##  Chapter 0 Debris disks around main-sequence stars

Tim D. Pearce  Department of Physics, University of Warwick, UK

###### Abstract

[Abstract]

‘Debris disks’ are collections of small bodies around stars, such as the
Asteroid Belt and Kuiper Belt in our Solar System. These disks are composed of
objects smaller than planets, including asteroids, comets, dust, and dwarf
planets. We detect debris disks around a significant fraction of stars, and
these disks appear to be common components of planetary systems. Extrasolar
debris disks have a broad range of locations, shapes and features. This
chapter provides an introduction to debris disks around main-sequence stars.
It summarises our understanding of the field, and covers a wide range of
concepts from observations and theory. It describes how we detect extrasolar
debris disks, what we see, and what these observations tell us. It also
describes how debris disks evolve, and how they interact with planets. The
chapter concludes by discussing several unsolved questions in debris-disk
science.

###### keywords:

Debris disks, circumstellar disks, circumstellar dust, circumstellar gas,
exozodiacal dust, planetesimals, planetary system formation, planetary system
evolution, collisional processes

Contents

Learning objectives Learning objectives
Learning objectives Learning objectives
Learning objectives Learning objectives
1. Introduction: what are debris disks? 1
2. Observations of extrasolar debris 2
1. Dust observations 1
2. Gas observations 2
3. Debris-disk theory 3
1. Origins of debris disks 1
2. Why do debris disks look different at different wavelengths? 2
3. Size distribution and the collisional cascade 3
4. Planet-debris interactions 4
5. Models of warm and hot dust 5
4. Unsolved problems in debris-disk science 4
5. Conclusions 5

### Learning objectives

By the end of this chapter, you should understand:

  * •

What a debris disk is

  * •

How we observe debris around main-sequence stars

  * •

Where debris is located around stars

  * •

How debris evolves through dynamical forces and collisions

  * •

How planets interact with debris

  * •

What the major questions are in debris-disk science

[

Glossary]

Apoastron (or apastron) The point on an eccentric orbit around a star which is
furthest from the star.

Back scattering Where light scattered by a dust grain is deflected by almost
${180^{\circ}}$ from its incident angle.

Blackbody A theoretical body that is a perfect absorber and emitter of
radiation.

Blackbody radius The distance a blackbody would have to lie from a star to
have a certain temperature.

Blowout size The size of a dust grain just small enough to be blown away from
a star by radiation pressure or stellar winds.

Catastrophic collision A collision where the largest surviving fragment has
less than half the mass of the original body.

Clump An overdensity that does not extend all the way around the star.

Cold dust Dust in the outer regions of planetary systems, with typical
temperatures of order ${30\;{\rm K}}$.

Collisional cascade Bodies colliding and breaking up into smaller bodies,
which then collide and break into even smaller bodies, etc.

Continuum Component of an SED that is relatively smooth, as opposed to the
sharp features at spectral lines.

Coronagraph A device that blocks out starlight, allowing fainter objects to be
resolved.

Debris Solid objects smaller than planets, such as asteroids, comets, dust and
dwarf planets.

Debris disk A population of debris bodies, such as the Asteroid Belt and
Kuiper Belt in the Solar System.

Exozodi Warm dust near the habitable zone in extrasolar systems, which may be
analogous to Zodiacal dust in the Solar System.

Extreme debris disk A debris disk with an unusually high luminosity, typically
above ${1\%}$ of the star’s luminosity.

Forward scattering Where light scattered by a dust grain is deflected only
slightly from its incident angle.

Gamma factor The ratio of dust’s actual location to its blackbody radius.

Halo A population of small grains on eccentric orbits, which extend out beyond
the main debris disk.

Hill radius For a body orbiting a star, the distance around the body where its
gravity dominates over that of the star.

Hot dust Dust very close to stars, with temperatures of order ${1000\;{\rm
K}}$. Also known as a hot exozodi.

Hot exozodi Another name for hot dust.

Hybrid disk A young disk with large amounts of gas but relatively small
amounts of dust. It may contain primordial gas but collisional dust, and be
transitioning from a protoplanetary disk into a debris disk.

Infrared excess Flux from dust, which makes a system brighter at infrared
wavelengths than would be expected from the star alone.

Interferometer Several telescopes combined together to produce higher-
resolution images.

Main-sequence star A star that fuses hydrogen into helium in its core. Most
stars, including the Sun, are in this phase of their lives.

Mean-motion resonance (MMR) A dynamical interaction that occurs if the orbital
periods of bodies are near simple fractions of each other.

Metallicity The abundance of elements other than hydrogen and helium in an
object.

Nominal MMR location The semimajor axis where two bodies in the ${(p+q):p}$
MMR have an orbital-period ratio of exactly ${(p+q):p}$.

Optically thin Describes a medium or object where almost all incident light is
transmitted through it.

Order (of MMR) The value of $q$ in the ${(p+q):p}$ MMR.

Periastron The point on an eccentric orbit around a star which is closest to
the star.

Phase function The relationship between the scattered-light brightness and the
scattering angle.

Planetary system At least one star, plus any planets and other material that
formed from its protoplanetary disk.

Planetesimal A solid object which is smaller than a planet but larger than a
dust grain, such as an asteroid.

Polarisation The direction in which an electromagnetic wave’s electric field
oscillates.

Poynting-Robertson (P-R) drag A drag force arising from photons hitting a
moving dust grain.

Protoplanetary disk A massive disk of gas and dust surrounding a young star,
from which planets and debris may form.

Radiation pressure A force arising from photons hitting a dust grain, which
acts in the direction away from the star.

Scattered light Light reflected off dust grains.

Scattering (dynamical) A short-term dynamical interaction, occurring when two
bodies make a close approach to each other.

Scattering angle The angle between the incident photon’s path and the
scattered photon’s path.

Secular interaction A long-term dynamical interaction, occurring over
timescales much longer than orbital periods.

Spectral-energy distribution (SED) A plot of the relationship between flux and
wavelength.

Spectral lines Narrow spikes or dips in an SED, which correspond to specific
quantum processes in atoms or molecules.

Stirring A dynamical process that excites debris orbits, causing debris bodies
to collide destructively.

Thermal emission Photons radiated as heat from objects.

Transition disk A disk of gas and dust around a young star, with a cavity at
its inner region. May be transitioning from a protoplanetary disk to a debris
disk.

Trojan Objects on a similar orbit to a planet, in a 1:1 MMR and located about
$60^{\circ}$ ahead of or behind the planet.

Volatiles Substances that easily vaporize.

von Zeipel-Kozai-Lidov mechanism A secular interaction, sometimes called the
Kozai mechanism, where a body oscillates between a low-eccentricity orbit with
high inclination, and a high-eccentricity orbit with low inclination.

Warm dust Dust located near the habitable regions of planetary systems, with
temperatures of order ${300\;{\rm K}}$.

Zodiacal dust Interplanetary dust in the Solar System.

[

Nomenclature]

ALMA |  The Atacama Large Millimeter/submillimeter Array
---|---
GPI |  The Gemini Planet Imager, on the Gemini South Telescope
HST |  The Hubble Space Telescope
JWST |  The James Webb Space Telescope
MMR |  Mean-motion resonance
P-R drag |  Poynting-Robertson drag
SED |  Spectral-energy distribution
SPHERE |  The Spectro-Polarimetric High-contrast Exoplanet REsearch instrument, on the VLT
VLT |  The Very Large Telescope

###  1 Introduction: what are debris disks?

Our Solar System is a ‘planetary system’, which means a system of bodies
orbiting one or more stars. It contains the Sun, planets and moons, but also
many small objects, such as asteroids, comets, dwarf planets and dust.
Collectively, these small objects are called ‘debris’. Debris exists almost
everywhere in the Solar System, from Sun-grazing comets in the inner regions,
to interplanetary dust, the Asteroid Belt, Kuiper Belt, and long-period comets
further out. Debris is also not unique to the Solar System; we detect debris
around other stars too. We think that all stars probably host debris in some
form, some of which is similar to debris in the Solar System, and some
different. Figure 1 shows some types of debris detected so far.

Figure 1: Some of the debris found in planetary systems. The star is the large
yellow circle, and the two smaller circles are planets.

A collection of debris in a planetary system is called a ‘debris disk’. This
term can either mean all the debris in a planetary system, or it can mean
individual debris populations, like the Asteroid Belt or Kuiper Belt. The box
below provides a very brief outline of a debris disk and how it evolves, to
bear in mind as you read this chapter. Each of the concepts mentioned will be
explained later.

[chap1:box1]Key concept: outline of a debris disk

To picture a debris disk, imagine a collection of bodies in a planetary
system. These range in size from small dust grains up to asteroids, and
possibly dwarf planets. These bodies break apart over time due to violent
collisions and other processes. This fragmentation releases dust and gas,
which we can detect in extrasolar systems. As the debris bodies get smaller
they experience different forces, and when they get small enough they are
removed from the system by radiation forces. This means that debris disks lose
mass over time.

This chapter focuses on debris around ‘main-sequence’ stars, which are stars
in the mid-stage of their lives. Other chapters cover debris at other stages
in a star’s life. This chapter also focuses on extrasolar debris, with other
chapters covering Solar System bodies. The first part of this chapter
describes observations of extrasolar debris disks (Section 2), and the second
part describes our theoretical understanding of debris (Section 3). The final
part discusses some unanswered questions in debris science (Section 4).
Throughout this chapter, new terms are highlighted in quotation marks, and
these terms are listed in the glossary.

