Lecture 10: Icy Bodies in Outer Solar System & Debris Disk Evolution

Star Formation and the Origins of Planetary Systems

Lecture 10: Icy bodies in outer solar system & debris disk evolution

Background reading: Credit: NASA Luu & Jewitt 2002, ARA&A ; Wyatt 2008, ARA&A; Hughes et al. 2018, ARA&A Thanks to M. Wyatt for slides on debris disks Logistical roundup (1/2):

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Remaining questions from SPF #9 will be answered at the end of this lecture, not during the lecture summary.

Please sign up for a time slot to give your presentation (via Doodle poll to be sent by Ewine) . Star Formation and the Origins of Planetary Systems

Lecture 10: Icy bodies in outer solar system & debris disk evolution

Background reading: Credit: NASA Luu & Jewitt 2002, ARA&A ; Wyatt 2008, ARA&A; Hughes et al. 2018, ARA&A Thanks to M. Wyatt for slides on debris disks 486958 Arrokoth

• Classical Kuiper Belt Object • farthest & most primitive object visited by spacecraft • 21 + 15 km contact binary

Lecture 10: Icy bodies in outer solar system & debris disk evolution Do you want to build a snowman?

Background reading: Credit: NASA, Arrokoth Luu & Jewitt 2002, ARA&A ; Wyatt 2008, ARA&A; Hughes et al. 2018, ARA&A Thanks to M. Wyatt for slides on debris disks Quiz: What does the size of the contact binary components tell you about their collision velocities? Summary Lecture 9 Key point(s) Key ﬁgure/table

2. Planetesimal to Model planetesimal swarm statistically with distributions of important parameters. For a select few objects, achieve runaway growth from planetesimals into embryos up to isolation mass, embryo growth deﬁned by Hill sphere.

3a. Terrestrial Isolation mass embryos in inner disk up to ~0.1 Mearth (from #2). Then need gravitational planet formation interactions to push embyos onto colliding orbits. Giant impact phase responsible for many scenario "odd features" of Solar System's terrestrial planets. Earth took ~80 Myr to form.

In contrast, Jupiter took <3.8 Myr to form. Two classical models for gas giant formation: core 3b. Gas giant planet accretion & gravitational instability. Former takes nearly too long, latter requires massive, cold formation models disk at correct time in disk evolution. Alternative model: pebble accretion! Combined with streaming instability, it can solve most timescale problems for formation.

Three kinds of migration within gas disk, depending on mass ratio of planet to star and disk to star. Type I moves planets inward; II & III are not exclusively in one direction. Observables of 4. Planet migration migration are spiral arms driven by planets and gaps (for certain sizes). Migration of planet can excite high eccentricities/inclinations in smaller planetesimals, leading to impacts. !7 SPF course progress: where are we now? Date SPF # Who Lecture 18 Feb. 1 EvD Motivation, history, & observational facilities 20 Feb. 2 EvD Pre-stellar cores, cloud collapse 25 Feb. 3 EvD SEDs, embedded protostars 27 Feb. 4 EvD Outﬂows & jets 3 Mar. 5 EvD High mass star formation 5 Mar. P1 TAs Practice exercises #1 (Star formation) 10 Mar. 6 MM Pre-main sequence star types, stellar birthline 12 Mar. 7 MM Circumstellar disks 24 Mar. 8 MM Disk evolution & planet formation (Planet formation) 26 Mar. 9 MM Planet formation: Jovian vs terrestrial planets 31 Mar. 10 MM Icy bodies in outer solar system, debris disk evolution 2 Apr. 11 EvD Condensation processes, meteorites, missions 7 Apr. 12 EvD Chondrules, planetary atmospheres 9 Apr. 13 MM Extrasolar planets 14 Apr. P2 TAs Practice exercises #2 16 Apr. 14 MM Astrobiology (Life formation) !8 Disk evolutionary stages overview SPF #8

Stage 1) Envelope infall 2) Viscous evolution 3) Disk clearing

• Matter falls onto disk faster • Infall rate lower. Disk evolves viscously, Disk material already accreted than can be redistributed. under the action of its own friction. by protostar and protoplanets, Features • Global instabilities possible. • Outward angular momentum transport or driven away by energetic processes: • Disk grows with time. allows matter to fall in to star. (winds, photoevap., tidal encounters)

5 6 7 Depends on disk mass & environment: tff : ~ Few x 10 yr ~Few x 10 yr, up to 10 yr Timescale 103 − 107 yr after stage #2.

