Gas in Debris Disks

(1)

Stockholm University Department of Astronomy

Licentiate Thesis

Gas in debris disks

Maria Cavallius

Supervisor: Alexis Brandeker

Co-supervisor: Markus Janson

(2)

(3)

Abstract - English

This licentiate thesis gives an introduction to gas in debris disks. The topic lies at the intersection between exoplanets and astrobiology, exploring what young planets and their surroundings are made of, and where we fit into the bigger picture.

Debris disks exist during the late stages of planet formation. They are made up mainly of dust and rocks, and can be thought of as scaled-up, younger versions of our own asteroid- and Kuiper belts. During the last 5–10 years it has become clear that gas is also present, which gives us a unique opportunity to probe the contents, chemistry, and history of the systems. My own work, presented in Chapter 8, has helped constrain the water content of comets in the specific system β Pictoris.

The knowledge gained from studying debris disks is a piece in the puzzle of understanding other planetary systems as well as our own solar system’s place among them. Ultimately, we may even learn of conditions reminiscent of those around Earth.

(4)

Abstrakt - Svenska

Den här licentiatavhandlingen ger en introduktion till gas i fragmentskivor. Ämnet ligger vid mitten av vägkorsningen mellan exoplaneter och astrobiologi och utforskar vad unga planeter och deras omgivning är gjorda av, samt var vi passar in på det stora hela.

Fragmentskivor existerar under de senare stadierna av planetbildning. De är gjorda till mestadels av damm och stenar, och kan föreställas som upskalade och yngre versioner av våra egna asteroid- och Kuiperbälten. Under de senaste 5–10 åren har det blivit klart att även gas förekommer, vilket ger oss ett unikt tillfälle att utforska dessa systems innehåll, kemi och historia. Mitt eget arbete, presenterad i Kapitel 8, har hjälpt till att sätta gränser för vatteninnehållet av kometer i det specifika systemet β Pictoris.

Kunskapen vi får från att studera fragmentskivor är en bit av det pussel kring förståelsen av andra planetsystem, likväl hur vårt eget solsystems platsar in bland dem. Vi kan även lära oss om förhållanden som påminner om de kring jorden.

ii

(5)

Paper included in this thesis

“Upper limits on the water vapour content of the β Pictoris debris disk”,

Cavallius, M., Cataldi, G., Brandeker, A., Olofsson, G., Larsson, B., and Liseau, R., 2019, A&A, 628, A127

Contribution to the paper:

• I reduced the data from raw form, wrote the script that calculates the flux upper limit for two different gas spatial profiles, and modified the radiative transfer code pythonradex (Cataldi 2018) to calculate gas mass as a function of flux.

• I produced all figures and tables.

• I wrote the bulk of the text.

A copy of the paper can be found in Chapter8.

(6)

(7)

1 Introduction

Gas in debris disks is a fairly new, rapidly growing area of research. Debris disks offer a window into the conditions under which planets form and evolve, and gas observations work particularly well for learning about the chemical make-up of the systems. From that information we can deduce the possible composition of planets, and whether they might be suitable for life to emerge. Furthermore, it is crucial to find out whether the conditions in our solar system are common; if they are, it seems likely that life with some kind of similarity to what we know will have arisen somewhere else in the Universe, too.

My work focuses on the elemental composition of gas in debris disks. I have used, and will in the future use, spectroscopy to search for emission lines in the gas of debris disks. I can thereby constrain chemical abundances and the types of processes that are important in the specific disks. This knowledge will further our understanding of what goes on in young exoplanetary systems as well as the history of our own solar system.

The thesis is laid out as follows. In Chapter 2 I start by outlining star and planet formation. The resulting debris disk phase is introduced in Chapter 3. Chapters 4 and 5 go through the topics of dust and gas in debris disk in more detail, including detection methods and observational results. The system I have been working on, β Pictoris, is presented is Chapter6. Chapter7puts the topic of gas in debris disks into an astrobiological context, and looks ahead to the future of observations. Finally, Chapter 8 presents my paper published in Astronomy & Astrophysics.

(10)

(11)

2 Star and planet formation

In order to set the stage for debris disks, this chapter briefly goes through the subject of star and planet formation. Figure [2.1] illustrates the different phases that are discussed.

Much of the material in this chapter follows the textbook byde Pater & Lissauer(2015).

2.1 A star forms

The life of a planetary system begins with a cold and dense molecular cloud in the interstellar medium (panel a in Figure [2.1]). These clouds are initially in hydrostatic equilibrium, where gravity is balanced by internal pressure caused by ordinary thermal gas pressure, magnetic field pressure, turbulent motion and rotation. If the balance is disturbed, e.g.

by a collision with another cloud, a shock wave from a nearby supernova or from passing through a galactic spiral arm, some regions can become overdense. A dense region, or core, will then be subjected to forces that may no longer be in equilibrium.

A simplified argument leads to a distinction between stable and unstable cores. Dis- regarding magnetic field pressure as well as any external pressures, the virial theorem states that for systems in equilibrium, the gravitational potential energy Epot is related to the kinetic energy Ekin by

E_pot = −2E_kin. (2.1)

If |Epot| > 2Ekin, gravity will dominate and cause the core to collapse. Since turbulence and rotation are often negligible, the kinetic energy can be assumed to simply be the thermal energy of the gas. The core mass for which Equation (2.1) precisely holds is the

(12)

2. Star and planet formation

Figure 2.1: Schematic view of star and planet formation. The timescales and distances correspond to the evolution of a Sun-like star. Note that debris disks often are found well into the star’s main-sequence phase. Image fromGreene (2001).

dividing line between the two regimes, and is given by the Jeans mass (Jeans 1902) M_Jeans ≈

kT

Gµ_am_amu

3/2

√1

ρ, (2.2)

where k is the Boltzmann constant, T is the temperature, G is the gravitational constant, µ_a is the particle mass in atomic mass units, mamu is one atomic mass unit and ρ is the gas density. If a core has a higher mass than the Jeans mass, which is typically around one solar mass (Kippenhahn et al. 2012), its pressure equilibrium is not stable. The core’s self-gravity then causes it to contract, and it begins accreting mass from its surroundings (panel b). If energy from the inner forces is lost, for instance via radiation, the collapse continues and the core becomes denser. This in turn causes the collapse to proceed even faster. Throughout the collapse and accretion, the temperature of the core increases., and the object becomes a proto-star (panel c).