###  2 Observations of extrasolar debris

Many people know that we can detect extrasolar planets. We also detect
extrasolar debris, with the first such detection made in the 1980s around the
star Vega (Aumann et al., 1984). Since then, we have detected debris around at
least 600 main-sequence stars within ${200\;{\rm pc}}$ of Earth (Matthews et
al., in prep.). Surveys find debris around ${20\%}$ of main-sequence stars,
and this ${20\%}$ almost certainly underestimates the true fraction of stars
with debris disks, because modern instruments are only sensitive to the
brightest disks (Wyatt, 2008). For example, the Solar System’s Asteroid and
Kuiper Belts, were they located around another star, would be too faint to
detect with current technology.

There are several techniques for detecting extrasolar debris. These range from
individual flux measurements, which hint that debris is present, to resolved
images that show debris structures in exquisite detail. Figure 2 shows several
extrasolar debris disks, resolved with different instruments and showing
different types of debris. Each of these disks have distinct features, which
will be discussed throughout this chapter. This section explains how we detect
debris, which is done by observing dust and gas, and what these observations
show.

Figure 2: Observations of dust around main-sequence stars. These are ‘cold’
debris disks in the outer regions of planetary systems, at 10s or 100s of au
from their stars. Each panel shows a different system, with the star at the
centre. Each panel gives the system name in the top left, and the image
wavelength followed by the instrument name in the bottom right. In images c)
to f), coronagraphs were used to block out the star, so no data are available
inside the filled areas. References: a) Marino et al. (2018), b) Booth et al.
(2023), c) Schneider et al. (2014), d) Boccaletti et al. (2018), e) Golimowski
et al. (2006), f) Hom et al. (2024).

####  1 Dust observations

Most of our information about extrasolar debris disks comes from observations
of dust. This is because dust has a large surface area, so is brighter and
easier to detect than larger objects. When dust gets illuminated by a star, it
emits photons in two main ways: ‘scattered light’, and ‘thermal emission’.
These processes let us detect extrasolar dust.

[chap1:box1]Key concept: dust is seen in scattered light and thermal emission

  * •

Scattered light. This is where light from a star gets reflected off a dust
grain.

  * •

Thermal emission. This is where a grain radiates heat as photons.

Scattered light and thermal emission emit photons at different wavelengths.
For scattered light, emitted photons have similar wavelengths to the incident
photons. This means that dust seen in scattered light has a similar spectrum
to the star. For thermal emission, the emitted wavelengths depend on dust
temperature, with colder grains emitting at longer wavelengths. The
temperature depends on distance to the star, with more-distant dust being
colder. This temperature is often used to categorise dust:

  * •

‘Cold dust’: dust at temperatures of order ${30\;{\rm K}}$. Located in the
outer regions of planetary systems, at 10s to 100s of au from stars.

  * •

‘Warm dust’: temperatures of order ${300\;{\rm K}}$. Distances of order
${1\;{\rm au}}$, which is near the habitable zone.

  * •

‘Hot dust’: temperatures of order ${1000\;{\rm K}}$. Located very close to
stars, at ${0.1\;{\rm au}}$ or less.

Temperature is not the only factor that sets the wavelengths of dust emission.
Another important factor is grain size, with smaller grains emitting at
shorter wavelengths.

[chap1:box1]Key concept: observations detect grains with sizes similar to the
observing wavelength

When we observe dust, we detect grains with sizes similar to the observing
wavelength. This is due to a combination of two effects:

  * •

Grains are inefficient at emitting photons with wavelengths larger than the
grain size.

  * •

Smaller debris is more numerous. The smallest dust dominates a debris disk’s
surface area, so these grains can absorb and emit more photons.

These two effects mean that emission at one wavelength is mainly from grains
with sizes around that wavelength. The instruments that detect extrasolar
debris mainly operate between sub-micron and millimetre wavelengths, because
debris is too faint at wavelengths longer than this. This means that we cannot
directly detect extrasolar debris larger than a few centimetres.

##### Spectral-energy distributions (SEDs)

The first detections of extrasolar debris were made by analysing ‘spectral-
energy distributions’ (SEDs), which are relationships between a system’s flux
and wavelength. These SEDs made it clear that debris exists in planetary
systems, even though we could not see it directly at the time. Figure 3 shows
the SED of the  Pictoris system, which hosts at least two dust populations.

Figure 3: SED of the  Pictoris system. This system has an ‘infrared excess’,
indicating the presence of debris. Red diamonds show measured fluxes, and
lines are models. The star flux (blue line) dominates at shorter wavelengths,
but cannot reproduce the data at longer, infrared wavelengths. This infrared
excess demonstrates that two debris populations are present: a colder outer
disk, and a warmer inner disk. The fluxes from these populations are the red
and orange lines respectively. Most of the debris flux comes from the outer
disk, but that disk does not produce enough flux around 10 µm to reproduce
observations, which is why the inner-disk model is also needed. The black line
is the combined flux from the star and debris models, which reproduces the
observational data. The inset shows the locations of debris in the system. The
data and modelling are described in Yelverton et al. (2019).

Individual objects have different SEDs, depending on their temperature and
composition. A star’s SED is similar to that of a ‘blackbody’, which is a
theoretical body that is a perfect absorber and emitter of radiation. A star’s
SED peaks at wavelengths that depends on its temperature, and declines at
longer wavelengths. The SEDs of isolated stars are known very accurately, so
if a system’s SED deviates from the expected star SED, then other objects must
be present. This can be used to detect dust in planetary systems. The dust
causes the measured flux (red diamonds on Figure 3) to significantly deviate
from the stellar SED (blue line). Since dust is colder than stars, the thermal
emission from dust peaks at longer wavelengths. This peak is often at infrared
wavelengths, so systems with dust are sometimes said to have ‘infrared
excesses’. Scattered light from dust also contributes, but this component is
difficult to detect in SEDs because it is very similar to the star, and much
fainter.

The dust quantity and location can be calculated from SEDs. Dust quantity is
related to its brightness, which can be calculated as the total system flux
minus the stellar flux. Dust in debris disks is ‘optically thin’, meaning it
has a low optical depth and hence no dust is hidden from view. This means the
dust brightness can be converted directly into dust quantity, by making some
assumptions about its optical properties (e.g. Equation 5 in Krivov and Wyatt
2021).

Dust location can also be inferred from SEDs. The SED of dust is similar to a
blackbody, and peaks at a wavelength that depends on its temperature. Fitting
a blackbody to the dust SED yields a temperature $T_{\rm BB}$, which can be
converted to a ‘blackbody radius’ $r_{\rm BB}$ using

$r_{\rm BB}=1\;{\rm au}\;\left(\frac{T_{\rm BB}}{278\;{\rm
K}}\right)^{-2}\left(\frac{L_{*}}{\;{\rm L_{\odot}}}\right)^{1/2},$ (1)

where $L_{*}$ and $\;{\rm L_{\odot}}$ are the luminosity of the star and Sun
respectively. However, the blackbody radius $r_{\rm BB}$ often does not
correspond to the actual location of the dust, $r_{\rm d}$, because grains are
not perfect blackbodies. To account for this, we multiply $r_{\rm BB}$ by the
empirical ‘Gamma Factor’ $\Gamma$:

$r_{\rm d}=\Gamma r_{\rm BB}.$ (2)

The value of $\Gamma$ varies between about 1 and 4, and depends on star
luminosity (Pawellek and Krivov, 2015).

SEDs can identify cold dust in the outer regions of systems, and also warmer
dust closer to stars. The example on Figure 3 shows a system with both cold
and warm dust, where two blackbodies are required to fit the observations.
These two blackbodies peak at different wavelengths, implying that the system
hosts dust at two different temperatures (and hence two different locations).

##### Resolved images of cold dust

SEDs are useful for constraining the dust quantity, and its rough location.
However, SEDs are often less informative than resolved images, because
resolved images reveal the shape and extent of the dust distribution. Figure 2
shows some resolved images, and about 200 debris disks have now been
resolved111Catalogues of resolved debris disks are available at
circumstellardisks.org/ and astro.uni-jena.de/index.php/theory/catalog-of-
resolved-debris-disks.html.. Some resolved images are made using one
telescope, whilst others are ‘interferometric’, where multiple telescopes are
combined to produce higher-resolution images.

Resolved observations show dust in either scattered light or thermal emission,
depending on the observing wavelength. Scattered-light observations have
relatively short wavelengths, typically around ${1\;{\rm\upmu m}}$, which is
where stars are brightest (Figure 3). This is because scattered photons have
similar wavelengths to incident photons, so scattered light from dust peaks at
the same wavelengths as the star. Since the star is orders of magnitude more
luminous than dust, scattered-light observations often require ‘coronagraphs’,
which block out starlight to reveal fainter debris. Panels c to f of Figure 2
show scattered-light observations, with coronagraphs marked by the filled
areas. Since coronagraphs obscure the region around the star, scattered-light
observations tend to resolve cold dust in the outer regions of planetary
systems.

