug
2015 [157] showed the possibility of the formation of a bilobate shape by a
low-velocity collision, assuming non or small cohesion
($\leq$$100\,\mathrm{Pa}$) and a collision speed of $1.5\,\mathrm{m/s}$.
Furthermore, the formation of bilobed objects by sub-catastrophic collisions
was shown by Jutzi and Benz 2017 [158], who derived that such an evolution is
more likely to happen than collision-avoiding or a catastrophic breakup of
planetesimals. In the following, we assume that sub-catastrophic collisions do
not change the morphology, micro- and macro-porosity, mechanical properties
and volatile abundances of the largest surviving fragment. Thus, this fragment
has the exact same properties as the planetesimal before the collision, with
the exception of mass and shape.

####  4.2.2 Catastrophic Collisions

If the largest fragment after a collision possesses less than half of the
initial mass, we term the collision as catastrophic. The difference from a
super-catastrophic collision (see Section 4.2.3) is that catastrophic
collisions are not energetic enough to compact or destroy pebbles or to
significantly reduce the amount of volatiles. The formation of comet 67P from
a catastrophic collision and the following re-accumulation of its current
mass, with conservation of volatiles and low bulk density, was proposed by
Schwartz et al. 2018 [159]. Jutzi and Michel 2020 [160] showed that the
material ejected and not re-accreted is indeed the most processed part of the
original object. However, the available simulations do not take a pebble
structure of the colliding planetesimals into account. As seen for radiogenic
heating (see Section 4.1), the microphysical properties of the material can
have a huge impact on the collisional outcome (see, e.g., [161]). In addition,
it should also be studied how differentiated bodies behave in collisions. With
all these uncertainties in mind, we assume here that bodies that re-
accumulated after a catastrophic impact still consist of pebbles and contain a
large percentage of the volatiles contained in the planetesimal predecessors.
In contrast to the objects stemming from sub-catastrophic collisions (see
Section 4.2.1), bodies arising from catastrophic collisions are rubble piles
and may consist of spatially separated parts stemming from different regions
of the precursor planetesimals. We also assume that this rubble is so
mechanically weak [161] that its outer shape does not survive the
gravitational re-accretion process. Thus, re-accumulated bodies from sub-
catastrophic collisions should not possess voids on length scales exceeding
that of the pebble size.

####  4.2.3 Super-Catastrophic Collisions

The term super-catastrophic collisions describes impacts that provide enough
energy to destroy the pebble structure and to sublimate the volatile
constituents. In this case, no pebbles or ices will remain inside the object,
which is indicated in Figure 1 by grey colour. Super-catastrophic collisions
occur at high relative velocities. Objects that gravitationally re-accumulate
after a super-catastrophic collision among planetesimals are rubble piles. In
contrast to the bodies stemming from catastrophic collisions (see Section
4.2.2), the rubble from super-catastrophic collisions is highly compacted, and
thus mechanically strong enough to survive the accretion process intact. Thus,
rubble piles from super-catastrophic collisions possess macro-porosity on
length scales characteristic for the collisional outcome, and reduced
microporosity due to compaction of the dusty material upon impact.

##  5 Discussion - Which Planetesimal Can Become a Comet?

With the limited knowledge about actual collisional encounters and outcomes
(see Section 4.2), we try in the following to physically characterise a
planetesimal after 4.6 Gyrs of thermal and collisional evolution. The
formation and evolution scenarios described above may end in a variety of
bodies, which we divide into three categories (see Figure 1 for an overview):

  * •

Icy Pebble Piles—Type A1 and Type B1

  * •

Icy Rubble/Pebble Piles—Type A2 and Type B2

  * •

Non-Icy Rubble Piles—Type A/B3

One very important question for researching comets is: Which of these types
could represent the comets currently observed in the solar system? In the
following, the most important physical properties, which can be used for the
validation of the formation/evolution model and the corresponding observables,
will be discussed. The expectation from the formation and evolution scenario
for each observable will be described and compared to real physical properties
of comets measured by (spacecraft) observations.

###  5.1 Intrinsic Physical Properties

We will start this discussion with those physical properties that are directly
provided by the formation and evolution process. These properties, such as
internal morphology and total porosity, are referred to as intrinsic physical
properties and can be used to directly link the formation and evolution of
planetesimals with the observable properties of contemporary comets in the
solar system. Table 1 summarises the different intrinsic properties of
cometary nuclei.

Table 1: This table presents an overview of the different proposed types of objects with their expected intrinsic physical properties that are discussed in detail in the following sub-sections. |  Type A1 |  Type B1 |  Type A2 |  Type B2 |  Type A/B3
---|---|---|---|---|---
|  |  |  |  |
Intrinsic physical properties | Icy pebble piles | Icy rubble/pebble piles |  Non-icy rubble piles
Internal morphology and pebble properties (Section 5.1.1) |  Pristine, pebbles, void size equals pebble size, voids filled with fractals |  Pristine, pebbles, void size equals pebble size, voids filled with fractals |  Pebbles, void size equals pebble size, fractals locally depleted |  Pebbles, void size equals pebble size, fractals locally depleted |  Pebbles are destroyed and highly compacted, rubbles remain, large void spaces between rubbles
Total porosity (Section 5.1.2) |  High pristine porosity |  Enhanced porosity in the interior, reduced porosity at ice shell locations, bulk porosity preserved |  High pristine porosity |  Heterogeneous, macro-scale mixture of material with enhanced and reduced porosity, pristine porosity may not be preserved |  No intra-rubble porosity, macro-scale voids between rubbles, bulk porosity smaller compared to pristine porosity
Dust-to-ice mass ratio (Section 5.1.3) |  Pristine dust-to-ice ratio, homogeneous distribution |  Interior depleted in ices, enriched ice shells - pristine ratio preserved |  Pristine ratio preserved, homogeneous distribution |  Heterogeneous mixture of material from depleted and enriched areas |  No ices
Binarity, flattening and rotational orientation (Section 5.1.4) |  Many binaries, flattened shape and aligned along the principal axis, more prograde rotating objects |  Many binaries, flattened shape and aligned along the principal axis, more prograde rotating objects |  Pristine binarity is destroyed, creation of new binaries after collision is possible, random alignment and distribution of inclinations |  Pristine binarity is destroyed, creation of new binaries after collision is possible, random alignment and distribution of inclinations |  Pristine binarity is destroyed, creation of new binaries after collision is possible, random alignment and distribution of inclinations