As star formation takes place, the size of the proto-star decreases by several orders of magnitude. Conservation of angular momentum applies, and the result is that the rotational velocity greatly increases. At this point, any gas or dust particle falling towards the star now has to overcome the centrifugal force acting outwards in the particle’s frame

4

(13)

of reference. The centrifugal force works perpendicular to the axis of rotation, mean- ing that particles moving towards the midplane of the rotating structure do not feel it, whereas those moving radially inward do. Seeing as it is easier for particles to move to the midplane rather than inwards, the infalling matter takes the shape of a disk. Further contraction takes place as angular momentum is removed via bipolar outflow of gas.

Once the surrounding gas envelope is depleted and the system has further decreased in size, the protoplanetary disk becomes visible (panel d). As the name suggests, this is where any planets will form. At the centre of the system is a pre-main-sequence star, which over time contracts further to become a main-sequence star at the onset of hydrogen fusion in its core (low-mass stars like the Sun go through the T Tauri phase, in which their bright- nesses fluctuate greatly). Contraction will gradually slow and stop once the thermal and radiation pressures balance gravity, and the object again reaches hydrostatic equilibrium.

If the result of the proto-stellar phase is an object of less than 0.08 solar masses, it instead goes on to become a brown dwarf, since its central temperature will not reach the few mil- lions of Kelvin needed to start hydrogen fusion (Hayashi & Nakano 1963); it will, however, be hot enough for deuterium burning to take place. The internal forces in a brown dwarf are dominated by electron degeneracy pressure rather than radiation pressure from fusion.

After most of the gas has dissipated, a debris disk (panel e) is left. Despite what is written in the figure, debris disks are often seen far into the main-sequence phase. The larger objects built up during the protoplanetary disk phase are now partly ground back down to dust due to increased collision rates and velocities (see Chapter 3). The dust emits thermally in the infrared or sub-mm, or scatters the stellar light. Once the dust is largely either expelled or accreted, a system of fully formed planets and perhaps small belts of rocks and dust like the asteroid- and Kuiper belts are left (panel f).

The timescales of star formation vary greatly depending on mass. The sun reached its main-sequence phase in about 10 Myr, while a B-star can get there in only some tens of thousands of years (Pols 2011).

(14)

2.2 Planets appear

The protoplanetary disk contains copious amount of both dust and gas, but the process of turning the material into planets is not completely understood, and several different formation pathways are possible.

If the disk is high enough in mass, the gravitational instability model predicts that giant planets can form directly as a result of fragmentation within the disk, much like stars form in clouds. It is necessary for the disk to be highly gravitationally unstable due to e.g. rapid cooling, as weaker instabilities excite spiral density waves that transfer angular momentum outwards and spread the disk out, making it more stable. It is thought that gravitational instabilities can form massive planets under the right disk conditions.

For lower disk and/or planet masses, the core accretion model is widely accepted. The model predicts that dust grows to planet sizes via a succession of different mechanisms.

The smallest grains of µm size come together through the short-range van der Waals force, resulting in weakly bound aggregates. The cm-sized grains grow via collisions, the outcome of which depends on such things as relative masses, impact velocity, impact angle, porosity, chemical composition and “stickiness” due to e.g. surface ice (“ices” in planetary science refers to solid phase volatiles, e.g. water ice, CO or methane). Processes that result in accretion include the hit-and-stick mechanism between low-velocity aggregates, sticking due to surface effects and sticking due to penetration (Güttler et al. 2010). Bouncing is another possible outcome, with or without compaction and/or mass transfer. Destructive outcomes can also occur, e.g. erosion of larger bodies by smaller bodies or fragmentation of similar-sized bodies. The net result of these processes, despite some destructive outcomes, is that dust grains grow to sizes of tens of cm.

The dust orbits the star at Keplerian velocities. Since the gas is pressure-supported, it feels a lower gravity and consequently orbits at sub-Keplerian velocity. The velocity difference between the two components causes a drag force on the dust, which slows it down. Dust grains above or below the disk therefore settle to the midplane, thereby in- creasing the rate of collisions. The smaller grains are strongly coupled to the gas, while the larger ones tend to settle quicker.

6

(15)

The drag force also works in the radial direction; as the dust grains lose angular momentum they rapidly migrate towards the star. A peculiarity of the radial migration is that metre-sized “grains” have the highest migration rates. Kilometre-sized planetesimals are completely decoupled from the gas and remain on Keplerian orbits, but it is not possible to reach those sizes in time before the metre-sized objects spiral into the star (Weidenschilling 1977). This problem is known as the radial drift barrier.

A possible solution to the problem is dust traps. As the dust grains grow to larger sizes and gradually decouple from the gas, they stop migrating and create a pile-up. The grains heat the gas via the photoelectric effect, and the higher grain density means a higher gas temperature. The gas pressure therefore increases, creating a local pressure maximum.