Thermal-emission observations usually have longer wavelengths, typically
between ${10\;{\rm\upmu m}}$ and ${1\;{\rm mm}}$. For cold and warm dust, this
is where the dust’s SED peaks (Figure 3). At these wavelengths dust is often
much brighter than the star, so thermal observations generally do not require
coronagraphs. Panels a and b of Figure 2 show thermal observations; the star
is not visible on panel a, and does not outshine the dust on panel b. Like
scattered light, thermal images between ${10\;{\rm\upmu m}}$ and ${1\;{\rm
mm}}$ tend to show cold dust in the outer regions of systems. They can also
detect warm dust closer to stars, but cold dust is often more plentiful, so is
usually brighter.

The main difference between thermal and scattered-light observations is the
type of dust they probe. Thermal-emission observations have longer
wavelengths, so probe larger grains. Scattered-light observations have shorter
wavelengths, so probe smaller grains. Comparing scattered-light and thermal-
emission images reveals that debris disks look different at different
wavelengths. Typically, disks appear more compact at longer wavelengths
(thermal emission), and more extended at shorter wavelengths (scattered
light). This means that dust grains of different sizes have different spatial
distributions. Figure 4 shows an example, where one disk is resolved at three
different wavelengths, revealing three different shapes.

Figure 4: Dust around the star Fomalhaut, imaged at three different
wavelengths. The main dust ring (visible on all three panels) is slightly
elliptical, so the star is offset from its centre. Left panel: HST image
centred on a wavelength 0.6 µm, with a coronagraph to mask the star (Kalas et
al., 2013). Middle panel: JWST image at 25.5 µm, revealing the main ring and
also inner dust, which is not visible at other wavelengths (Gáspár et al.,
2023). Right panel: ALMA image at 1.3 mm, where the main ring and star are
detected (MacGregor et al., 2017).

The reason that disks look different at different wavelengths is that grains
of different sizes are affected by different forces. This will be explained in
Section 2, but generally, large grains are mainly affected by gravity, whilst
small grains are also affected by other forces. Thermal observations of large
grains should therefore trace the distribution of ‘planetesimals’, which are
objects smaller than planets but larger than dust, and which are thought to be
the source of dust in debris disks. We cannot detect planetesimals directly,
but they should be co-located with large grains, because they both experience
similar forces. Conversely, small grains can have very different orbits. They
can form ‘halos’, which are structures extending beyond the planetesimal belt,
comprising small grains which are driven onto wide orbits by non-gravitational
forces. Figure 2c shows a halo in scattered light, where the halo is the wide,
triangular structure below and to the left of the star.

[chap1:box1]Key concept: debris disks look different at different wavelengths

Grains of different sizes have different spatial distributions, so debris
disks look different at different wavelengths. Disks are usually more compact
at longer wavelengths and more extended at shorter wavelengths.

There are also other differences between scattered-light and thermal-emission
observations. Scattered-light images can be used to measure ‘polarisation’,
which is the orientation of the light’s electric-field oscillation. Light from
stars is unpolarised, meaning it oscillates in all directions, but scattered
light is polarised, meaning it preferentially oscillates in certain
directions. Polarisation measurements let us constrain various dust
properties, including the composition, size and porosity of dust grains.
Scattered-light observations also depend on the ‘phase function’, which is the
relationship between brightness and ‘scattering angle’ (the angle between the
incident photon’s path and the scattered photon’s path). A dust grain does not
scatter light equally in all directions; most light is ‘forward scattered’,
meaning it is only slightly deflected from its path, and less light is fully
reflected by ${180^{\circ}}$ (‘back scattered’). This means that disks seen in
scattered light tend to look brighter on the side between us and the star, and
fainter on the far side. Figure 2f shows an example, where the visible part of
the disk (top) is closest to us, and the far side (bottom) appears much
fainter.

##### Warm and hot dust from interferometry

One way to detect warm dust is from its infrared excess, like on Figure 3.
Another method is to use interferometry, which can separate the dust flux from
the star flux. This lets us detect dust located very close to stars.
Interferometry is used to detect both warm and hot dust, with fluxes around
${1\%}$ of the star’s flux.

Warm dust is detected at mid-infrared wavelengths, around ${10\;{\rm\upmu
m}}$. This dust appears to lie near the habitable zone, and some may be
analogous to the ‘Zodiacal dust’ between planets in the Solar System. Hence
extrasolar warm-dust populations are sometimes called ‘exozodis’, and we
detect them around 20 to ${30\%}$ of main-sequence stars (Ertel et al., 2020).
The other population is hot dust, which is detected at near-infrared
wavelengths around ${1\;{\rm\upmu m}}$. This dust appears to have temperatures
of at least ${1000\;{\rm K}}$, and is located very close to stars. Populations
of hot dust are sometimes called ‘hot exozodis’, and we also detect them
around 20 to ${30\%}$ of main-sequence stars (Ertel et al., 2020).

There are no strong correlations between warm and hot dust, with some stars
having both populations, some having one, and some having neither. Warm dust
is strongly correlated with cold dust, but hot dust is not. Warm and hot dust
both seem to be independent of the star’s age and spectral type; populations
are found around A- to K-type stars, with ages from 10s of Myr to several Gyr
(Ertel et al., 2020). Theoretical attempts to explain warm and hot dust are
discussed in Section 5.

##### Conclusions from dust observations

This section summarises our observational constraints on dust around main-
sequence stars. Figure 5 shows the locations, luminosities and ages of cold
and warm debris disks, from a sample of 179 systems222The sample and data are
from Pearce et al. (2022a) and references therein, including unpublished ALMA
data generously shared by Luca Matrà.. The extrasolar disks have typical
luminosities of $10^{-2}$ to ${10^{-5}}$ times those of their stars, meaning
these disks are much brighter than our Asteroid Belt and Kuiper Belt (both
around ${10^{-7}}$). This is because modern technology is unable to detect
dust as faint as ours around other stars. The figure shows that many disks lie
at tens or hundreds of au from their stars, and that some resolved disks are
very broad, and others very narrow. Debris-disk systems have ages from about
${10\;{\rm Myr}}$ to several Gyr, and disks around older stars are generally
fainter; this is consistent with the idea that debris disks lose mass over
time.

Figure 5: Locations, luminosities and ages of cold and warm debris disks. On
the left panel, orange bars show the widths of ALMA-resolved disks. Other
disks are shown as blue points; the widths of these disks are often
unconstrained from observations, so blue points show the approximate locations
of the disk centres. The right panel shows the decline in disk brightness with
age. The Asteroid Belt and Kuiper Belt are shown on both panels, and are much
less luminous than detected extrasolar disks.

Debris is found around main-sequence stars of all spectral types. Many of the
brightest and most-studied debris disks are around A-type stars, because these
massive stars are bright and often young, which makes debris easier to detect.
Disks are also found around many intermediate, FGK-type stars like our Sun.
Very few disks are found around M-type stars; this may be because these low-
mass stars have fainter disks, which would make them harder to detect (Luppe
et al., 2020). There may be a trend for disks around more luminous stars to
have larger radii (Matrà et al., 2018).

Resolved images show that many debris disks are not just symmetric, uniform
rings. Instead, they have very diverse shapes and structures. Some disks are
narrow and eccentric, like Fomalhaut on Figure 4. Others are broad and contain
gaps, like ${{\rm HD}\;107146}$ (Figure 2a). Some disks have warps, where the
inner and outer regions are misaligned (like  Pictoris, shown edge-on on
Figure 2e). Some have ‘clumps’, which are overdensities that do not extend all
the way around the star. Some disks have sharp edges, whilst others have
smoother edges (Imaz Blanco et al., 2023). However, there are no clear
detections of spirals in debris disks, which contrasts with the many spiral
detections in ‘protoplanetary disks’ (the young, massive disks of gas and dust
from which debris and planets form). Finally, most resolved, cold disks are
quite flat; disks seen edge-on in millimetre wavelengths typically have
vertical thicknesses that are a few percent of their radii.

Most debris disks do not vary between observations, but there are some
exceptions. Some disks with unusually high infrared excesses, dubbed ‘extreme
debris disks’, undergo large brightness changes (e.g. Meng et al. 2015). These
may be caused by collisions between large objects during terrestrial-planet
formation. Some resolved disks are also variable, such as AU Microscopii,
which hosts features seen to move away from the star over several years. Two
such features are visible on Figure 2d, as the two bumps above the left side
of the disk.

Studies have also searched for correlations between debris disks and various
system parameters. Some find that debris is more common in systems with low-
mass planets, and less common in systems with high-mass planets, although
other studies find no such correlations (e.g. Yelverton et al. 2020). Studies
also analysed the ‘metallicity’ of debris-disk stars, which means the
abundance of elements other than hydrogen and helium. No clear correlations
between star metallicity and debris are identified, although fewer disks may
be detected around lower-metallicity stars (e.g. Gáspár et al. 2016).

####  2 Gas observations

Dust is not the only detectable component of debris disks; we also see gas.
Some gas is co-located with known dust belts, and gas at other locations
appears to be released by comets. Both gas populations are discussed below.

##### Gas near dust belts

Gas in debris disks can be identified through ‘spectral lines’, which are
sharp features in SEDs at very specific wavelengths. Examples of spectral
lines can be seen on Figure 3, as the small spikes in the star’s SED. These
correspond to specific quantum processes, such as emission when an electron
moves to a lower energy level in an atom. Spectral lines can identify a
specific atom or molecule, and the lines on Figure 3 are associated with
processes in the star. However, gas in debris disks also has spectral lines,
and these are used to detect the gas333Spectral lines are also used to probe
dust compositions. For example, dust made of silicates has a spectral line
around ${10\;{\rm\upmu m}}$, which can be identified in SEDs..