####  5.1.1 Internal Morphology and Pebble Properties

Expectation
Planetesimals formed by the gentle collapse of a pebble cloud are initially
very homogeneous throughout the whole body, despite the possibility of size-
sorting of the pebbles while the cloud collapses [117]. The latter would
generate a gradient in the size of the void spaces between the pebbles, but
not necessarily in density. In any case, the size of the void spaces between
the pebbles is always on the order of the pebble size. As described above,
compaction due to lithostatic compression of large planetesimals would
decrease the void space in the inner parts of the objects. However, for
simplicity we excluded these bodies (i.e., $>$50 $\,\mathrm{km}$ in size) due
to their large sizes compared to typical comets. As pebble size is expected to
be on the order of millimetres to decimetres, density contrast on length
scales much larger than decimetres is not expected in the interior. For type
A1, no alteration of the internal structure due to evolutionary processes is
expected, and the internal morphology remains pristine, with pebbles and void
spaces of pebble size that are filled with fractals (see Section 3.3). For
type B1, the internal morphology is almost identical to A1, with the exception
that in the deep interior, the porosity is increased due to the evaporation of
ices, and in the ice shell(s), the pore size is reduced due to recondensation
of the ice(s). If a catastrophic collision occurred, fractals may have been
lost where the void spaces were opened. Therefore, fractals may be locally
depleted for type B1 and B2, but the internal morphology of pebbles and void
spaces remains unaltered because catastrophic collisions do not destroy the
pebble structure.

From the modelling point of view, pebble sizes are determined by the bouncing
barrier [37, 72]. For pebbles containing microscopic water-ice particles,
Lorek et al. 2018 [73] derived maximum pebble sizes on the order of 1 mm to 1
cm, depending on the heliocentric distance and specific PPD parameters. As to
the internal morphology of the pebbles, Lorek et al. 2018 [73] calculated
filling factors between 0.3 and 0.4. Pebble substructures and possible
inhomogeneous internal morphology of the pebbles have not been studied
extensively. However, for two reasons, inhomogeneity is expected: (i) pebble-
growth studies show that the size–frequency distribution of the building
blocks of pebbles has a certain shape and width [72, 73]; if the bouncing-
collision phase of the pebbles before gravitational collapse does not erase
all substructures, pebbles should still be characteristically inhomogeneous.
(ii) Based upon the size–frequency distribution of dust ejected into the
cometary coma, Fulle et al. 2020 [162] and Ciarniello et al. [163, 164]
derived a pebble-internal morphology model that is capable of explaining a
variety of comet observation facts.

With a super-catastrophic collision (type A/B3), pebbles and fractals are
destroyed, and the resulting rubble piles are highly compacted, and thus
relatively rigid. Within this rubble, large void spaces can remain. The size
of the rubble may vary and is not further constrained in this work.

Comparison to Observations
The internal morphology of comets is only measurable by instruments with the
ability to scan the interior of the objects. The Rosetta Mission was equipped
with instrument packages capable of performing these investigations, namely
Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT [165])
and Rosetta Radio Science Investigation (RSI [166]) instruments. Both devices
performed radar observations of the interior of the nucleus.

Their measurements showed that the observed volume of comet 67P is highly
homogeneous on length-scales larger than $3.3\,\mathrm{m}$ (CONSERT [167]).
However, CONSERT could not investigate the entire body, so the results are
limited to a fraction of the volume of comet 67P. CONSERT found a denser
surface layer for the uppermost $<25\,\mathrm{m}$ [168]. Such variation may be
explained by the redistribution of volatiles due to radiogenic heating (see
Section 4.1). RSI measurements showed an offset of the centre of gravity,
which indicates density difference of the two lobes. The big lobe seemed to be
slightly denser than the small lobe [169].

Direct observations of the pebbles have not been unambiguously performed.
Imaging of the surface of comet 67P with the highest spatial resolution was
performed by the CIVA instrument onboard the Philae lander [170] and showed
substructures with sizes of a few millimetres to one centimetre, which might
be identified as pebbles. Other, indirect methods have been applied by Blum et
al. 2017 [3] to derive the pebble size and result in values for the pebble
radii between 3 mm and 6 mm. Cometary trails have been investigated by Lisse
et al. 1998 [171], who found that a high abundance of macroscopic particles
with $\beta$ values of $\beta<10^{-3}$, corresponding to dust-particle sizes
of $\gtrsim$1 $\,\mathrm{mm}$, are present in the trails. Moreover, cometary
meteor showers exhibit particle sizes up to $\sim$$1\,\mathrm{cm}$ [172]. As
stated above, direct observational evidence of pebble substructures is not
available.

####  5.1.2 Bulk Porosity

Expectation
The bulk porosity of planetesimals is mainly influenced by formation processes
and can then be altered due to evolutionary processes. As a simple rule-of-
thumb, the packing density of a planetesimal consisting of two hierarchy
levels (dust/ice particles forming pebbles; pebbles forming planetesimals) is
$\Phi_{\mathrm{bulk}}=\Phi_{\mathrm{d}}\,\Phi_{\mathrm{p}}\approx 0.24$, with
$\Phi_{\mathrm{d}}\approx 0.4$ and $\Phi_{\mathrm{p}}\approx 0.6$ being the
packing densities of the dust/ice particles inside a pebble and of the pebble
packing inside the planetesimal, respectively [173]. For pebbles with
substructures, the internal packing might be $\Phi_{\mathrm{d}}<0.4$, as this
can be regarded as another hierarchy level [2]. Thus, the bulk porosity adds
up to $\sim$$76\,\%$. For larger planetesimals, the porosity is expected to
decrease with increasing depth due to lithostatic compression of the pebble
structure [150]. However, as described in Section 4.1, radiogenic heating can
affect even rather small bodies when they form early enough (type B1). The
outward diffusion of hyper- and super-volatiles goes along with a change in
porosity so that the porosity increases above the primordial value close to
the centre and decreases at locations where the volatiles condense. However,
when no volatiles are lost into space, the bulk porosity does not change and
remains pristine. For larger objects, a change of porosity can also be induced
due to the melting of water ice. When water ice melts, the pebbles collapse
and immerse into the water so the initial porosity is lost, and consequently,
the body shrinks. However, as this only happens close to the centre, the outer
layers maintain their pebbles and their porous structure. For type B2 bodies,
the pebbles from the various regions possess different dust-to-ice ratios,
which implies that the observed density across the surface and for different
depths changes. For the compacted structures of type A/B3, very little
porosity remains inside the rubble, but macroporosity may exist within it.
Thus, the bulk porosity of the entire body of a type A/B3 should be lower than
the pristine value.