Just interior to the pile-up, the gas now feels an additional pressure pointing towards the star. The effect is equivalent to an increase in gravity, so the gas orbits at super-Keplerian speed. Rather than slowing the dust grains down, the gas now speeds them up, causing them to move outwards. The opposite effects happens on the other side of the pressure maximum, and so dust interior to the trap is pushed out while dust exterior to it is pushed in. A self-induced dust trap has thus been created, and the increased collision rate at that location enhances the dust growth rate substantially (Gonzalez et al. 2017). Similar dust pile-ups can be created at the edges of a planet-induced gap (see Section4.5), at ice lines where gas species freeze out, or at vortices in a turbulent disk. It is also thought that the streaming instability plays a role. This model suggests that drifting dust particles in a turbulent disk concentrate into larger clumps of mm–cm-sized pebbles. These clumps produce a back-reaction of the surrounding gas by accelerating it and therefore feel less of a drag force. The clumps are then able to grow by accumulating inwards drifting particles, and once the local dust/gas ratio is large enough, they undergo direct gravitational collapse into planetesimals of a few hundred km in size (Johansen et al. 2012). The streaming instability can work on small scales, but does require a local enhancement in the dust/gas ratio to begin with. It is likely that dust traps and the streaming instability work concurrently.

Planetesimals grow to larger proto-planets via collisional accretion of pebbles and/or other planetesimals. The growth is oligarchic and continues until the planetesimals have

(16)

depleted their feeding zones, which may change if interactions with the disk causes the object to migrate. If a proto-planet reaches a high enough mass, roughly 10 M⊕, it also accretes substantial amounts of gas from its surroundings. Once the mass of the accreted gas is roughly equal to the mass of the solids, runaway gas accretion occurs, resulting in a solid core and an extended gas envelope (Pollack et al. 1996). This must be done within 10 Myr or so, as the gas will otherwise have dissipated from the disk. Proto-planets with lower masses continue accreting solids, and do so within 10 – 100 Myr, and may also accrete a small atmosphere.

The classic core accretion model has some trouble explaining giant planets via planetesimal- planetesimal collisions. The growth rate of planetary cores is simply too low for them to form and accrete gas before the protoplanetary disk has dissipated, especially on wide orbits where less material is available. Jupiter and Saturn, for instance, could not have formed where they are now in the time the disk material was available (Thommes et al.

2003). Newer results suggest that pebble accretion, where planetesimals collide with inward drifting pebbles, yields more efficient accretion (Ormel & Klahr 2010; Lambrechts

& Johansen 2012), in part due to the larger flux and in part because the growing planets tend to scatter large planetesimals away from themselves (Tanaka & Ida 1999). Gas drag inside a protoplanet’s Hill sphere can slow down pebbles sufficiently for them to spiral in and be accreted, which greatly reduces the time needed for larger planets to grow.

Smaller objects can come together via planetesimal-planetesimal collisions. A beauti- ful example was revealed when the New Horizons spacecraft flew by the primitive object Arrokoth in the Kuiper Belt (Figure [2.2]). Images showed the object to be bi-lobed, clearly indicative of a low-velocity collision (McKinnon et al. 2020).

The initial protoplanetary disk is gas-rich and dominated by aggregation and accretion of solids. Over the course of roughly 10 Myr the dust has literally settled, planets have formed, and gas has been accreted or photoevaporated. The relative velocities between the solid bodies then increase, and the net result of collisions becomes destructive. Rather than agglomeration of material into larger bodies, grinding down now dominates. The debris disk phase has begun.

8

(17)

Figure 2.2: The contact binary Arrokoth in enhanced-colour. The picture is a composite and shows the distinct bi-lobed, or snowman, shape. Image fromNASA (2020).

(18)

(19)

3 Debris disk basics

Debris disks are both a part and outcome of planet formation. While they build on the protoplanetary phase, the processes at play in the disks can drastically affect the appearance and composition of the final planetary system. The solar system’s zodiacal/interplanetary dust, asteroid belt, Kuiper Belt and scattered bodies are a remnant of our own debris disk phase.

Hundreds of debris disks have already been found (Wyatt 2018). They are some tens to hundreds of au in radial extent, and can have complex structures such as gaps, warps and other asymmetries that may be the result of planets interacting with the disk (e.g.

Wyatt (2020)). The disks are dominated by rocky material ranging from µm-sized dust grains to km-sized planetesimals and planets. Gas is sometimes present in small quantities, and may be either leftover from the formation process (primordial) or more recently released (secondary). They typically appear after roughly 10 Myr and can persist for several tens or even hundreds of Myr (Rieke et al. 2005) before their dust contents are accreted or expelled from the system.

Any planets will have already formed, and some may actively be accreting new rocky material. In general, however, the material built up in the protoplanetary disk is gradually ground back down to dust through planetesimal collisions. This is a result of the increased collisional velocities and collision rates compared to the protoplanetary disk phase. Small grains no longer experience the damping force of gas drag and therefore move faster. Planetesimals, however, were never subject to strong gas drag to begin with, and require some kind of stirring to accelerate them and excite their eccentricities.

The exact mechanism is not clear - there may be some pre-stirring in the protoplanetary phase due to e.g. turbulence (Brauer et al. 2008), delayed stirring after gas dispersal

(20)

3. Debris disk basics

due to stellar flybys (Kenyon & Bromley 2002), self-stirring at later times caused by the growing planetesimals themselves (Kenyon & Bromley 2010; Kennedy & Wyatt 2010), or planetary stirring once the planets have formed (Mustill & Wyatt 2009).

Through observations of their dust, gas and structure, debris disks offer insight into the results of the protoplanetary phase, the composition and properties of the material in young planetary systems, and the dynamics of planets yet to be discovered. Since it is often much easier to probe the debris disk than the planets themselves this phase offers a unique, and time-limited, window into planetary interiors and environments.

3.1 History and definition

In 1984 the Infrared Astronomical Satellite (IRAS) observed Vega and, by accident, discovered the first debris disk, through the thermal emission of the circumstellar dust (Au- mann et al. 1984). This so-called infrared excess occurs because the dust grains absorb stellar photons and re-emit the energy in the infrared (or sub-mm). Subsequent surveys showed that infrared excess is common around main sequence stars, see e.g.Habing et al.