The gas most commonly considered in debris disks is carbon monoxide, or CO.
This is because CO has strong spectral lines that are relatively easy to
detect, located at wavelengths around ${1\;{\rm mm}}$. These are emission
lines, meaning they correspond to spikes in the SED (rather than dips). Figure
6 shows an ALMA image of CO gas in the  Pictoris system (right panel),
compared to a ‘continuum’ image of millimetre-sized dust (left panel).
‘Continuum’ means the component of an SED that is relatively smooth, as
opposed to the sharp features at spectral lines.

Figure 6: Dust and gas in the  Pictoris system, imaged by ALMA (Dent et al.,
2014). The left panel shows millimetre-sized dust, and the right panel shows
CO gas. The star and plus symbols mark the star and a detected planet,
respectively. The disk is seen edge on, and each panel has the same scale and
spans about 350 au from left to right. The gas lies at a similar location to
the dust, and there is a clump in the gas on the right side of the image.

CO is detected in a few tens of nearby debris disks, which tend to be in young
systems (Hughes et al., 2018). Most CO detections are around A-type stars, but
there are some around Sun-like stars too. The amount of gas in debris disks is
significantly less than in protoplanetary disks, and the origin of debris-disk
gas is unclear. One possibility is that CO in debris disks is released during
collisions between debris bodies with a high ‘volatile’ content, where
‘volatiles’ are substances that easily vaporize. Another possibility is that
the gas is primordial, left over from the gas-rich protoplanetary disk.

Gas teaches us about the composition of debris. Using CO observations and
collisional arguments, it was shown that planetesimals in several extrasolar
debris disks contain similar quantities of CO and CO2 as Solar System comets
(e.g. Matrà et al. 2017). Gas can also teach us about disk rotation. For a
rotating disk, light from the part rotating away from us is slightly
redshifted, and light from the part rotating toward us is slightly
blueshifted. Since spectral lines occur at specific wavelengths, we can use
them to measure the redshift at different points in a gas disk. This yields
the disk’s rotation direction (e.g. Matrà et al. 2017).

##### Extrasolar comets

Gas also lets us detect exocomets around other stars. As a comet approaches a
star, it heats up and releases gas. If this gas lies between us and the star,
then we may detect the gas in absorption. This means we see dips in the star’s
SED, corresponding to spectral lines in the gas. Some absorption lines vary
with time, often over hours, which implies that we detect individual comets as
they pass close to stars.

One of the most-studied exocomet systems is  Pictoris, which has very frequent
and significant absorption events. The comets responsible for this absorption
appear to have ‘periastron’ distances of order ${0.1\;{\rm au}}$, where
‘periastron’ means the point on an orbit that is closest to the star. Surveys
detect variable absorption indicative of comets around about 14% of stars, and
there may be a tentative correlation between this variable absorption and hot
dust (Rebollido et al., 2020).

###  3 Debris-disk theory

The first part of the chapter summarised debris-disk observations. This second
part summarises our theoretical understanding of debris disks. Section 1
outlines how we think debris disks form, and Section 2 explains why they look
different at different wavelengths. Section 3 describes how dust is produced
in debris disks, and what this implies about larger debris bodies. Section 4
details how planets interact with debris, and Section 5 describes our efforts
to understand warm and hot dust.

####  1 Origins of debris disks

Stars form when a giant cloud of gas and dust collapses under its own gravity.
As it collapses, the cloud fragments into smaller parts. Each part becomes
hotter and denser, and eventually forms one or more protostars at its core.
Some material has too much angular momentum to fall directly onto the core,
and this material collapses down into a disk around the protostar(s). This is
the protoplanetary disk. After a few Myr, the protoplanetary disk disperses.
The actual dispersion process is unknown, but it seems to be relatively fast.
Some observed disks may currently be in this dispersion phase, such as
‘transition disks’ and ‘hybrid disks’, but this is unclear.

After dispersion, much of the gas and dust from the original protoplanetary
disk has gone. It may have formed into planets, accreted onto a star, or been
blown away. What is left is a young planetary system, containing one or more
stars, planets, planetesimals, and perhaps small quantities of gas and dust.
The planetesimals, which can be thought of as remnant bodies left over from
planet formation, comprise the young debris disk. Over time these
planetesimals collide with each other, releasing the dust that we see (Section
3).

####  2 Why do debris disks look different at different wavelengths?

Figure 4 showed that debris disks look different at different wavelengths.
This is because different wavelengths probe different grain sizes, and
different grain sizes have different spatial distributions. This section
examines the physical reasons behind this.

[chap1:box1]Key concept: different bodies experience different forces

Larger debris, such as asteroids and dwarf planets, are predominantly affected
by gravity. Smaller debris, such as dust, are also affected by non-
gravitational forces. This causes different debris sizes to have different
spatial distributions, and so debris disks look different at different
wavelengths. The distribution of larger grains tends to be more confined than
that of smaller grains.

##### Forces on debris

Debris orbiting a star is subject to several forces, as well as the inward
pull of the star’s gravity. These additional forces are described below.

###### Radiation pressure

‘Radiation pressure’ arises due to photons from the star hitting a dust grain,
and this force acts in the opposite direction to gravity. Since both gravity
and photon flux scale with $r^{-2}$, where $r$ is the distance to the star,
the main effect of radiation pressure is to reduce the net inward pull on the
grain. The gravitational force is

$\boldsymbol{F}_{\rm grav}=-\frac{GM_{*}m_{\rm
d}}{r^{2}}\boldsymbol{\hat{r}},$ (3)

where $G$, $M_{*}$ and $m_{\rm d}$ are the gravitational constant, star mass
and grain mass respectively, and $\boldsymbol{\hat{r}}$ is the unit vector in
the star-grain separation direction. For a grain on a circular orbit, the
combined effect of radiation pressure and gravity produces a net radial force
of

$\boldsymbol{F}_{\boldsymbol{r}}=\boldsymbol{F}_{\rm grav}(1-\beta),$ (4)

where $\beta$ is a positive value denoting the ratio of radiation pressure to
gravity (Burns et al., 1979). The $\beta$ value depends on grain size, shape,
composition and star type, with smaller grains generally having larger $\beta$
values. This means that smaller grains are usually more affected by radiation
pressure than larger grains.

To show the effect of radiation pressure, consider a body on a circular orbit,
which releases two dust grains. One grain has ${\beta=0}$, and the other has
${\beta>0}$. The grain with ${\beta=0}$ feels only gravity, so would enter a
circular orbit. Conversely, the grain with ${\beta>0}$ would enter a non-
circular orbit, with its furthest point (‘apoastron’) outside the release
point. If $\beta$ were high enough, then radiation pressure would overcome
gravity, and the grain would be unbound and blow out of the system. This
occurs if the grain is smaller than the ‘blowout size’. For grains released
from circular orbits, blowout occurs if ${\beta\geq 0.5}$, which corresponds
to a blowout size of ${1\;{\rm\upmu m}}$ for Sun-like stars and
${10\;{\rm\upmu m}}$ for more-luminous A0-type stars.

[chap1:box1]Key concept: the smallest dust is around the blowout size

Radiation pressure is stronger for smaller grains, and grains smaller than the
blowout size are usually blown away. Hence the smallest dust in a debris disk
is usually around the blowout size.

###### Poynting-Robertson (P-R) drag

Like radiation pressure, ‘Poynting-Robertson drag’ (P-R drag) is caused by
photons from the star hitting the dust grain. An orbiting grain has some non-
radial velocity component, so the grain ‘sees’ photons arriving at a slight
angle, with a small velocity component opposing the grain’s motion. This
results in a drag force. The combined effects of gravity, radiation pressure
and P-R drag result in a net force

${\color[rgb]{0,0,0}\boldsymbol{F}\;=\;\;}{\color[rgb]{1,0,0}\underbrace{\color[rgb]{0,0,0}\boldsymbol{F}_{\rm
grav}(1-\beta)}_{\mathclap{\color[rgb]{1,0,0}\text{Gravity + rad.
pressure}}}}{\;\;-\;\;}{\color[rgb]{1,0,0}\underbrace{\color[rgb]{0,0,0}\beta|\boldsymbol{F}_{\rm
grav}|\left(\frac{\dot{r}_{\rm
d}}{c}\boldsymbol{\hat{r}}\;+\;\frac{\boldsymbol{v}_{\rm
d}}{c}\right)}_{\color[rgb]{1,0,0}\text{P-R drag}}}$ (5)

where $\boldsymbol{v}_{\rm d}$ is the dust velocity, $\dot{r}_{\rm d}$ is the
radial component of $\boldsymbol{v}_{\rm d}$, and $c$ is the speed of light
(Burns et al., 1979). The first term is the combination of gravity and
radiation pressure (Equation 4), and the second term is P-R drag.

P-R drag has two main effects. It causes grains to spiral inwards towards the
star, and causes eccentric orbits to become more circular. The timescales for
P-R drag are generally much longer than orbital periods; for example, a grain
with ${\beta=0.1}$, released at ${1\;{\rm au}}$ from the Sun, would take 4000
years to spiral down to the Solar radius.