Comparison to Observations
The porosity of a whole body can be derived from its volume, mass and material
density. Material composition and porosity can be estimated by measurement of
the electric permittivity [174], but this procedure is model-dependent and
relies on calibration experiments [175]. Measurements of total porosity with
high resolution were only performed for comet 67P, resulting in values for the
bulk packing density of $\Phi_{\mathrm{bulk}}=0.15$ to
$\Phi_{\mathrm{bulk}}=0.37$. The RSI instrument measured values between
$\Phi_{\mathrm{bulk}}=0.25$ and $\Phi_{\mathrm{bulk}}=0.30$ [176]. An estimate
of $\Phi_{\mathrm{bulk}}=0.21$ to $\Phi_{\mathrm{bulk}}=0.37$ was retrieved by
directly measuring the pebble density by Grain Impact Analyser and Dust
Accumulator (GIADA [177, 178]). Moreover, permittivity measurements done by
CONSERT provided a range of $\Phi_{\mathrm{bulk}}=0.15$ to
$\Phi_{\mathrm{bulk}}=0.25$ [167]. The lower value of
$\Phi_{\mathrm{bulk}}=0.15$ leaves room for a third hierarchy level, i.e., for
pebbles with substructures, whereas the upper value requires the pebbles to be
homogeneous.

Due to the overall high porosity of comet 67P, evolutionary processes that
considerably reduce the porosity, such as, e.g., super-catastrophic
collisions, can be excluded.

####  5.1.3 Dust-to-ice Mass Ratio

Expectation
The dust-to-ice mass ratio (DIMR) of a planetesimal is given by the material
distribution inside the pebble cloud that undergoes the gravitational
collapse. The DIMR depends on the location of formation as well as on the
preceding mixing processes of the materials during pebble growth. We refer to
the DIMR at cloud collapse as pristine, but it should be noted that this DIMR
is not necessarily equal to the DIMR of the solar nebula or of the bulk
protoplanetary disc outside the various snowlines. During the thermal and
collisional evolution of the planetesimals, the DIMR can be altered.

For comet types A1 and A2, the pristine DIMR is globally and locally
preserved. Throughout the entire volume, the distribution of ices is
homogeneous down to the pebble scale. For type B1, the bulk abundances of all
ices are preserved, but the local DIMR is changed. The interior of the
planetesimal is depleted in ices (higher DIMR), and the ice layers are
enriched in ices (lower DIMR). The near-surface layer remains mostly pristine
in the DIMR, despite locations where material was ablated by collisions. As
type B2 is the breakup product of a differentiated body, the distribution of
ices is inhomogeneous and depends on the depth of the place inside the body
where the rubble was originally stored. The manner in which such a body re-
accumulates the collisional fragments determines the distribution of the ices
[150]. Whether the DIMR of the rubble is changed compared to the pristine
value depends on the details of the preceding catastrophic collision event.
For types B1 and B2, super-volatiles could be lost entirely if the
corresponding threshold temperature was reached at the moment of the
collision. Type A/B3 does not contain any ices due to the hyper-velocity
nature of the collision event.

Comparison to Observations
The dust-to-ice mass ratio $F$ can also be addressed by porosity and density
estimations, as shown by Lorek et al. 2016 [179] and Patzold et al. 2019
[180]. For cometary refractory material, the material density is not known and
can only be constrained within a range of reasonable values. Measurements by
Rosetta found an organic-to-mineral mass ratio of roughly 1:1 [181]. Typical
densities of organic matter (1000–2000 $\,\mathrm{kg/m^{3}}$), combined with
typical densities of minerals (2600–5000 $\,\mathrm{kg/m^{3}}$), result in an
expected density range of 1800–3500 $\,\mathrm{kg/m^{3}}$ for the refractory
material of a comet. GIADA measured comparable densities with
$1925^{+2030}_{-560}\,\mathrm{kg/m^{3}}$ [182]. Some particles showed a bulk
density >4000 $\,\mathrm{kg/m^{3}}$. For water and CO2 ice, the densities are
$\rho_{\mathrm{H_{2}O}}=934\,\mathrm{kg/m^{3}}$ and
$\rho_{\mathrm{CO_{2}}}=1600\,\mathrm{kg/m^{3}}$, respectively. Porosity
estimations for comet 67P are shown in Section 5.1.2. With this, one can
calculate the dust density $\rho_{d}$ with:

$\rho_{d}=\frac{f_{d}\,\rho_{\mathrm{n}}}{1-f_{\mathrm{H_{2}O}}\frac{\rho_{\mathrm{n}}}{\rho_{\mathrm{H_{2}O}}}-f_{\mathrm{CO_{2}}}\frac{\rho_{\mathrm{n}}}{\rho_{\mathrm{CO_{2}}}}-\Phi}$
(6)

with $f_{d}+f_{\mathrm{H_{2}O}}+f_{\mathrm{CO_{2}}}=1$ the mass fractions of
dust, water and CO2, respectively, $\rho_{\mathrm{n}}=532\,\mathrm{kg/m^{3}}$
the nucleus density [169] and bulk porosity $\Phi$. The results for varying
DIMR are shown in Figure 2. From this plot, one can constrain the global
porosity and the ice content. Porosities larger than $\sim$$81\%$ cannot be
explained with reasonable dust densities and should therefore be excluded. For
a porosity of $76\%$ (see Section 5.1.2), the DIMR has a range of 3 to 4
depending on the assumed CO2 fraction. For the smallest porosity of $63\%$
derived from Rosetta instruments, only a small range of DIMR values between
$0.8$ and $2.5$ is reasonable.

These values are in agreement with the review written by Chourkoun et al. 2020
[183] about the refractory-to-ice(s) mass ratio of comet 67P. In this work,
the authors showed, based on different Rosetta observations, that the DIMR is
most probably higher than 3 (see Figure 5b in [183]). An upper limit of the
DIMR, which is in agreement with most of the Rosetta measurements, can be
between 6 to 8. Only two papers argue for much higher maximum values. The
works claiming higher DIMR values are based on coma dust grain density
estimation around perihelion [182] and on the analysis of the fallback of
volatile-bearing chunks in the northern hemisphere [184].