(1996).

Though initially thought to be virtually gas-free, it now seems that small amounts of gas are in fact present in many debris disks. There is, however, not enough gas to affect the dynamical evolution of the dust; although debris disks contain less than 0.1 M^⊕ of dust while protoplanetary disks typically contain more than ten times that (Wyatt 2018), the former have much higher dust/gas ratios.

Historically debris disks were distinguished from protoplanetary disks by their lack of gas, but as mentioned above, this dividing line no longer holds. Although debris disks are typically older than 10 Myr, this is not a strict limit, and so age is not an appropriate separating factor either. Instead, it is now common to use optical depth as a guideline.

Debris disks are optically thin across the spectrum, whereas protoplanetary disks are often very optically thick, especially at optical and infrared wavelengths. An easily calculated observational proxy of the optical depth is the ratio of infrared to bolometric luminosities, L_IR/L_bol. Debris disks emit mainly in the infrared, and may even outshine the star in

12

(21)

Figure 3.1: Illustration of the effect of a dust disk or belt on the observed SED (NASA Spitzer Space Telescope 2005). The yellow distributions correspond to the system on the right, while the grey ones show the SEDs of the system(s) above for comparison. While a full disk increases the brightness smoothly at long wavelengths, a belt will appear as a bump only at the wavelengths corresponding to its temperature.

this wavelength range; nevertheless, protoplanetary disks contain much more dust and are consequently brighter. A debris disk will have a value of roughly LIR/L_bol < 10⁻² (Hughes et al. 2018).

3.2 Discovering the disks: infrared excess

Infrared excess, though not sufficient to classify an object as having a debris disk, is the tool used to discover candidates. It appears as a contribution to the spectral energy distribution (SED), superimposed on the blackbody curve of the star, see Figure [3.1]. Because Earth’s atmosphere is mostly opaque to infrared, it is necessary to use space telescopes to observe the thermal radiation.

Like for the stellar blackbody curve, the peak in energy density occurs at different wavelengths for different dust temperatures. However, because small dust grains are imperfect emitters at long wavelengths (Hughes et al. 2018), the dust cannot be described by a

(22)

blackbody function. The grains are overheated, and the long-wavelength part of the SED therefore drops off more steeply than for blackbodies. To describe the SED analytically a modified blackbody function is constructed by multiplying by a factor (Williams et al.

2004)

1 − exp

− (λ₀/λ)^β

. (3.1)

β, which usually has a value between 0.5–1 (Holland et al. 2017; Sibthorpe et al. 2018), is linked to the power law index of the grain size distribution. This is commonly taken to go as (Draine 2006; Hughes et al. 2018)

N (a) ∝ a^−q (3.2)

where a is the grain size. The power law index q is then related to β via

β = (q − 3)βS, (3.3)

where βS is β in the small particle limit, which is 1.5–2 for most astronomical dust com- positions (Hughes et al. 2018). Physically, β is the dust opacity index parameter,

κ_ν ∝ ν^β, (3.4)

here working in frequency ν instead of wavelength.

Because βS is more or less constant, β is directly connected to q - that is, the long- wavelength behaviour of the SED is directly connected to the grain size distribution (see also Section4.3.1). The typical grain size is often estimated as λ0/2π.

Rather than fitting Equation (3.1) to the entire SED, it can be easier to determine q from just the (sub-)mm region, using

q = α_mm− α_Planck

β_S + 3 . (3.5)

Here αmmis the observed spectral index at (sub)-mm wavelengths while αPlanckis the spectral index of the Planck (blackbody) function between two measured wavelengths, given an inferred disk temperature. In the Rayleigh-Jeans limit of long wavelengths αPlanck = 2.

14

(23)

3.3 The dust and gas of a typical debris disk

The observed SED of a debris disk may contain contributions from several different populations of rocky material, each of which adds their own unique fingerprint to the combined SED. The grain sizes affect the shape of each component’s contribution, while the temperature shifts it towards shorter or longer wavelengths. Since the temperature mainly depends on the distance to the star, spatial information carries over to the spectral regime, enabling us to disentangle the fingerprints. Figure [3.2] shows an example of a modelled debris disk system where different populations each contribute to the total SED, as well as a rough overview of the grain sizes and temperatures involved.

The innermost part of the disk, up to a few au from the star, contains hot dust with temperatures above 150 K. The dust can be observed in the near-infrared and has fast collisional timescales. The exozodi, analogous to the solar system’s interplanetary dust that is responsible for zodiacal light, is made up of warm dust with slower collisional timescales and is visible in the mid-infrared. There may also be larger objects at this location, equivalent to the solar system’s asteroid belt. The outer disk consists of rocky bodies with temperatures below 100 K, has slow collisional timescales and is observable in the infrared, far-infrared and sub-mm. The outer disk is comparable to the Kuiper Belt and is located at tens of au. From the Kuiper Belt analogues and beyond there exist a halo of very small grains on hyperbolic orbits stretching to hundreds of au.

Gas is also sometimes present in debris disks. Due to its much smaller quantities it is more difficult to observe, so there is not much statistical evidence of its distribution.

Unlike the dust, the gas does not (to our current knowledge) seem to have typical, distinct populations in the disk. Because the dust and gas contents act and are observed in such different ways, the two components will be discussed in detail in separate chapters.

3.4 Occurrence rates

Differences in observing wavelength and instrument sensitivities make it difficult to directly compare detection rates of debris disks between surveys. Despite that, it is possible to make rough estimates and to note some general trends in the known debris disk

(24)

(a) The spectral contributions of the different dust populations to the total SED of a debris disk around an A0V star, based loosely on the β Pic and Vega systems. In this illustration, hot dust (not shown) is located in the inner part of the exozodi. Adapted fromHughes et al.(2018).