###### Stellar winds

The effects of stellar winds are similar to radiation pressure and P-R drag.
Winds reduce the net inward pull on grains, make them spiral inwards, and
circularise orbits. The combined force of stellar winds plus gravity has a
very similar form to Equation 5, only with $\beta$ replaced by the ratio of
the wind-pressure force to gravity, and $c$ replaced by the wind speed.

###### Other forces

Several other forces also affect debris. These include the Lorentz force,
which affects charged grains as they move through magnetic fields. Another
force is gas drag, which can be important for small grains embedded in gaseous
disks. There are also other radiation forces, which affect spinning or
asymmetric bodies. Gravitational interactions with planets can also affect
debris orbits, as detailed in Section 4.

##### Forces on different grain sizes

The forces in the previous section are the reason why debris disks have
different shapes at different wavelengths. The strengths of these forces vary
with grain size, so grains of different sizes have different orbits. This
means that different grain sizes have different spatial distributions, which
is why debris disks look different at different wavelengths.

Large grains, with sizes of millimetres to centimetres, essentially only feel
the force of gravity. They are much less affected by other forces than small
grains are. The orbits of large grains should be similar to those of even
larger debris bodies, which would also move predominantly under gravity. This
is why resolved observations of cold dust at millimetre wavelengths, which
detect large grains, are thought to trace the distribution of larger, unseen
planetesimals.

Unlike large grains, small grains are strongly affected by other forces.
Grains smaller than a millimetre are susceptible to radiation or wind
pressure, so their orbits can be highly eccentric or even unbound. This means
that debris disks are often more extended at shorter wavelengths, which probe
smaller grains. The halos in some systems are small grains on eccentric
orbits, which were released from collisions in a smaller planetesimal belt
(e.g. Figure 2c). These grains acquired wide orbits due to their large $\beta$
values. As well as halos, small grains can also extend inwards of their
release locations, because P-R and wind drag make them spiral inwards. This
inward migration is one possible way to supply exozodis (see Section 5).

####  3 Size distribution and the collisional cascade

Modern instruments can only detect dust and gas in extrasolar debris disks.
Bodies larger than dust, like planetesimals and dwarf planets, are currently
undetectable. However, we think that all debris disks contain such larger
bodies, for two reasons. First, the Solar System’s Asteroid and Kuiper Belts,
which are thought to be similar to extrasolar disks, comprise a range of
bodies from dust to dwarf planets. Second, dust cannot live as long as a star,
yet a high fraction of stars have dust. This implies that grains get
replenished somehow, and we think that replenishment occurs through collisions
between planetesimals. This section summarises our understanding of collisions
and the debris-size distribution.

[chap1:box1]Key concept: dust in debris disks comes from violent collisions

The lifetimes of individual dust grains are much shorter than the ages of
stars. For typical parameters, grains survive for around ${1\;{\rm Myr}}$
before being destroyed by collisions, whilst the ages of debris-disk stars are
tens or thousands of Myr. This means that the dust in debris disks cannot be
left over from system formation. Instead, we think dust is continually
replenished by collisions between larger bodies.

##### Collisions

When two bodies collide, there are several possible outcomes. The bodies could
either merge, bounce, or break apart. The extreme is a ‘catastrophic
collision’, where bodies undergo significant fragmentation, and the largest
fragment has less than half the mass of the original body. Which outcome
occurs depends on the collision velocity, and the strength and composition of
the bodies.

Dust in debris disks comes from the collisional fragmentation of
planetesimals. This means that collisions must be violent enough to break
planetesimals apart. The required collision speed can be predicted by
considering the impact energy required for a catastrophic collision, $Q_{\rm
D}^{*}$. This depends on the sizes of the bodies, and follows a V-shaped
dependence as shown on Figure 7. Large bodies like dwarf planets are held
together by gravity; in this regime, the bigger the body, the stronger it is.
Conversely, smaller bodies like dust are held together by material strength;
in this regime, the smaller the body, the stronger it is. Bodies are therefore
strongest if they are very small or very large, and weakest at some
intermediate size. Figure 7 shows that collision speeds in debris disks must
be at least 10s or 100s of metres per second to release dust, although this
depends on the debris composition.

Figure 7: Collision speed required to break up two equal-sized bodies made of
basalt, adapted from Costa et al. (2024). If the collision speed is above the
black solid line, then a catastrophic collision occurs, resulting in
significant fragmentation. Such a collision would produce a significant amount
of dust.

[chap1:box1]Key concept: debris disks lose mass and get fainter over time

Collisions grind debris into smaller and smaller sizes, which eventually blow
out of the system or sublimate near the star. This means that debris disks
lose mass over time. Also, once the largest bodies start colliding, the amount
of dust starts dropping. This means that debris disks become fainter over
time, so they are easier to detect around younger stars. This can be seen on
the right panel of Figure 5, where older debris disks are generally fainter.

##### Debris-size distribution

Larger debris collides and breaks into smaller bodies, and those smaller
bodies collide and break into even smaller bodies. This grinding of debris
into ever-smaller bodies is called a ‘collisional cascade’. Given sufficient
time, a collisional cascade reaches a steady state, and debris assumes a
particular size distribution. This is approximated by the powerlaw

$n(s){\rm d}s\propto s^{-3.5}{\rm d}s,$ (6)

where ${n(s){\rm d}s}$ is the number of bodies with radii between $s$ and
${s+{\rm d}s}$ (Dohnanyi, 1969). The steep index of ${-3.5}$ means that
smaller bodies significantly outnumber larger bodies; for example, there would
be 300 times as many bodies with radii between ${0.1}$ and ${1\;{\rm mm}}$ as
there would be between ${1}$ and ${10\;{\rm mm}}$. The upper end of the size
distribution is set by the largest bodies, and the lower end is set by the
blowout size. This size distribution is shown on Figure 8.

[chap1:box1]Key concept: small debris dominates emission, large debris
dominates mass

Bodies in a debris disk have a steep size distribution, meaning that smaller
bodies are much more numerous than larger bodies. The index of $-3.5$ in
Equation 6 means that a disk’s total surface area (and hence brightness) is
dominated by the smallest grains, whilst its total mass is dominated by the
largest bodies.

Real size distributions would deviate from the simple powerlaw of Equation 6.
Realistic distributions would be complicated at small sizes by the effects of
blowout, P-R drag and winds. Also, at large sizes, bodies would take longer to
enter the collisional cascade and start breaking up, so the largest bodies may
not follow a collisional size distribution until later in the system’s life.
However, despite these complications, we think that Equation 6 is a reasonable
estimate of the debris-size distribution.

Figure 8: Theoretical size distribution of bodies in a debris disk (Equation
6). Smaller bodies are much more numerous than larger bodies, and the smallest
dust is at the blowout size. In this example the largest body is arbitrarily
set to 200 km, but we do not actually know the sizes of the largest bodies in
debris disks. More-realistic models of size distributions have additional
features, but most follow this rough shape.

##### Stirring

For collisions to release dust, debris orbits must intersect (for collisions
to occur), and have high relative velocities (for collisions to be violent).
This means that debris orbits must be excited, i.e. have significant
eccentricities and/or mutual inclinations. However, we think that debris forms
with unexcited orbits, due to conditions in the protoplanetary disk. This
implies that some process then excites debris. The debris-excitation process
is called ‘stirring’, and is thought to have happened in all observed debris
disks.

We do not know how debris disks get stirred. Several stirring models have been
proposed, but it is difficult to distinguish them using current observations,
and each model has potential problems when considered in isolation. Current
models include:

  * •

Self-stirring, where debris bodies excite each other. Self-stirring could
operate in some disks, but others would need implausibly high masses for this
mechanism to work (Krivov and Wyatt, 2021).

  * •

Planetary stirring, where debris gets excited by dynamical interactions with
planets. However, planet stirring could be inhibited by the self gravity of
massive debris disks.

  * •

Flyby stirring, where another star passes close to the system and excites
debris. However, flybys do not seem common enough to explain the high fraction
of stars with observed dust (Kenyon and Bromley, 2002).

  * •

Pre-stirring, where planetesimals are already stirred in the protoplanetary
disk. One way this could happen is if planetesimals formed on excited orbits,
but this process is currently unclear.

####  4 Planet-debris interactions

So far, the theory section has mainly described processes occurring within
debris disks. However, debris does not exist in isolation. Many planetary
systems host both planets and debris, and these objects can gravitationally
interact with each other. For example, Neptune dominates the dynamical
evolution of Kuiper Belt objects, and Jupiter carves gaps in the Asteroid
Belt. Similar interactions should occur in extrasolar systems, and we even see
it in some cases. For example, we detect a planet orbiting  Pictoris which is
probably responsible for that disk’s warp.

Many extrasolar debris disks have features that imply planetary interactions,
such as gaps, sharp edges, and eccentric shapes. We usually cannot detect the
planets responsible, because they would lie in the outer regions of systems,
which is where planet-detection techniques struggle. However, we can use
features in observed debris disks to infer the properties of unseen planets.
Figure 9 shows the predicted population of unseen planets inferred from debris
disks.

Figure 9: Unseen exoplanets inferred from debris disks (red diamonds, from
Pearce et al. 2022a), compared to Solar System planets (black circles) and
known exoplanets (grey dots, from exoplanet.eu, accessed Feb 2024). Some of
the inferred planets may soon be detected by JWST, which is sensitive to
planets above 0.1 Jupiter masses in the outer regions of systems.