Figure 2: This plot shows the resulting dust density for varying dust-to-ice
mass ratios and porosities. The green-coloured area indicates reasonable dust
densities. The given CO2 percentage corresponds to the CO2 content of the
total ice mass.

####  5.1.4 Binarity, Flattening and Rotational Orientation

Expectation
Numerical simulations have shown that gravitationally unstable pebble clouds
can collapse into binary planetesimals. These objects rotate in a prograde
manner in $80\%$ of the simulations [132]. This finding is almost not affected
by different parameters influencing streaming instability. Such a formation of
binaries results in very similar compositions of both bodies because they form
from the same reservoir of material. The radii of both bodies would also be
very similar [185]. The spinning of the planetesimals induced by the collapse
results in a flattened shape [186]. Additionally, the parts of such a binary
align over time because this reduces the energy of the system. The alignment
can be followed by a reduction of the distance between both bodies until they
contact due to, e.g., Kozai–Lidov cycling, the YORP and BYORP effects, tides,
collisions or gas drag [186]. However, the collapse of a pebble cloud can lead
to a wide variety of binary distances, including contacting binaries [131].
The survival of binaries in collisions was addressed by Nesvorny et al. 2019
[187], and they found that more tightly bound binaries have a higher survival
probability than wider ones. Regarding radiogenic heating, due to the small
contact area compared to the total area, the influence is negligible and
should be equal for each body individually. It should be mentioned that the
binarity of low-density objects also has important consequences for the escape
of dust particles when dust activity is present (see, e.g., [188, 189]).

Comparison to Observations
Many of the observed cometary nuclei show a binary shape. The most detailed
observed one, comet 67P, exhibits this in great detail. However, the formation
of binary shapes is still discussed and researched. As shown before, the
formation of binaries is an intrinsic characteristic of formation by a
collapsing pebble cloud. Nesvorny et al. 2019 [132] showed that for binaries
that have formed by capturing another object, the distribution of inclinations
would favour retrograde over prograde rotations. Comparison to the known
binaries in the Kuiper belt shows that the distribution of binary inclinations
can be best explained by direct formation of binaries from a single source
[132]. Arrokoth shows alignment of the two lobes, which is in agreement with
the predicted scenario [186]. However, for comet 67P, the observation of
layered surface structures surrounding each lobe [190, 191, 192] suggests that
the lobes formed individually and contacted later.

###  5.2 Derived Physical Properties

Table 2: This table presents an overview of the different proposed types of objects with their expected derived physical properties, which are discussed in detail in the following sub-sections. |  Type A1 |  Type B1 |  Type A2 |  Type B2 |  Type A/B3
---|---|---|---|---|---
|  |  |  |  |
Derived physical properties | Icy pebble piles | Icy rubble/pebble piles |  Non-icy rubble piles
Cometary activity (Section 5.2.1) Instruments: Camera, dust collector, gas detector |  Possible everywhere at the surface, activity will not change when eroded |  Possible everywhere at the surface, but activity changes when eroded |  Possible everywhere at the surface, but activity changes when eroded |  Possible at specific locations, erosion can change activity patterns |  Not possible
Thermal conductivity (Section 5.2.2) Instruments: Thermal IR, microwave, in situ temperature sensors |  Low network and radiative conductivity at night, radiative part strongly increases at day due to strong temperature dependence |  High radiative thermal conductivity in the interior, the shells have a moderately increased network conductivity, and the mantle material behaves like Type A1 |  Low network and radiative conductivity at night, radiative part strongly increases at day due to strong temperature dependence |  Different locations are either dominated by the low network, or the varying radiative thermal conductivity |  Relatively high network conductivity inside the rubbles, the large voids in between are dominated by radiation
Tensile strengths (Section 5.2.3) Instruments: e.g. camera (cliff collapse) |  Ultra low intra-pebble tensile strength and low inter-pebble tensile strength |  Ultra low intra-pebble tensile strength and low inter-pebble tensile strength, both enhanced in ice-enriched areas and decreased at in ice-depleted areas |  Ultra low intra-pebble tensile strength and low inter-pebble tensile strength |  Ultra low intra-pebble tensile strength and low inter-pebble tensile strength, both enhanced in ice-enriched areas and decreased at in ice-depleted areas |  High intra-rubble tensile strength, but almost no tensile strength between the rubbles
Compressive strengths (Section 5.2.4) Instruments: Measurement of impact decelleration |  Low pressures required to compress the pebble material |  Low pressures required to compress the material in the mantle, the pressure required for compression is increased in the ice shells and decreased in the depleted interior |  Low pressures required to compress the pebble material |  Varying compression response of the material, depending on the ice fraction |  Rubbles require more compression pressure to be compacted to the same volume filling factor as the pebbles
Gas permeability (Section 5.2.5) Instruments: Gas detector |  High permeability inside the large voids between the pebbles and low permeability inside the pebbles |  Gas permeability is decreased in layers of enhanced ice content (ice shells), gas permeability is decreased where lice is less abundant |  High permeability inside the large voids between the pebbles and low permeability inside the pebbles |  Varying gas permeability at different locations at the surface and in the interior |  Very low gas permeability
Permittivity (Section 5.2.6) Instruments: Deep penetrating radar, DC geoelectric |  Homogeneous electrical permittivity on the surface and in the interior |  Varying electrical permittivity for different parts of the nucleus (mantle, shells, interior) |  Homogeneous electrical permittivity on the surface an in the interior |  Inhomogeneous electrical permeability on the rubble scale, but homogeneous inside the rubbles |  Homogeneous electrical permittivity inside the rubbles, but variations because of the large voids

####  5.2.1 Cometary Activity

Expectation
If we define cometary dust and gas activity as a state in which insolation
produces subsurface pressures large enough to overcome the cohesion of the
dust, then types A1, A2, B1 and B2 can in principle become active due to the
presence of volatile ices close to the surface. However, these objects show
significant differences, which are noteworthy and could become decisive to
answer the question of how comets formed and evolved. The distribution of
volatiles over the entire surface of the bodies is different. Due to the
homogeneity of types A1 and A2, these objects should become active at each
surface location given sufficient insolation. When the surface of a type-B1
object gets eroded locally, the activity can be different at this location
because an ice shell or the depleted interior could be excavated. We could
observe this effect by local variations of the outgassing rates of different
volatile species. For type B2, the different ice-containing rubble is
distributed inhomogeneously over the whole body. Hence, also for type B2 we
expect locally varying outgassing rates. Type A/B3 cannot show cometary
activity driven by ice sublimation as it no longer contains any ices.