(b) The different zones of debris disk dust, with typical observational wavelengths and temperatures. Images using a given observational wavelength will be dominated by grains of that size (see Section 4.3). Note that some authors label the 300 K “hot” dust as

“warm” instead. From Su & Rieke(2014).

Figure 3.2: Schematics of typical debris disk dust populations. Planets are shown to give an idea of what sculpts the gaps, but are not meant to suggest any kind of typical architecture. Systems may not contain all of the components, and the extent of the different regions varies greatly.

16

(25)

population. It is useful to draw a distinction into cold, warm and hot dust.

The two Herschel Space Observatory (Herschel) surveys DEBRIS and DUNES targeted the cold Kuiper Belt analogue regions. They found that the overall completeness-adjusted incidence rates for 275 F,G and K stars lie around 28%, with the rates for F stars being clearly higher than the rest at 37%, though there is significant variation within each spectral type (Sibthorpe et al. 2018). As intuitively expected, the incidence rate is higher among young stars, e.g 9 out of 19 in the β Pictoris moving group (Riviere-Marichalar et al. 2014).

Warm dust has an occurrence rate of roughly 13%, peaking at 36 % for A stars (Mennes- son et al. 2014). The warm dust is more likely to be found in systems that have already been shown to harbour a cold component, pointing to a possible link between the two populations, such as inwards migration of small dust grains via Poynting-Robertson drag (see section4).

Interestingly, hot dust has similar detection rates to cold dust, but the detection rate goes up with age. It can therefore not be generated in a steady state process (Ertel et al. 2014). The hot dust is thought to be transported in from colder reservoirs farther out, since any parent bodies would quickly be depleted due to collisions at the radii the hot dust is observed (Kral et al. 2018).The decay of excess emission from the hot inner regions of the debris disks tends to go faster than for the cold outer regions (Su et al. 2006).

Very few M stars have been found to host debris disks. Given the fact that we do observe both protoplanetary disks and many fully formed planetary systems around M stars, the small detection rate may simply be due to observational difficulties, e.g. the removal of small grains by strong stellar winds (Matthews et al. 2014).

As always, the absence of detections does not necessarily mean the absence of material. The solar system’s Kuiper Belt, placed at a distance similar to the systems targeted by far-infrared surveys, would not be detectable with our current technology (Vitense et al. 2012).

(26)

(27)

4 Dust

Dust is the most conspicuous feature of a debris disk. It is perhaps natural to expect the dust we observe to be leftover from earlier phases, but according to our current knowledge, that is not physically possible. The primordial dust that has not been incorporated into larger objects has a much shorter lifetime than the stellar system, so it will either have been either expelled from the disk or spiralled inwards and accreted onto the star (Wyatt 2018).

4.1 Forces acting on the dust

Dust is collisionally generated at different places in the disk, and can be moved to new locations or expelled from the system via several different forces. Stellar radiation pressure can push the grains into hyperbolic orbits if

β ≡ F_rad Fgrav

≥ 1

2 (4.1)

where Frad and Fgrav are the radiation and gravitational forces, respectively. Any grains smaller than this blowout size will be dominated by outwards pressure and escape the system. The β used here is unrelated to the one used in the modified blackbody; the shared notation is an unfortunate coincidence. Since both Frad and Fgrav are proportional to 1/r², β is independent of stellar distance. The radiation pressure depends, among other things, on the grain chemical composition, size and shape (Arnold et al. 2019). Al- though β generally increases with decreasing grain size, certain conditions can therefore cause small grains of e.g. 0.1 µm in size to be relatively unaffected by radiation pressure.

(Cataldi 2016).

Poynting-Robertson (PR-) dragacts to lower the angular momentum of grains and dampen

(28)

4. Dust

their eccentricities. A grain will absorb stellar radiation and re-emit it isotropically in its own reference frame, but not in the star’s. The grain’s orbital movement will cause the emission in the forward direction of motion to be blueshifted and introduce a net braking force, which removes angular momentum and forces the grain to slowly spiral towards the star. PR-drag primarily affects grains smaller than or of cm-sizes.

Stellar wind has especially important effects for sub-µm-sized grains. The flow of charged particles from the star does not have a large enough momentum flux density to significantly push the grains outwards, however, their low velocities cause a drag effect, the so-called corpuscular drag. The effect is similar to PR-drag, serving to circularise orbits and decrease orbital radii.

The end result of radiation pressure, PR-drag and stellar wind is that primordial grains are removed from the disk.

4.2 Dust generation

The fact that we observe dust in systems much older than the typical grain lifetimes must mean that dust is continuously produced. The material that was built up during the protoplanetary phase is ground back down to dust grains through what is known as a collisional cascade. Kilometre-sized planetesimals collide in the disk, producing smaller objects that then collide, eventually grinding down to grains.

The grain size distribution mentioned in Section 3.2, N(a) ∝ a^−q, is derived theoret- ically from the assumption of a steady-state collisional cascade, which yields q = 3.5 (Dohnanyi 1969). Numerical simulations that include physics like size-dependent velocity distributions and tensile strengths show more complex behaviour, such as a wavy grain size distribution rather than a simple power law (e.gThébault & Augereau (2007)), but they support the general trend. This can be seen as a feature of new grains being continuously produced; had there, for instance, been enough time to remove the smallest grains, q would have a lower value, as is the case for zodiacal dust in the solar system.

It is worth noting that observations also seem to agree with q = 3.5, as explored in e.g.

the survey of PLanetesimals Around TYpical and Pre-main seqUence Stars (PLATYPUS) 20

(29)

4. Dust

(MacGregor et al. 2016).

Planetesimals and planets are intrinsically faint, and observations are typically completely dominated by the much more numerous small grains. However, the continuous replen- ishment of grains means that their emission traces their parent planetesimals, providing valuable information about the properties of these unseen populations.