SED Class Class 0, early Class I Late Class I, Class II (opt. thick disk) Class III (opt. thin disk)

Pre-main sequence stars: Pre-main sequence star: Protostar Weak-lined T Tauris Star type Classical T Tauri − Herbig AeBe (Towards zero-age main sequence) Lectures SPF #3, #6 SPF #3, #6, #7, #8, #9 SPF #10

!9 Disk evolutionary stages overview SPF #8

Stage 1) Envelope infall 2) Viscous evolution 3) Disk clearing

5 6 7 Depends on disk mass & environment: tff : ~ Few x 10 yr ~Few x 10 yr, up to 10 yr Timescale 103 − 107 yr after stage #2.

SED Class Class 0, early Class I Late Class I, Class II (opt. thick disk) Class III (opt. thin disk)

!10 2) Deﬁning debris disks

Haisch et al. (2001) (SPF#3, 8) Hernandez et al. (2007) (SPF#7)

50%

1) Disk clearing stage

2 Myr

"protoplanetary" disk "debris" disk

!11 (gassy) (rocky) 3) Solar System's Kuiper Belt & Oort Cloud 1. Protoplanetary disk evolutionary stage #3: disk clearing 2. Debris disks & their evolution 3. Analyze Solar System's Kuiper Belt & Oort Cloud as preserved remnants of #1 & #2 Disk clearing stage timescales Haisch et al. (2001) ▪ Jovian planet formation and migration must occur Hernandez et al. (2007) while gas still present in disk. ▪ Near-IR warm dust surveys show decreased fraction (Near-IR) of stars with disks in clusters after ~2 Myr

SPF#7 Ansdell et al. (2016, 2017) 2 Myr ~1.5 Myr (Sub-mm) ≤3 Myr ▪ Some decrease also found in longer wavelength ≤5 mid- and far-IR surveys, but mm surveys show ≤10 Myr decrease only after 3 Myr, with some (cold outer) disks surviving up to 10 Myr. Disk evolution and dispersal, as seen through SEDs Multiple paths from protoplanetary (gas-rich, ‘thick’) to debris (gas-poor, ‘thin’) disks: Grain growth Disk + dispersal?

SPF#8 Class II Class II Star ?

Gap formation? SPF#8, 9

Class II Class III Merin et al. Quiz: In what order does the disk clear out in the sequence below?

inner middle outer

Hartmann et al. (2016)

Disk

Class II Star Class II Class III Mechanisms for disk dispersal

▪ Accretion onto star ▪ Material used for planet formation ▪ Stellar winds ▪ Photoevaporation ▪ External (e.g., Orion) ▪ stellar UV ▪ Close encounters with other stars ⇒ stripping

Merin et al. Hollenbach et al. 2000, PPIV Photoevaporation

Stellar or external UV heats surface layer of disk to high temperatures ⇒ thermal sound speed large enough to overcome gravitational pull ⇒ flow

If layer stays neutral (PDR) ⇒ gas ≈ several 103 K If layer ionized ⇒ gas ≈ 104 K (SPF#6)

photo- accretion evaporation

Hollenbach et al. 2000, PPIV UV switch

Alexander et al. (2014)

Once accretion rate drops and cannot keep up anymore with photoevaporation rate, inner disk drains quickly

"transition disk" = disk with inner hole or gap. Sometimes see "pre-transition" disk as gapped vs with hole. Hollenbach et al. (2000) 1. Protoplanetary disk evolutionary stage #3: disk clearing 2. Debris disks & their evolution 3. Analyze Solar System's Kuiper Belt & Oort Cloud as preserved remnants of #1 & #2 Debris disks

Debris disks are (1) older disks which have (2) lost their gas and where dust is produced in situ by (3) collisions of planetesimals.