Comparison to Observations
The first-ever observed cometary nucleus was the nucleus of comet 1P/Halley.
Halley was expected to show global activity, but when the Giotto spacecraft
arrived, only $\sim$$1/3$ of the surface was contributing to global activity
[193]. A similar observation was made for comet 19P/Borrelly — one distinct
jet originated from the cometary nucleus, which actually consisted of three
smaller outbursts [194]. In contrast to other comets, comet 81P/Wild 2
possessed a diverse and complex variety of surface structures [195]. Longer-
exposure camera images revealed the presence of many jets around the entire
nucleus. More than twenty highly collimated jets were observed, which
indicated a heterogeneous surface. In addition, analysis of captured particles
indicated that comet Wild 2 may have experienced aqueous alteration in the
past [196]. Comet 9P/Tempel 1 showed rather variable dust activity, with
frequent natural outbursts all over the surface [197]. In comparison to the
above-mentioned comets, 103P/Hartley 2 had very distinct activity patterns.
During the flyby of the EPOXI spacecraft [198], water vapour emission was
detected at the waist of nucleus. Localised CO2-active areas also showed
ejection of solid water ice chunks of up to cm size. In addition, solid ice
particles were also observed in an area where only water was active.

Comet 67P is by far the best-studied comet, and this is why we are aware of
several local activity hotspots (such as sunset jets; see, e.g., [199]),
although the nucleus seems to be globally active [200]. The activity pattern
changed with time because of seasonal variations of solar illumination and
because of material that fell back onto the nucleus [184]. During perihelion,
the southern hemisphere showed an increase of CO2 activity that led to the
ejection of larger ice-containing chunks (up to several cm in size [201]) and
to a bluing of the surface because more water-ice-containing pebbles were
excavated by CO2 erosion (for details see [164]). These chunks either escaped
into space or fell back into the northern hemisphere of the nucleus. Although
we understand the principle of how gas activity leads to the ejection of
pebbles or chunks from the surface, it is still not known how to explain the
particle-size distribution in the coma [3]. The smallest (sub-)micrometre-
sized particles cannot be lifted directly from the surface because of their
strong adhesion forces. This means that the chunks or pebbles must
disintegrate in the coma after lift-off to produce the observed fraction of
small particles in the coma. Fulle et al. 2020 [202] proposed that pebbles
possess a substructure called agglomerates, typically ranging from micrometre
to millimetre in size. Probably charging effects, fast rotation of the pebbles
or extreme illumination conditions lead to break up of the pebbles into
unbound agglomerates with a size distribution similar to the observed one.

####  5.2.2 Thermal Conductivity

Expectation
Heat can be transported by conduction, radiation, gas diffusion and convection
in the case of fluid material. The latter mechanism can be neglected in
contemporary comets because they have certainly cooled down, even if they had
at some point reached the critical temperature for water-ice melting [150].
Further, heat transport by gas diffusion can be neglected in most cases due to
the low gas pressures involved. For the conduction and radiation of thermal
energy, material and structural properties determine the efficiency of heat
transport. In a granular medium, conduction is less effective than in solid
material due to the reduced contact areas between neighbouring particles,
which is described by the so-called Hertz factor. For pebbles, heat conduction
is reduced further because of the granularity inside the pebbles. Therefore,
and due to the large void spaces between the pebbles, thermal radiation
contributes to the energy transport and can even dominate for large pebbles
and high temperatures, as shown in Bischoff et al. 2021 [149] (their Figure
1). Only for low temperatures (<100 $\,\mathrm{K}$ for pebbles with
$5\,\mathrm{mm}$ radius) does heat conduction dominate, but then the thermal
conductivity is extremely small (<$10^{-3}\,\mathrm{W/(K\,m)}$).

For the five types of bodies proposed, this means the following: Types A1 and
A2 with their pebbles show low network conduction, and radiation dominates for
higher temperatures. For type B1, the shell structure influences the
conductivity such that the interior with reduced ice content shows decreased
network conductivity compared to the pristine material due to the higher
porosity and the low internal temperatures. As the ice shells are enriched
with material, their network conductivity is locally increased. For the outer
pristine material, the network conduction is the same as for types A1 or A2.
For type B2, which possess regions of different dust-to-ice ratios, thermal
conductivity will vary among the different locations. Ice-depleted areas,
which possess higher porosities, are subject to strong day–night thermal
conductivity variations. Areas of higher ice content generally possess higher
thermal conductivity because of the network part, but temperature changes do
not have the same importance as for the ice-depleted parts. In case of type
A/B3, the rubble is expected to be compacted, and therefore, network
conduction is the relevant transport process.