4.3 Imaging

Debris disks have been observed using photometry with telescopes like IRAS, Spitzer and Akari. The high angular resolution of e.g. the Hubble Space Telescope (HST ), the Gemini Planet Imager (GPI ) and the Atacama Large Millimeter/submillimeter Array (ALMA) have now made it possible to obtain detailed images as well.

Images of the dust component can be made both for the thermal emission of the grains, as well as the light that scatters off them. It is worth noting that both methods are most sensitive to dust grain sizes approximately equal to the observing wavelength (Hughes et al. 2018). At any given observing wavelength, only grains larger in size than that wavelength are efficient emitters. However, small grains are much more common than large ones. The combination of the two effects is that observed emission will be dominated by the smallest grains capable of emitting at the observing wavelength. For this reason, small grains can be seen in optical and infrared, while large grains or pebbles are better observed in sub-mm or mm emission.

Since small grains are mainly sensitive to radiation pressure while larger pebbles are dominated by collisions and gravity, grains of a given size will be confined to specific locations in the disk, see Figure [3.2]. Observations at different wavelengths of the same disk can therefore reveal different radial extents or structures, and multi-wavelength studies are complementary, see Figure [4.1].

(30)

4. Dust

Figure 4.1: The Fomalhaut debris disk in optical scattered light with HST (Kalas et al. 2013), far-infrared 70 µm scattered light with Herschel (Acke et al. 2012) and 1.3 mm thermal emission with ALMA (MacGregor et al. 2017). Notice the pericenter glow in far-infrared and apocenter glow in mm. The 180°phase shift at long wavelengths is caused by the disk’s eccentricity (see Section4.5. Adapted from Hughes et al.(2018).

4.3.1 Thermal emission

Thermal imaging can be directly compared to the contribution the thermally emitting grains make to the SED. The temperature of the grains determine the wavelengths of their spectral contribution, but their temperature does not solely depend on their stellar distance. Because the small grains are not perfect emitters, they have hotter-than-blackbody temperatures. The signature the grains imprint on the SED therefore makes it seem as if they are closer to the star than they actually are. Comparing the stellar distance expected from the SED to the imaged disk then reveals the degree of overheating. Since the smallest grains are also the hottest and dominate the thermal emission, the minimum grain size can also be deduced. While the blowout size sets the theoretical lower bound for grain sizes in the system, the observed minimum grain size is often several times larger, possibly because the physics of grain collisions in the small grain limit are more complex (Pawellek & Krivov 2015).

4.3.2 Scattered light

Scattered light imaging can yield a great deal of information. In general, the absorption, emission and scattering of light in the disk depend on physical properties of the dust, such as grain size, elemental composition and porosity (Hughes et al. 2018). Scattered light images give results that can be used to work backwards and constrain those properties, though observational parameters are often set by several different factors working

22

(31)

4. Dust

together, complicating the picture.

Because dust grains scatter preferentially in certain directions, the scattered light is polar- ized and can thus be separated from the unpolarized stellar light. Grains larger than the observing wavelength tend to forward scatter, but smaller grains scatter in all directions and are therefore not captured by polarimetry observations.

Dust composition does not significantly alter the SED of thermal observations, but it does influence the albedo of the grains in scattered light observations. The dust albedo over all scattering angles is difficult to obtain, so the relative colors of the disk and star are often used as a differential albedo instead. Certain organic compounds have distinct, identifying colors, but a degeneracy between albedo and mass makes difficult to distin- guish between low-albedo carbon-rich dust and high-albedo dust rich in silicates and/or ice (Hughes et al. 2018).

The disk colour alone cannot tell us about grain porosity, because large and porous grains can mimic small and compact grains in their scattering properties. However, colour can be used in conjunction with an assumed scattering phase function (light intensity as a function of scattering angle) and polarizability curve (degree of linear polarization as a function of scattering angle). For instance, the scattering phase function and dust colors together give constraints on the minimum grain size; small grains scatter in the Rayleigh regime and will therefore be bluer than the larger ones, which have roughly neutral colors.

A comprehensive analytical approach to estimating both the absorption, emission and scattering cross sections in the interaction between photons and dust grains is Mie the- ory. In these models, it is possible to vary such parameters as minimum grain size, size distribution, composition, opacity and porosity. A set of initial conditions is then used to perform inverse modelling. However, the scattering phase function and polarizability curve are difficult to determine, unless an analytical axisymmetric disk model is used.

That assumption is not likely to hold, as discovered with scattered image observations, and so empirically determined, more complex functions are often used. These, however, suffer from uncertainty caused by viewing angle.

(32)

4. Dust

4.4 Spectroscopy

While imaging of debris disks is particularly good at revealing the morphology of dust and distribution of different grain sizes, spectroscopy is useful for more precise determi- nations of grain properties, as well as for determining dynamics through radial velocity observations.

The observed spectral signatures of dust in debris disks depend on the observation wavelength. In the mid-infrared regime, from about 10 to 70 µm, silicates dominate the dust emission. The emission comes from the abundant small grains, which have been heated to a minimum of 200 K (Hughes et al. 2018). The grains seem to have both amorphous and more crystalline components, the latter of which indicates that some heating or collisional processing must have taken place in the disk (Mittal et al. 2015). Refractory elements, often carbon, as well as ices can be seen, and grains are found to be porous aggregates (e.g. Lebreton et al. (2012), Olofsson et al. (2016)). All in all, the dust of debris disks seems to be not too different from that of the solar system.

The conclusions reached from thermal observations do not always match those from scattered light (e.g.Rodigas et al.(2015)). The SED may point to one grain size distribution, and the observed scattered light colours or scattering phase function to another. The tension can be explained if each method is probing a different dust population with its own grain properties, or perhaps we need more refined underlying models, e.g. a size distribution more complex than a power law.

4.5 Morphology

Figure [4.2] shows some examples of the wide variety of structure seen in debris disks.