This section outlines what happens in planet-debris interactions. There are
three types of interaction: ‘scattering’ interactions, ‘secular’ interactions,
and ‘mean-motion resonances’. Figure 10 shows a typical interaction between an
eccentric planet and a broad, external debris disk. Three debris populations
are highlighted, each undergoing a different type of interaction. The effect
of each interaction on debris is explained below.

Figure 10: Diagram of a typical planet-debris interaction. In this example the
planet’s orbit is eccentric, and the disk’s mass is negligible. The left panel
shows orbital eccentricities and semimajor axes, and the right panel shows
positions. Debris is coloured by interaction on both panels: scattered debris
is blue, secular is yellow, and resonant is red. On the right panel, the star
is at the centre, the planet’s orbit is the black line, and the planet is the
black circle. Only two resonant populations are shown, but in reality there
can be debris in many different MMRs, each with different shapes on the right
panel.

###### Scattering interactions

Scattering happens when two bodies pass near each other. This is a rapid,
short-range interaction, which changes the semimajor axes, eccentricities and
orientations of orbits. Scattering interactions are often invoked to explain
gaps and sharp edges in debris disks, and scattering of debris by planets can
also drive planet migration (e.g. Friebe et al. 2022).

Small bodies get scattered if they pass within a few ‘Hill radii’ of a planet,
which is the region where the planet’s gravity dominates over that of the
star. For a planet on a circular orbit, the Hill radius is

$r_{\rm H}=a_{\rm p}\left(\frac{m_{\rm p}}{3M_{*}}\right)^{1/3},$ (7)

where $m_{\rm p}$ and $a_{\rm p}$ are the planet mass and semimajor axis,
respectively. Scattered debris is shown in blue on Figure 10. On the left
panel, the blue region shows orbits passing within several Hill radii of the
planet. Scattered bodies are confined to this region, jumping from one orbit
to another with each scattering event. On the right panel, scattered debris
forms a diffuse cloud. Bodies may get repeatedly scattered, and eventually
ejected from the system.

###### Secular interactions

Secular interactions occur over timescales much longer than orbital periods.
They change the eccentricities and orientations of orbits, so are often
invoked to explain eccentric or warped debris disks. An eccentric planet would
make external debris oscillate in eccentricity. For a low-eccentricity planet
interacting with coplanar debris, debris eccentricity would oscillate up to a
maximum

$e_{\rm max}\approx\frac{5}{2}\frac{a_{\rm p}}{a}e_{\rm p},$ (8)

where $a$ is the debris semimajor axis and $e_{\rm p}$ is the planet
eccentricity. The debris orientation would also evolve, which results in an
eccentric disk aligned with the planet’s orbit. This is visible on Figure 10,
where secular debris is yellow. The waves on the left panel, and the spirals
on the right panel, would tighten over time.

Secular interactions also occur if the planet is inclined, which makes debris
inclinations oscillate. In case of extreme inclinations, the ‘von
Zeipel–Kozai–Lidov mechanism’ can occur, where orbits oscillate between having
low eccentricity with high inclination, and high eccentricity with low
inclination.

###### Mean-motion resonances (MMRs)

Mean-motion resonances (MMRs) occur if orbital periods are close to simple
multiples of each other. For example, Neptune and Pluto are in the 3:2 MMR,
meaning that Neptune completes three orbits for every two of Pluto. MMRs can
keep orbits stable; Pluto’s orbit overlaps Neptune’s, but the 3:2 MMR ensures
the bodies never come close enough to scatter. MMRs can also make bodies
unstable, by making gravitational perturbations accumulate; for example, some
gaps in Saturn’s rings arise through MMRs with its moons.

MMRs are denoted using the notation $(p+q):p$, so for example the 3:2 MMR has
${p=2}$ and ${q=1}$. The ‘nominal’, or central, location of an MMR is derived
from the ratio of orbital periods. For an MMR outside a planet’s orbit, this
is

$a_{\rm res}=a_{\rm p}\left(\frac{p+q}{p}\right)^{2/3},$ (9)

where $a_{\rm res}$ is the nominal semimajor axis of the resonance. Generally,
the closer a body’s semimajor axis is to $a_{\rm res}$, the greater the effect
of the resonance. The effect also depends on the ‘order’ of the resonance,
$q$, where lower $q$ usually means a stronger effect.

Resonant debris is shown in red on Figure 10. Two populations are shown:
‘Trojans’ in the 1:1 MMR, which share the planet’s orbit, and another
population with nominal semimajor axis $a_{\rm res}$. Resonant debris
oscillates in eccentricity, whilst its semimajor axis stays close to the
nominal location (left panel). This debris forms distinct structures, which
are symmetric around the planet’s position (right panel). MMRs are often used
to explain clumps in debris disks, such as the possible clumps in  Eridani
(Figure 2b).

####  5 Models of warm and hot dust

This last section specifically discusses warm and hot dust. Some warm dust may
be released from planetesimal belts near the habitable zone, like the Asteroid
Belt in the Solar System. However, some systems have too much warm dust to be
compatible with this model. This is because warm dust is much closer to stars
than cold dust, so its collisional evolution is much faster. This would cause
planetesimal disks with sufficient mass at these locations to quickly grind
away to nothing, so local collisional cascades cannot be the source of all
warm dust. Hot dust is even closer to stars than warm dust, so this problem is
even more acute. We therefore think that other mechanisms are responsible for
hot dust, as well as some populations of warm dust.

Warm dust may originate further out in the system, then get transported
inwards to the habitable zone. Several mechanisms have been proposed to do
this. In one model, dust from a distant planetesimal disk migrates inwards
through P-R or wind drag (Reidemeister et al., 2011). In another model, warm
dust is released from comets as they travel through the habitable zone, which
is probably how Zodiacal dust is replenished in the Solar System (Bonsor et
al., 2014). In a third model, warm dust is released by a single giant
collision, rather than a steady state collisional cascade. Each of these
models can explain observed warm dust, without requiring massive planetesimal
disks in the habitable zone.

Hot dust is harder to explain. This appears to be very small, very hot grains,
located very close to stars (Kirchschlager et al., 2017). However, these
grains should rapidly sublimate or blow away, so we do not know how these
populations survive. Many models have been proposed, but none are completely
successful. Again, we think that hot dust originates further out and gets
transported inwards, but the above models for warm dust do not work for hot
dust. Dust migration via P-R drag is incompatible with hot-dust observations
(e.g. van Lieshout et al. 2014), and cometary supply would require
unphysically high inflow rates (Pearce et al., 2022b). Instead, some mechanism
may trap hot dust near the star. This could be stellar magnetic fields (e.g.
Kimura et al. 2020), or gas released by sublimating grains (Pearce et al.,
2020), but both models have problems. Hot dust is an area of significant
research, but it currently remains a mystery.

Warm and hot dust could hinder searches for Earth-like exoplanets. Soon, new
facilities will try to image Earth-like planets in the habitable zone, and
characterise their atmospheres. The hope is to assess the planets’ potential
for life. However, dust could act as noise, producing emission and making
planet observations difficult. Therefore, there is considerable interest in
understanding warm and hot dust, partly to mitigate its effect on future exo-
Earth searches.

###  4 Unsolved problems in debris-disk science

We have made substantial progress in understanding debris disks over the past
few decades. However, there are still many unanswered questions. This final
part of the chapter lists some of the biggest questions, which are all active
areas of research.

###### How massive are debris disks?

Currently, we cannot detect anything larger than a centimetre in extrasolar
debris disks. This means we do not know how big, or numerous, the largest
bodies are. We therefore do not know the masses of extrasolar disks, because
disk masses should be dominated by the largest bodies (Section 3). Several
studies attempted to estimate disk mass by extrapolating the mass in observed
dust, which requires assumptions about the size distribution and the largest-
body size. However, these inferred masses are often unrealistically large,
which is an issue known as the debris-disk-mass problem (Krivov and Wyatt,
2021). The solution to this problem could be that the largest bodies are much
smaller than those in the Solar System, or that the actual size distribution
is different to our models. Either way, determining the masses of debris disks
would help us understand their origin, evolution, and how they interact with
planets.

###### How are debris disks stirred?

We often assume that debris must be stirred to induce destructive collisions.
However, we do not know how this happens, or whether different disks get
stirred by different processes. The idea that debris needs stirring at all is
also coming under scrutiny. Answering these questions would teach us about
debris evolution, and the transition from protoplanetary disks to debris
disks.

###### Where does cold gas come from?

There are several plausible origins for the gas that is co-located with dust
disks. Gas could be primordial, meaning it is left over from the
protoplanetary disk, or secondary, meaning it is continually released. Since
only some gas species are observed, like CO, we do not know how much gas
exists in other species, like hydrogen. Primordial and secondary models
predict very different ratios of observable to non-observable gas, so
answering where gas comes from would help constrain how much is present. This
has implications for debris composition and disk dynamics.

###### What forms debris-disk structures?

Debris disks have diverse shapes and features (Figure 2). This diversity is
sometimes ascribed to planets, but there are also alternative explanations.
For example, debris structures could result from stellar flybys, or reflect
where solids form in protoplanetary disks. Answering why debris disks are
diverse would teach us about the architectures, formation and evolution of
planetary systems.