Comparison to Observations
Instead of the thermal conductivity $\lambda$, often the thermal inertia
$\Gamma=\sqrt{\lambda\rho c}$ is measured for small solar system objects, with
$\rho$ and $c$ being the mass density and heat capacity of the material,
respectively. However, these properties are often not known with high
accuracy, and additionally, the temperature dependency of all these values is
often not taken into account. As described above, the temperature dependency
can be crucial for highly porous pebble-structured materials. Thus, measured
values of the thermal conductivity or thermal inertia should be considered
with caution and in the corresponding temperature range. For comet 67P,
several instruments onboard Rosetta and Philae were able to measure
temperatures. On the orbiter, Visible InfraRed and Thermal Imaging
Spectrometer (VIRTIS) [203] measured the surface temperature at depths of tens
of micrometres. Self-heating and shadowing effects were observed by VIRTIS
[204]. However, VIRTIS had a lower limit for temperature detection of
$\sim$$156\,\mathrm{K}$ due to instrument noise. The Microwave Instrument for
the Rosetta Orbiter (MIRO) [205] used wavelengths of $0.5\,\mathrm{mm}$ and
$1.6\,\mathrm{mm}$, resulting in penetration depths on the order of a few
millimetres to centimetres [3]. The MIRO temperature data are difficult to
interpret because the measurement depth is comparable to the diurnal skin
depth [206, 207], and therefore a wide temperature range contributes to the
measured brightness temperature. Marshall et al. 2018 [208] found a best-
fitting thermal inertia of $80\,\mathrm{J/(K\,m^{2}\,s^{0.5})}$ under the
assumption of a complex roughness distribution when comparing MIRO and VIRTIS
data. Onboard the lander Philae, Multipurpose Sensors for Surface and
Subsurface Science (MUPUS) [209] was capable of probing the surface with the
MUPUS PEN (thermal probe) and the MUPUS TM (16 resistance temperature
detectors and an infrared radiometer). They found a best-fitting thermal
inertia of $85\,\mathrm{J/(K\,m^{2}\,s^{0.5})}$ [210]. Assuming a heat
capacity of $560\,\mathrm{J/(kg\,K)}$ (as used in Bischoff et al. 2021 [149])
and a density of $532\,\mathrm{kg/m^{3}}$ (for the bulk nucleus, [169]), these
thermal inertia values translate into thermal conductivities of
$\sim$$0.02\,\mathrm{W/(K\,m)}$. As described before, the uncertainty in heat
capacity and density of the measurement spots is forwarded into uncertainties
of the thermal conductivity. Thus, such a value alone cannot be used to
conclude the kind of structure of the cometary surface. The method proposed by
Bischoff et al. 2021 [149], which allows the distinction between micro- and
macro-porous subsurface structures by relating the sunrise temperatures to the
insolation at noontime, could not be used with measured data of comets due to
the lower limit of available temperature data. However, in future missions to
comets, such as ESA’s Comet Interceptor [211], the application of this method
should be kept in mind when measuring surface temperatures.

####  5.2.3 Tensile Strength

Expectation
The cohesion of granular matter is in general influenced by the material
composition, its structure and the observed length scale. The tensile stress a
body can withstand before it breaks is called the tensile strength. For non-
porous solid material, the tensile strength is highest due to the direct
contact of the atoms and is typically found in the MPa range. Tensile strength
is reduced by any kind of porosity, granularity or roughness because of the
reduction of contact area among the atoms. For objects composed of micrometre-
sized grains, i.e., for the inside of pebbles, the tensile strength is on the
order of kPa [212, 67]. For pebble-piles, the tensile strength is further
reduced to a few Pascals or even less, depending on pebble size [173, 134,
54]. For planetesimals formed from pebbles, such a low tensile strength is
expected on the metre-scale or above. Compaction due to collisions or
redistribution of volatiles leads to higher tensile strength values. The
relation between volume-filling factor and tensile strength has been measured
for several materials, such as silica, graphite and organics, and depends
strongly on the compaction [212, 213, 214, 67]. Applying this knowledge to the
five types of bodies discussed at the bottom of Figure 1 leads to the
conclusion that types A1 and A2 possess low tensile strength on the order of 1
Pa down to the length scale of the pebble size. As shown in Section 4.2, sub-
catastrophic and catastrophic collisions can occur without causing significant
damage to the pebble structure. Hence, the tensile strength is not affected by
collisional evolution in these two cases. However, differentiation causes
significant changes of the tensile strength. Locations of enhanced ice content
will possess higher tensile strength values, whereas depleted volatile
material consequently leads to a decrease in tensile strength. This is why the
redistribution of material in the rubble in type B2 leads to variation of the
tensile strength over the surface and volume of these bodies. The material of
type A/B3 bodies is highly compacted, and this is why the rubble should have a
high intra-rubble tensile strength. However, the tensile strength between the
rubble particles is almost zero, which means that the rubble is only bound by
gravity.

Comparison to Observations
As described above, the tensile strength of a body varies for different length
scales. For large scales of several metres to 100 m, the tensile strength of
comet 67P was estimated by the observation of cliff collapses [215] and found
to be on the order of 1 Pa, as expected for a pebble-pile body. For length
scales of a kilometre or above, the tensile strength is difficult to measure
because of the increased importance of gravitational binding. The central
hydrostatic pressure of comet 67P, for example, is on the order of 10 Pa, and
thus larger than the expected tensile strength of a loose pebble pile.
However, for bodies with radii of several kilometres or above, a memory effect
can lead to increased tensile strength as shown by Blum et al. 2014 [134].
These results may indicate why the lower limits of the tensile strengths for a
number of comets are slightly above the canonical 1 Pa value [44]. Much
smaller length scales can be probed through the breakup of cometary meteors in
Earth’s atmosphere. These typically millimetre-sized bodies possess tensile
strengths on the order of 1–10 kPa [134] and may thus represent intact pebbles
or fragments thereof.

####  5.2.4 Compressive Strength

Expectation
Compressive strength describes the ability of a material to withstand
pressures tending to reduce size. For granular materials, this material
property depends on the volume-filling factor of the material as well as on
the grain properties, such as shape and size distribution. This is why the
compressive strength of a granular medium cannot be seen as a single value,
but should rather be considered a volume-filling-factor-dependent value that
changes with respect to the applied compressive stress (see Figure 3). The
reason is that fluffier materials can be compacted much easier in comparison
to more compact structures. The functional behaviour of the compression curve
of granular materials was derived using theoretical considerations and
laboratory experiments [216]. The result is that the response of the volume-
filling factor to compressive stress can be described by an S-type function
(see Figure 3), with a transition regime that is characterised by the so-
called turnover point, $p_{m}$. Homogeneous granular materials are compressed
in the transition regime I. Larger pressures cannot lead to any further
compaction because the grains are already positioned in the densest possible
packing. For pebble piles, however, the compression function can be separated
into two different regimes, namely transition regime II, in which the pebbles
are brought into a denser packing without destruction [150]; and transition
regime III, in which the pebbles cannot withstand the applied pressure and
are, hence, destroyed [217].

Figure 3: Response function of a granular material to compressive stress. The
green curve shows the reaction of a homogeneous, i.e., non-hierarchical,
granular material, whereas the blue curve represents the volume-filling factor
of a pebble-pile structure, i.e., a hierarchical material. Both functions can
be described by S-shaped curves as shown by [216]. The homogeneous material
can only be compressed in a single stage (transition regime I), while for the
hierarchical material, first the pebble packing will be compressed (transition
regime II), then at higher pressures the pebbles will be deformed and
destroyed (transition regime III; dashed curve).

For type A1 and A2 bodies, low-stress compressive strength should be low and
comparable to the tensile strength. For types B1 and B2, the general behaviour
should be similar, but due to the enhanced volume-filling factor at the ice
shell, the compressive strength should be increased, and inhomogeneously
distributed in type B2. The compact rubble in bodies of type A/B3 possess a
high compressive strength on length scales smaller than the rubble size.