Different physical mechanisms can explain the observations, and although planets are not always required to replicate observed patterns, they are often capable of it. A drawback when analysing scattered light images is having to subtract the bright star. The inner region of the disk will still contain artefacts from the analysis, hence there is an inner working angle within which the disk cannot be reliably observed. The outer region of the disk is sometimes too faint to be observed, so our understanding of the disk’s extent both

24

(33)

4. Dust

Figure 4.2: Collection of scattered light and thermal emission images showing a variety of different asymmetries. In most images the central star has been blocked by a coronagraph. The scale bars represent 50 au. Mosaic taken fromHughes et al.(2018), with individual images fromMilli et al.

(2017, panel a),Schneider et al.(2016, panel b), S. Marino (private communication with Hughes, panel c),Schneider et al.(2014, panels d and h), Apai et al. (2015, panel e),Kalas et al. (2015, panel f), Dent et al. (2014, panel g), and Konishi et al. (2016, panel i). Smoothing has been applied in some cases.

inwards and outwards can be lacking (Hughes et al. 2018).

Radial gaps in the dust distribution can be caused by gravitationally perturbing planets.

They sweep up material as they orbit, and because of overlapping resonances with planetesimals, the region near a planet can become chaotic which clears it of material (Wisdom 1980). The resonances carve out gaps with specific edge shapes depending on the planet mass, location and eccentricity (Chiang et al. 2009;Mustill & Wyatt 2012). The resonant perturbations can only apply to planetesimals within a small range of orbital periods, but many planetesimals may become trapped in resonances during planet migration.

Some observed broad rings are consistent with self-stirred disks, while narrow rings may

(34)

4. Dust

require multiple planets shepherding the inner and outer edges (Boley et al. 2012), or e.g.

an external perturber (Nesvold et al. 2017). It should be fairly easy even for planets of only a few Earth masses to open up broad and shallow gaps (Ricci et al. 2015). Self- stirring causes dust to be produced at increasingly larger radii as time goes on (Kenyon

& Bromley 2010; Kennedy & Wyatt 2010) and ice lines or cometary sublimation show up as a truncation of the disk in the inner region (Morales et al. 2011; Jura et al. 1998).

Rare events like giant collisions (Wyatt & Dent 2002) or stellar flybys (Kenyon & Bromley 2002) can also cause increased dust production at specific radii (i.e. rings/belts), but it’s unlikely that all the examples we observe are caused by these.

Eccentric disks can be caused by dust-gas interactions, recent giant collisions, planets on eccentric orbits or even companion stars producing secular (as opposed to periodic) perturbations (Lyra & Kuchner 2013; Hughes et al. 2018; Wyatt 2018). An eccentric planet can be responsible for large scale asymmetries such as arcs or swept-back wings (“moths”) (Lee & Chiang 2016), though the latter could also come about from interactions between the disk and the interstellar medium (Maness et al. 2009;Debes et al. 2009). If an eccentric planet is inclined with respect to the disk, it can produce a warp (see Sec- tion6.1), though it might be necessary to invoke multiple planets to sustain the structure (Apai et al. 2015). An eccentric planet in a dynamically cold (not very eccentric) disk may also produce a spiral structure (Wyatt 2005). The eccentric disk in itself will also cause interesting effects; in mid- to far-infrared, the higher temperature close to the star will cause the pericenter to be brightest, while in (sub-)mm the accumulation of dust grains leads to the apocenter being brightest (Pan et al. 2016).

The existence of resonant orbits caused by planetary migration will eventually make the planetesimal distribution clumpy (Wyatt 2003). Observing clumps can therefore help constrain the mass, location and migration history of the planet. Another origin of clumps could be giant collisions. Although the dust released in this way would expand too quickly for it to be plausible to observe the original clump, the ejected material will continue in different, eccentric orbits that all cross at the point where the impact occurred (Jackson et al. 2014; Kral et al. 2015). Tidal disruption of a planet would also cause a clumpy structure, and is statistically more likely than a giant collision.

26

(35)

4. Dust

Finally, the vertical structure of debris disks can be used to gauge the system’s velocity distribution, and thereby the masses of the planets responsible for the spread (Thébault

& Augereau 2007;Quillen et al. 2007).

The many types of structure thus give valuable information about the contents of the disks as well the processes within them.

(36)

(37)

5 Gas

Though debris disks are generally gas-poor, some systems contain gas in amounts large enough to be observable. If the gas is primordial, observations shed light on the initial conditions of the system. If the gas is instead of secondary origin, it comes from the dust, and the two components are therefore intimately linked. In that case, the gas can yield information about dust composition and the system’s dynamics during a time of active accretion onto planets (Wyatt 2018). Whether the gas is primordial or secondary, its composition reveals the building materials of the system and may indicate potentially habitable conditions.

The first debris disk gas detection was absorption lines from Ca and Na in the β Pictoris system in 1975 (Slettebak 1975), 8 years earlier than IRAS found its infrared excess (Au- mann et al. 1984). The circumstellar gas was at first thought to be distributed in a sphere, so β Pic and similar systems were for a while known as “shell stars” (Slettebak & Carpenter 1983). Today we know the gas is in the shape of a disk, though there are asymmetries as well as deviations from the dust disk.

5.1 Occurrence rates

Before diving into the numbers, it is important to note that statistics about gas in debris disks can be difficult to interpret. Absorption and emission spectroscopy can yield different results for the same system, surveys of debris disk gas have not been uniform in sensitivity or sample selection, and sample sizes have been limited to roughly 50 disks (e.g. Dent et al. (2005);Hales et al. (2014)).