###### Are debris disks connected to planets?

It has long been thought that debris disks interact with unseen planets
(Section 4). Now, JWST offers the first real chance to detect these planets,
and finding them would support our current ideas about disk sculpting and
stirring. Conversely, not finding planets could imply that debris and planets
are less linked than currently thought, and could prompt a rethink about why
disks have the shapes and features that they do.

###### What is hot dust?

No model has fully explained how hot dust survives in the face of sublimation
and blowout, especially across a wide range of star ages and spectral types.
Determining its nature would help us understand the innermost regions of
planetary systems, and how material flows across systems. It would also help
us mitigate the effect of dust on future exo-Earth imaging.

###  5 Conclusions

Debris is one of the major constituents of planetary systems. As instruments
and techniques improve, we are detecting and imaging debris around more and
more stars. We are also learning how debris evolves, where it comes from, and
how it interacts with planets. The field of debris disks is a relatively small
but growing area of astrophysics, and has potential to teach us about the
formation, evolution and architecture of planetary systems.

_see also_ Several excellent reviews cover debris-disk observations and theory
in much more detail. These include Hughes et al. (2018), Krivov (2010), Marino
(2022), Matthews et al. (2014), Wyatt (2008) and Wyatt
(2020).[Acknowledgments]  I thank Mark Booth, Meredith Hughes, Grant Kennedy,
Alexander Krivov and Sebastian Marino for their expert advice and suggestions.
I also appreciate the feedback on readability and understandability from Allan
Cheruiyot, Abigail Falk, Jonathan Jackson, Jamar Kittling, Junu Lee, Elias
Mansell, Yamani Mpofu, Aliya Nurmohamed, Francesca Pearce, Cat Sarosi and
Brianna Zawadzki. I am grateful for support from a Warwick Prize Fellowship,
made possible by a generous philanthropic donation, and from UKRI/EPSRC
through a Stephen Hawking Fellowship.