Comparison to Observations
The only available estimations of the compressive strength come from the
landing attempts of Philae on the nucleus of comet 67P. Heinisch et al. 2019
[218] determined an upper limit of 800 Pa, while O’Rourke et al. 2020 [217]
derived an upper limit of only 12 Pa for the compressive strength. Based on
the compression model for granular matter under reduced gravity conditions by
Schräpler et al. 2015 [216], these low values can be interpreted as being due
to loosely packed pebble-sized bodies on the surface of comet 67P [217].

####  5.2.5 Gas Permeability

Expectation
The gas permeability of a small solar system body is determined by its
porosity and the characteristics of the pore spaces, such as their size
distribution and percolation properties. Tortuosity describes the actual
length of the path the gas takes divided by the closest distance between the
start and end points. Hence, high tortuosity hinders the gas flow, whereas low
values of tortuosity provide favourable gas-flow conditions. For
planetesimals, the gas permeability therefore depends on the porosity
distribution inside the body. For larger pebbles, the gas permeability
increases. Therefore, bodies of types A1 and A2 possess relatively high gas
permeability. However, if the redistribution of volatiles due to radiogenic
heating results in filling the voids in the ice shell (types B1 and B2), the
gas permeability can be greatly reduced, and the flow could even be stopped if
the pores are closed completely. In the deep interior, the permeability could
be increased where icy pebbles are extinct, but this depends on whether there
are pebbles consisting only of ices, leaving large voids behind, or pebbles
that are mixtures of ice and dust, with the voids created by ice evaporation
being small. For type B2 bodies, the permeability is inhomogeneous and follows
the distribution of rubble from the interior, the ice shell or the pristine
mantle. As type A/B3 bodies do not contain any ices which could sublimate, gas
permeability is not of interest. In general, the gas permeability directly
influences the possible pressure build-up inside a body with evaporating
volatiles, which can lead to ejection of material if the cohesion is overcome.

Comparison to Observations
Measurements of the gas permeability of the cometary subsurface material are
not directly possible. However, using thermophysical models for the
interpretation of the gas production rates of comets may shed light into the
vapour transport inside the cometary nucleus. This was done by, e.g., Gundlach
et al. 2020 [219], who found that a pebble pile can explain the observations
of the dust and gas emission of comet 67P around perihelion. Skorov et al.
2021 [220] investigated how variations of porosity and inhomogeneities of the
surface material affect the outgassing behaviour. They found high influence
due to porosity changes, but only minor contributions due to cavities and
cracks. Skorov et al. 2022 [221] showed that heterogeneous microstructures of
dust layers can be neglected, so that effectively a homogeneous dust layer is
a valid assumption for modelling outgassing. Further modelling of the
transport characteristics was performed by Reshetnyk et al. 2021 [222], which
is useful for the application to comet observations.

####  5.2.6 Permittivity

Expectation
Permittivity is a measure of the electric polarisability of a material in
response to an electric field and is dependent on the frequency of the
electromagnetic wave, porosity, temperature and composition of the body. It
can be divided into a real and an imaginary part. Brouet et al. 2014 [223]
investigated the permittivity of porous granular matter in different grain
size ranges. Besides refractory material, water ice can have a large influence
due to the strong dependency of the permittivity on frequency. For frequencies
below $10^{4}\,\mathrm{Hz}$, the permittivity $\epsilon$ is roughly three
orders of magnitudes higher than above $10^{4}\,\mathrm{Hz}$ [224]. This
effect could be used to investigate the water-ice abundance. Due to the
homogeneity of objects of types A1 and A2, the permittivity is homogeneous
throughout the whole body. The differentiation in type B1 objects results in a
radial gradient of the permittivity. As describe above, water ice and silica
can have similar permittivities in some frequency ranges. Therefore,
distinction between the two is only possible in frequency regimes in which the
materials possess different permittivities. For objects of type B2, the
permittivity is distributed inhomogeneously, following the rubble material
composition. As A/B3 bodies are by definition ice-free, there is no influence
due to water-ice permittivity, but the permittivity is expected to be
homogeneous inside single rubble.

Comparison to Observations
With the Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT)
[165], the permittivity of comet 67P was investigated with a frequency of 90
MHz [225, 174, 168]. The relative permittivity ranged from 1.7 to 1.95 in the
subsurface ($<$25 m) and from 1.2 to 1.32 in the interior. A denser surface
layer or a difference in composition could result in this dichotomy [168],
which could have evolved due to activity and redistribution of volatiles. The
interior seems to be more porous. This characteristic is similar to that of a
type B1 body, but the length scales could be different, and more detailed
simulations are needed to address this point. Further, the Surface Electric
Sounding and Acoustic Monitoring Experiment (SESAME) [226] instrument package,
including the permittivity probe onboard Philae, found hints of a more
compacted surface layer compared to the interior [227]; however, the
instrument only probed the first metres. Additionally, MIRO data can be used
to address the material properties, as performed by Bürger et al. (subm.)
[228] for optical constants in the millimetre-wavelength range, which are
linked to the permittivity. They found that a pebble-structured surface model
can fit the measured MIRO data. In general, the Rosetta results of
permittivity suggest high homogeneity, similar to bodies of type A1 and A2.

##  6 Conclusions and Open Questions

In this review, we presented our current understanding of planetesimal
formation and evolution in the context of comets being possibly the most
primitive survivors of these eras. We illustrated the most crucial processes
and pathways from protoplanetary dust to contemporary bodies of the solar
system in Figure 1. As ices are an important ingredient of comets, comet
formation as macroscopic bodies must start beyond the snowlines of the
volatiles and super-volatiles found in comets, e.g., CO2 and CO. Through three
phases of coagulation (see Figure 1 and Section 2), pebbles consisting of
microscopic ice and dust grains form in the size range of millimetres to
decimetres and cannot grow further due to growth barriers. These pebbles get
concentrated by hydrodynamic effects, leading to streaming instability, which
enhances the concentration of pebbles to the gravitational-instability limit,
followed by a gentle collapse of the pebble cloud into a many-kilometre-sized
object. These planetesimals follow a broad size–frequency distribution, but to
evolve into comets, their size cannot exceed 50 km due to the lithostatic
pressure, which destroys the pebbles for larger planetesimal sizes. Present
numerical models of the collapse stage do not have the resolution to predict
frequency at the small end of the expected size distribution of planetesimals,
particularly for sizes in the 1-10 km size range applicable to comets. Here,
more numerical work is needed to investigate the expected properties of the
smallest planetesimals.