That being said, it is clear that many systems contain a gaseous component well into

(38)

5. Gas

the debris disk phase. Intermediate-mass stars of spectral types A and B have the highest gas detection rates, and younger stars tend to have more gas than older ones. The results seem intuitive; high mass stars have more primordial gas and solids to produce secondary gas, and gas around young stars has had less time to accrete or be expelled from the system. Hughes et al. (2018) summarise observations for AB stars with ages below 50 Myr and show detection rates of 14/35, 3/17 and 5/8 (roughly 34, 18 and 63%) for CO, O I and C II, respectively. The low mass F, G and K stars show detection rates of 2/34 and 1/12 (6 and 8%), for CO and O I. CO has even been detected in the 1–2 Gyr old debris disk η Corvi (Marino et al. 2017).

5.2 Detection

When it comes to detecting debris disk gas, two dividing lines can be drawn: atomic versus molecular gas, and absorption versus emission spectroscopy.

Firstly, there is a difference between atomic and molecular gas. Atomic gas is mainly radiatively excited and absorbs or emits via electronic transitions. There is also a small probability of collisional excitation at lower energies where the star is dim, giving rise to e.g. the forbidden fine structure line of oxygen at 63 µm. Atomic gas is found at all distances to the star.

Molecular gas is located in regions where UV radiation from the star or the interstellar radiation field is not intense enough to dissociate it, or has not had time to. If the gas is of secondary origin, it is also necessary to have a region sufficiently dense for planetesimal collisions to produce enough gas to be observable, which may not be straightforward at large radii. Low-energy rotational transitions are typically the only ones excited, which mainly happens through collisions between the molecules and electrons. Long-wavelength observations in the mm-regime are therefore needed, and that has been challenging for current telescopes. Since Herschel is no longer active, ALMA is the only telescope to target that wavelength range with sufficient sensitivity to detect the small amounts of molecular gas. Many different atomic species have been detected - Mn, Mg, Fe (Malamut et al. 2014), C, O, Cl, S, Si, and Al (Roberge et al. 2014) in 49 Ceti alone. CO re- mains the only observed molecule, and the relationship between the atomic and molecular

30

(39)

5. Gas

components is not yet completely understood (Hughes et al. 2018).

Secondly, there is a difference between absorption and emission spectroscopy. Absorp- tion spectroscopy works well in systems that are more or less edge-on, since our line of sight then includes more of the disk. The column density is therefore higher, and the stellar photons have a larger probability of being absorbed by the gas on their way to us.

Absorption spectroscopy has tended to give most detections in the hot, inner regions of the disk (Hughes et al. 2018).

Emission spectroscopy can be used for the outer regions of tens to hundreds of au, where the large reservoirs of gas are located. Since an excited atom or molecule emits randomly in all directions, only a fraction of the emission reaches our telescopes. Because of that, and because it can be difficult to disentangle the faint signal from that of the bright star, the method is less sensitive than absorption spectroscopy. However, it has the advantage of working for all inclination angles, and with spectro-spatial observations it is possible to map the gas morphology out to large distances. This strategy has revealed cold gas located up to several hundreds of au from the host star in several systems (e.g. Matrà et al. (2017a,b)). Since absorption and emission spectroscopy tend to probe somewhat separate regions, they can be used in combination to get a more complete picture of the system.

5.3 The origins of the gas

The gas discovered in β Pic in 1975 illustrated two main routes of producing secondary gas. One component of the absorption lines was time-variable and redshifted from the stellar velocity. This is a telltale sign of the so-called falling evaporating bodies (FEBs);

material coming close to the star and sublimating under the high temperatures, thereby releasing gas (Ferlet et al. 1987).

Another component of the absorption line profiles was constant in time and had the same velocity as the star (Vidal-Madjar et al. 1986). The cause of this signal is gas in the outer part of the disk which, if it is secondary, is released from icy and rocky

(40)

5. Gas

material similar to the comet-like bodies of the Kuiper Belt¹. Collisions between large bodies containing volatiles can heat up the material and release gas into the surroundings (Zuckerman & Song 2012). The same type of collisional desorption can happen for small grains if they are accelerated outwards via radiation pressure and collide at high enough velocities (Czechowski & Mann 2007). Finally, small grains can undergo photodesorption from their surfaces as a result of stellar radiation (Chen et al. 2007). Observations of secondary gas can therefore reveal the composition of both the surfaces and interiors of solid bodies, which is otherwise not accessible.

Distinguishing between primordial and secondary gas is often a matter of timescales.

Observing for instance molecular gas species with dissociation lifetimes shorter than the age of the system must mean the gas is secondary. This approach hinges on accurate knowledge of the lifetime of a species in the conditions of a specific disk. It is of course also possible that secondary gas is of a species that happens to have a long lifetime. Pri- mordial gas is thought to be able to survive in some systems, possibly with the help of a braking mechanism counteracting radiation pressure or (self-)shielding in dense regions (e.g. Matrà et al.(2017a)). In other systems the gas is expected to have been lost to vis- cous accretion onto the star (Lynden-Bell & Pringle 1974) or photo-evaporated (Alexander 2008). Kral et al.(2017) showed that it is possible to explain the gas of most systems with a secondary generation mechanism, using a semi-analytical model for the creation of CO, C and O. Some disks contain non-negligible amounts of both primordial and secondary gas, and are termed “hybrid disks”.

5.4 Mass and composition

A key to understanding processes in a debris disk is gas mass. If enough gas is present (Mgas/Mdust ≥1, Besla & Wu (2007)), it can interact with the dust and sculpt the disk, causing for instance rings which could be mistaken for signs of planets. Gas can influence the dynamics of large bodies by altering their orbits and thereby the probability of gravitational interaction or collision with other bodies. Gas accretion onto planets may also be taking place, building up or changing their atmospheres. To understand the late stages

1Although FEBs are sometimes called ‘exocomets’ because of their star-grazing orbits, I will use

‘comet-like’ or ‘cometary’ to refer to the icy objects in the cold outer parts of a system.

32

Gas in Debris Disks