42

* Aumann et al. (1984) Aumann HH, Gillett FC, Beichman CA, de Jong T, Houck JR, Low FJ, Neugebauer G, Walker RG and Wesselius PR (1984), Mar. Discovery of a shell around alpha Lyrae. ApJ 278: L23–L27. 10.1086/184214.
* Boccaletti et al. (2018) Boccaletti A, Sezestre E, Lagrange AM, Thébault P, Gratton R, Langlois M, Thalmann C, Janson M, Delorme P, Augereau JC, Schneider G, Milli J, Grady C, Debes J, Kral Q, Olofsson J, Carson J, Maire AL, Henning T, Wisniewski J, Schlieder J, Dominik C, Desidera S, Ginski C, Hines D, Ménard F, Mouillet D, Pawellek N, Vigan A, Lagadec E, Avenhaus H, Beuzit JL, Biller B, Bonavita M, Bonnefoy M, Brandner W, Cantalloube F, Chauvin G, Cheetham A, Cudel M, Gry C, Daemgen S, Feldt M, Galicher R, Girard J, Hagelberg J, Janin-Potiron P, Kasper M, Le Coroller H, Mesa D, Peretti S, Perrot C, Samland M, Sissa E, Wildi F, Zurlo A, Rochat S, Stadler E, Gluck L, Origné A, Llored M, Baudoz P, Rousset G, Martinez P and Rigal F (2018), Jun. Observations of fast-moving features in the debris disk of AU Mic on a three-year timescale: Confirmation and new discoveries. A&A 614, A52. 10.1051/0004-6361/201732462. 1803.05354.
* Bonsor et al. (2014) Bonsor A, Raymond SN, Augereau JC and Ormel CW (2014), Jul. Planetesimal-driven migration as an explanation for observations of high levels of warm, exozodiacal dust. MNRAS 441 (3): 2380–2391. 10.1093/mnras/stu721. 1404.2606.
* Booth et al. (2023) Booth M, Pearce TD, Krivov AV, Wyatt MC, Dent WRF, Hales AS, Lestrade JF, Cruz-Sáenz de Miera F, Faramaz VC, Löhne T and Chavez-Dagostino M (2023), Jun. The clumpy structure of $\epsilon$ Eridani’s debris disc revisited by ALMA. MNRAS 521 (4): 6180–6194. 10.1093/mnras/stad938. 2303.13584.
* Burns et al. (1979) Burns JA, Lamy PL and Soter S (1979), Oct. Radiation forces on small particles in the solar system. Icarus 40 (1): 1–48. 10.1016/0019-1035(79)90050-2.
* Costa et al. (2024) Costa T, Pearce TD and Krivov AV (2024), Jan. Increasing planet-stirring efficiency of debris discs by ’projectile stirring’ and ’resonant stirring’. MNRAS 527 (3): 7317–7336. 10.1093/mnras/stad3582. 2311.10461.
* Dent et al. (2014) Dent WRF, Wyatt MC, Roberge A, Augereau JC, Casassus S, Corder S, Greaves JS, de Gregorio-Monsalvo I, Hales A, Jackson AP, Hughes AM, Lagrange AM, Matthews B and Wilner D (2014), Mar. Molecular Gas Clumps from the Destruction of Icy Bodies in the $\beta$ Pictoris Debris Disk. Science 343 (6178): 1490–1492. 10.1126/science.1248726. 1404.1380.
* Dohnanyi (1969) Dohnanyi JS (1969), May. Collisional Model of Asteroids and Their Debris. J. Geo. Res. 74: 2531–2554. 10.1029/JB074i010p02531.
* Ertel et al. (2020) Ertel S, Defrère D, Hinz P, Mennesson B, Kennedy GM, Danchi WC, Gelino C, Hill JM, Hoffmann WF, Mazoyer J, Rieke G, Shannon A, Stapelfeldt K, Spalding E, Stone JM, Vaz A, Weinberger AJ, Willems P, Absil O, Arbo P, Bailey VP, Beichman C, Bryden G, Downey EC, Durney O, Esposito S, Gaspar A, Grenz P, Haniff CA, Leisenring JM, Marion L, McMahon TJ, Millan-Gabet R, Montoya M, Morzinski KM, Perera S, Pinna E, Pott JU, Power J, Puglisi A, Roberge A, Serabyn E, Skemer AJ, Su KYL, Vaitheeswaran V and Wyatt MC (2020), Apr. The HOSTS survey for exozodiacal dust: observational results from the complete survey. AJ 159 (4), 177. 10.3847/1538-3881/ab7817. %****␣main.bbl␣Line␣75␣****2003.03499.
* Friebe et al. (2022) Friebe MF, Pearce TD and Löhne T (2022), May. Gap carving by a migrating planet embedded in a massive debris disc. MNRAS 512 (3): 4441–4454. 10.1093/mnras/stac664. 2203.03611.
* Gáspár et al. (2016) Gáspár A, Rieke GH and Ballering N (2016), Aug. The Correlation between Metallicity and Debris Disk Mass. ApJ 826 (2), 171. 10.3847/0004-637X/826/2/171. 1604.07403.
* Gáspár et al. (2023) Gáspár A, Wolff SG, Rieke GH, Leisenring JM, Morrison J, Su KYL, Ward-Duong K, Aguilar J, Ygouf M, Beichman C, Llop-Sayson J and Bryden G (2023), Jul. Spatially resolved imaging of the inner Fomalhaut disk using JWST/MIRI. Nature Astronomy 7: 790–798. 10.1038/s41550-023-01962-6. 2305.03789.
* Golimowski et al. (2006) Golimowski DA, Ardila DR, Krist JE, Clampin M, Ford HC, Illingworth GD, Bartko F, Benítez N, Blakeslee JP, Bouwens RJ, Bradley LD, Broadhurst TJ, Brown RA, Burrows CJ, Cheng ES, Cross NJG, Demarco R, Feldman PD, Franx M, Goto T, Gronwall C, Hartig GF, Holden BP, Homeier NL, Infante L, Jee MJ, Kimble RA, Lesser MP, Martel AR, Mei S, Menanteau F, Meurer GR, Miley GK, Motta V, Postman M, Rosati P, Sirianni M, Sparks WB, Tran HD, Tsvetanov ZI, White RL, Zheng W and Zirm AW (2006), Jun. Hubble Space Telescope ACS Multiband Coronagraphic Imaging of the Debris Disk around $\beta$ Pictoris. AJ 131 (6): 3109–3130. 10.1086/503801. astro-ph/0602292.
* Hom et al. (2024) Hom J, Patience J, Chen CH, Duchêne G, Mazoyer J, Millar-Blanchaer MA, Esposito TM, Kalas P, Crotts KA, Gonzales EC, Kolokolova L, Lewis BL, Matthews BC, Rice M, Weinberger AJ, Wilner DJ, Wolff SG, Bruzzone S, Choquet E, Debes J, De Rosa RJ, Donaldson J, Draper Z, Fitzgerald MP, Hines DC, Hinkley S, Hughes AM, López RA, Marchis F, Metchev S, Moro-Martin A, Nesvold E, Nielsen EL, Oppenheimer R, Padgett D, Perrin MD, Pueyo L, Rantakyrö F, Ren BB, Schneider G, Soummer R, Song I and Stark CC (2024), Mar. A uniform analysis of debris discs with the Gemini Planet Imager II: constraints on dust density distribution using empirically informed scattering phase functions. MNRAS 528 (4): 6959–6984. 10.1093/mnras/stae368. 2402.00214.
* Hughes et al. (2018) Hughes AM, Duchêne G and Matthews BC (2018), Sep. Debris Disks: Structure, Composition, and Variability. ARA&A 56: 541–591. 10.1146/annurev-astro-081817-052035. 1802.04313.
* Imaz Blanco et al. (2023) Imaz Blanco A, Marino S, Matrà L, Booth M, Carpenter J, Faramaz V, Henning T, Hughes AM, Kennedy GM, Pérez S, Ricci L and Wyatt MC (2023), Jul. Inner edges of planetesimal belts: collisionally eroded or truncated? MNRAS 522 (4): 6150–6169. 10.1093/mnras/stad1221. 2304.12337.
* Kalas et al. (2013) Kalas P, Graham JR, Fitzgerald MP and Clampin M (2013), Sep. STIS Coronagraphic Imaging of Fomalhaut: Main Belt Structure and the Orbit of Fomalhaut b. ApJ 775 (1), 56. 10.1088/0004-637X/775/1/56. 1305.2222.
* Kenyon and Bromley (2002) Kenyon SJ and Bromley BC (2002), Mar. Collisional Cascades in Planetesimal Disks. I. Stellar Flybys. AJ 123 (3): 1757–1775. 10.1086/338850. astro-ph/0111384.
* Kimura et al. (2020) Kimura H, Kunitomo M, Suzuki TK, Robrade J, Thebault P and Mitsuishi I (2020), Apr. Hot grain dynamics by electric charging and magnetic trapping in debris disks. P&SS 183, 104581. 10.1016/j.pss.2018.07.010.
* Kirchschlager et al. (2017) Kirchschlager F, Wolf S, Krivov AV, Mutschke H and Brunngräber R (2017), May. Constraints on the structure of hot exozodiacal dust belts. MNRAS 467 (2): 1614–1626. 10.1093/mnras/stx202. 1701.07271.
* Krivov (2010) Krivov AV (2010), May. Debris disks: seeing dust, thinking of planetesimals and planets. Research in Astronomy and Astrophysics 10 (5): 383–414. 10.1088/1674-4527/10/5/001. 1003.5229.
* Krivov and Wyatt (2021) Krivov AV and Wyatt MC (2021), Jan. Solution to the debris disc mass problem: planetesimals are born small? MNRAS 500 (1): 718–735. 10.1093/mnras/staa2385. 2008.07406.
* Luppe et al. (2020) Luppe P, Krivov AV, Booth M and Lestrade JF (2020), Dec. Observability of dusty debris discs around M-stars. MNRAS 499 (3): 3932–3942. 10.1093/mnras/staa2608. 1910.13142.
* MacGregor et al. (2017) MacGregor MA, Matrà L, Kalas P, Wilner DJ, Pan M, Kennedy GM, Wyatt MC, Duchene G, Hughes AM, Rieke GH, Clampin M, Fitzgerald MP, Graham JR, Holland WS, Panić O, Shannon A and Su K (2017), Jun. A Complete ALMA Map of the Fomalhaut Debris Disk. ApJ 842 (1), 8. 10.3847/1538-4357/aa71ae. 1705.05867.
* Marino (2022) Marino S (2022), Feb. Planetesimal/Debris discs. arXiv e-prints , arXiv:2202.0305310.48550/arXiv.2202.03053. 2202.03053.
* Marino et al. (2018) Marino S, Carpenter J, Wyatt MC, Booth M, Casassus S, Faramaz V, Guzman V, Hughes AM, Isella A, Kennedy GM, Matrà L, Ricci L and Corder S (2018), Oct. A gap in the planetesimal disc around HD 107146 and asymmetric warm dust emission revealed by ALMA. MNRAS 479 (4): 5423–5439. 10.1093/mnras/sty1790. 1805.01915.
* Matrà et al. (2017) Matrà L, MacGregor MA, Kalas P, Wyatt MC, Kennedy GM, Wilner DJ, Duchene G, Hughes AM, Pan M, Shannon A, Clampin M, Fitzgerald MP, Graham JR, Holland WS, Panić O and Su KYL (2017), Jun. Detection of Exocometary CO within the 440 Myr Old Fomalhaut Belt: A Similar CO+CO2 Ice Abundance in Exocomets and Solar System Comets. ApJ 842 (1), 9. 10.3847/1538-4357/aa71b4. 1705.05868.
* Matrà et al. (2018) Matrà L, Marino S, Kennedy GM, Wyatt MC, Öberg KI and Wilner DJ (2018), May. An Empirical Planetesimal Belt Radius-Stellar Luminosity Relation. ApJ 859 (1), 72. 10.3847/1538-4357/aabcc4. 1804.01094.
* Matthews et al. (2014) Matthews BC, Krivov AV, Wyatt MC, Bryden G and Eiroa C (2014), Jan., Observations, Modeling, and Theory of Debris Disks, Beuther H, Klessen RS, Dullemond CP and Henning T, (Eds.), Protostars and Planets VI, 521–544, 1401.0743.
* Meng et al. (2015) Meng HYA, Su KYL, Rieke GH, Rujopakarn W, Myers G, Cook M, Erdelyi E, Maloney C, McMath J, Persha G, Poshyachinda S and Reichart DE (2015), May. Planetary Collisions Outside the Solar System: Time Domain Characterization of Extreme Debris Disks. ApJ 805 (1), 77. 10.1088/0004-637X/805/1/77. 1503.05610.
* Pawellek and Krivov (2015) Pawellek N and Krivov AV (2015), Dec. The dust grain size-stellar luminosity trend in debris discs. MNRAS 454 (3): 3207–3221. 10.1093/mnras/stv2142. 1509.04032.
* Pearce et al. (2020) Pearce TD, Krivov AV and Booth M (2020), Aug. Gas trapping of hot dust around main-sequence stars. MNRAS 498 (2): 2798–2813. 10.1093/mnras/staa2514. 2008.07505.
* Pearce et al. (2022a) Pearce TD, Launhardt R, Ostermann R, Kennedy GM, Gennaro M, Booth M, Krivov AV, Cugno G, Henning TK, Quirrenbach A, Barcucci AM, Matthews EC, Ruh HL and Stone JM (2022a), Mar. Planet populations inferred from debris discs. Insights from 178 debris systems in the ISPY, LEECH, and LIStEN planet-hunting surveys. A&A 659, A135. 10.1051/0004-6361/202142720. 2201.08369.
* Pearce et al. (2022b) Pearce TD and et al. (2022b), Nov. Hot exozodis: cometary supply without trapping is unlikely to be the mechanism. MNRAS 517 (1): 1436–1451. 10.1093/mnras/stac2773. 2209.11219.
* Rebollido et al. (2020) Rebollido I, Eiroa C, Montesinos B, Maldonado J, Villaver E, Absil O, Bayo A, Canovas H, Carmona A, Chen C, Ertel S, Henning T, Iglesias DP, Launhardt R, Liseau R, Meeus G, Moór A, Mora A, Olofsson J, Rauw G and Riviere-Marichalar P (2020), Jul. Exocomets: A spectroscopic survey. A&A 639, A11. 10.1051/0004-6361/201936071. 2003.11084.
* Reidemeister et al. (2011) Reidemeister M, Krivov AV, Stark CC, Augereau JC, Löhne T and Müller S (2011), Mar. The cold origin of the warm dust around $\epsilon$ Eridani. A&A 527, A57. 10.1051/0004-6361/201015328. 1011.4882.
* Schneider et al. (2014) Schneider G, Grady CA, Hines DC, Stark CC, Debes JH, Carson J, Kuchner MJ, Perrin MD, Weinberger AJ, Wisniewski JP, Silverstone MD, Jang-Condell H, Henning T, Woodgate BE, Serabyn E, Moro-Martin A, Tamura M, Hinz PM and Rodigas TJ (2014), Oct. Probing for Exoplanets Hiding in Dusty Debris Disks: Disk Imaging, Characterization, and Exploration with HST/STIS Multi-roll Coronagraphy. AJ 148 (4), 59. 10.1088/0004-6256/148/4/59. 1406.7303.
* van Lieshout et al. (2014) van Lieshout R, Dominik C, Kama M and Min M (2014), Nov. Near-infrared emission from sublimating dust in collisionally active debris disks. A&A 571, A51. 10.1051/0004-6361/201322090. 1404.3271.
* Wyatt (2008) Wyatt MC (2008), Sep. Evolution of debris disks. ARA&A 46: 339–383. 10.1146/annurev.astro.45.051806.110525.
* Wyatt (2020) Wyatt MC (2020), Extrasolar Kuiper belts, Prialnik D, Barucci MA and Young L, (Eds.), The Trans-Neptunian Solar System, 351–376.
* Yelverton et al. (2019) Yelverton B, Kennedy GM, Su KYL and Wyatt MC (2019), Sep. A statistically significant lack of debris discs in medium separation binary systems. MNRAS 488 (3): 3588–3606. 10.1093/mnras/stz1927. 1907.04800.
* Yelverton et al. (2020) Yelverton B, Kennedy GM and Su KYL (2020), Jun. No significant correlation between radial velocity planet presence and debris disc properties. MNRAS 495 (2): 1943–1957. 10.1093/mnras/staa1316. %****␣main.bbl␣Line␣300␣****2005.03573.