The first phase of planetesimal evolution is dominated by radiogenic heating
by short-lived radioactive nuclei, which can redistribute volatiles inside the
planetesimals. This phase is followed by collisional evolution, whose outcome
depends on the specific impact energy. In this review, we differentiate
between sub-catastrophic, catastrophic and super-catastrophic collisions. All
these evolutionary processes result in five distinct types of evolved
planetesimals, designated by us as types A1, A2, B1, BS and A/B3 (see the
bottom of Figure 1). Additionally, it should be kept in mind that thermal
alteration by solar illumination on long time scales regarding the path from
the Kuiper Belt or the scattered disc inwards can influence the abundances of
volatiles [136].

The Rosetta Mission to comet 67P Churyumov–Gerasimenko provided a huge number
of scientific results as a baseline for the study of comet formation and
evolution. However, there are still many open questions, and it should be kept
in mind that these detailed measurements are only available for one comet
whose representation of the class of all comets in general is unknown. Only
objects of type A/B3 as non-icy rubble piles can be excluded to represent a
contemporary comet. Icy pebble piles (objects of types A1 and B1) preserve
most of the pristine planetesimal properties and would be most interesting for
the understanding of planetesimal formation. However, the possibilities to
distinguish icy pebble piles from icy rubble/pebble piles (types A2 and B2)
are restricted. As shown in Tables 1 and 2, the only distinction between types
A1 and A2 seems to be the remaining amount of fractal dust aggregates and the
binarity. Additionally, the expected differences between the various types
need to be modelled numerically, as here we have only made a relatively
generic description of their physical properties. Hence, simulations of
collisional outcomes of colliding pebble piles are urgently required,
including features such as the survival of fractals in the void spaces between
the pebbles and differentiation of the bodies following heating episodes.

Measurements of the permittivity of ice and dust pebbles would be helpful to
investigate the possibility to differentiate between volatiles and super-
volatiles within comets and to compare observations with thermophysical
modelling of the radiogenic heating. However, this is a complex endeavour
because deep-penetrating radar requires the usage of large wavelengths. DC
geo-electric methods with high penetration depths require spacecraft missions
with at least two landers.

Further measurements of temperatures at the surface as well as in the upper
layers of cometary nuclei are needed to constrain the makeup of the cometary
subsurface through comparison with thermophysical models. However, as there
are many factors affecting temperature, such as surface roughness, self-
heating and shadowing, the models need to be applied with care. In general,
the cooling phase in the cometary night seems to be most promising because the
above influences are reduced, and models have shown that much information can
be extracted.

Future missions to and astronomical observations of comets may be able to test
the following most crucial predictions of the pebble-cloud-collapse model of
planetesimals and subsequent evolutionary processes into comets:

  * i

Strong positive correlation between the surface temperature at sunrise and the
insolation at local noon for a subsurface made of pebbles, in contrast to no
such dependency for a makeup without large void spaces [149], measurable by
thermal IR mapping. Such measurements would deliver, from remote observations
only, invaluable information about the presence and size of pebbles in a
shallow subsurface layer.

  * ii

Proof of the absence or presence of internal volatile differentiation of
comets, as predicted by Malamud et al. 2022 [150] for comets consisting of
pebbles, measurable by long-wavelength radar. Such measurements would deliver
information about the formation time and/or abundance of radiogenic nuclei and
about the thermal conductivity in the deep interior of the comet nucleus, and
thus would confirm or disprove the gravitational-collapse theory.

  * iii

Search for traces of the collisional evolution of cometary nuclei, measurable
by radar through the amplitude and length scale of internal inhomogeneities.
Due to the obvious distinction of the internal makeup of bodies of type A1,
B1, A2, B2 and A/B3 (see Figure 1), deep-penetrating radar measurements
covering the entire body would provide information about the internal
distribution of water ice, the refractory component and the void spaces inside
the body.

  * iv

Determination of the physical properties and orbital parameters of extinct
comets. Due to memory effect (see [134]) or differentiation (see [150]), the
depth to which dust activity is possible strongly depends on the original size
of the comet-precursor body, so larger comets should be going extinct on a
different timescale than smaller ones (see [229]).

  * v

Determine whether positive relief features [106] are local remnants of
impacts, measurable by high-frequency radar through local permittivity
enhancement. If moderate-velocity impacts on the surface of a planetesimal
lead to local compaction of the material and thus to loss of the pebble
structure, further dust activity is impossible due to considerable enhancement
of the tensile strength. Such measurements would deliver information about the
collision history of the planetesimals and the abundance of small-scale
(metre- to decimetre-sized) objects in the region in which the planetesimals
resided throughout most of their lifetime before becoming comets.

It should be noted that the picture of formation and evolution of
planetesimals drawn in this review cannot be complete because it ignores
evolutionary processes that are usually summarised under space weathering. We
again emphasise that we only provide one plausible, but not the only possible
scenario of the formation of planetesimals and evolution into comets.
Advantages of the pebble-collapse model of comet formation are that it is
entirely based on a large body of empirical evidence from the laboratory as
well as on established numerical simulations of hydrodynamic processes. The
pebble-collapse model explains a number of observations of comets,
particularly of comet 67P, such as the low bulk density, ultra-low mechanical
strength, low thermal conductivity, presence of ultra-low-density dust
particles and internal homogeneity. However, there are observations of comet
67P that the model cannot explain. Among these are the observed layering, the
presence and variety of macroscopic ($\gtrsim$$1\,\mathrm{m}$) geologic
features and the measured increase of permittivity in a shallow
($\lesssim$$25\,\mathrm{m}$) subsurface region, for which alternative
formation models may have explanations (unless they are evolutionary
processes). These models are discussed in Weissman et al. 2020 [4].

## Acknowledgments

The picture drawn in this review is the result of decades of research by
numerous scientists whom we would like to thank. We also acknowledge that
without the continuous support of funding agencies, foremost the Deutsche
Forschungsgemeinschaft DFG and the Deutsches Zentrum für Luft- und Raumfahrt
DLR, this work would not have been possible. This research was funded by DFG
grant number BL 298/27-1.

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