Merin et al. Debris disks were originally the ‘Vega phenomenon’

▪ Main sequence (MS) star, Vega (= α Lyrae) with circumstellar dust grains ▪ Calibration star for IRAS satellite → expected to see weak emission. Instead a powerful IR source was found, orders of magnitude brighter at 60 and 100 µm than Rayleigh- the photospheric emission Jeans tail Vega ▪ Vega was thus the first MS star apart from the Sun to have surrounding solid material. ▪ Thermal balance: small grains become hotter than big grains

Aumann et al. (1984), Backman & Paresce in PPIII The ﬁrst debris disk detections with IRAS satellite (1984): the Fab Four.

Rayleigh- ▪ Spatially resolved Jeans tail Vega even by IRAS 60 µm Fomalhaut ▪ Distance well known ▪ No near-IR excess

β Pic ε Eri

(Aumann et al. 1984) Courtesy: Paul Kalas, www.disksite.com Grain sizes and mass

▪ Although planetesimals have formed in these disks, some fraction of grains must be smaller than ~100 µm to emit far-IR radiation ▪ Values of grain size and total grain area depend on emissivity exponent β or grain size distribution exponent m -3 -3 -2 ▪ Minimum mass: all grains have size d=d0 with density 1 gr cm → small masses 10 – 10 MEarth ▪ Maximum mass: assume grain size distribution n(d)∝d-3.5 produced by collisional fragmentation, -3 with dmin=d0, dmax=1000 km (size of gravitational instability at 100 AU) and density 5 gr cm →

large masses up to 0.1 MSun Grain removal

▪ Small grains with 0.1 < d < 1 µm are ejected quickly (~104 yr) from system by radiation pressure.

▪ Large grains may spiral in due to Poynting-Robertsen radiation drag (~105-106 yr). Relativistic effect: dust absorbs photon (energy), thus acquires mass; to conserve angular momentum, the dust grain must drop to a lower orbit

▪ Most grains are therefore short lived and must be replenished by fragmentation of larger bodies

▪ Hence the term debris disks: the dust is produced continuously in situ by collisions of planetesimals and is no longer the original interstellar dust

▪ It is tempting to take the presence of debris dust as evidence for the presence of larger bodies (i.e., planets) but this is not necessarily the case. Analogous to Kuiper Belt in Solar System. Grain removal Many more (unresolved) debris disks thanks to Spitzer

• Only fraction of young stars has measurable mid-IR/far-IR excess

• General decline with age + stochastic events (collisions)?

• Contemporaneous with end of giant impact stage in planet formation...

Rieke et al. 2005 Few debrisdisks are spatiallyresolved. tensof structures seen. Several typesof

Thermal emission Scattered light (visible & (submillimeter) near-IR) Diversity of disk structures

Hughes et al. 2018 Debris disks can look very different at IR vs mm

Courtesy: Paul Kalas, www.disksite.com Example of structure in β Pic disk ▪ Fortuitous inclination (>80o) produces factor of 10 extra surface brightness → intensively studied at optical (since 1984), IR and mm (early ALMA) ▪ Wedge or ‘flaring’ disk; asymmetry in inner part possibly caused by orbiting large planet ▪ Planet discovered in 2008 ▪ Warps & clumps in outer part ▪ One clump contains asymmetric CO emission: exocomet collisions! Surface density

A key assumption : optically thin disk

Face-on view

etc…

Edge-on view ß Pictoris density profile

slope = -1 slope = -5

Heap et al. (2001)

▪ ß Pictoris : 2 power law disk profile ▪ Break around 120AU = outer edge of planetesimal disk (Augereau et al. 2001) Beta Pictoris 2 disks

HST Image credit: David Golimowski (Johns Hopkins University), NASA, ESA

- Secondary disk continuously replenished with small particles from primary disk? Beta Pictoris planet

Detection in 2008 System hosts a ~13 MJup planet on ~9 AU orbit. Track in "real time" through archival data!

On the move in 2010

Lagrange et al. 2009, 2010 2nd generation gas from exocomet collisions

Dent et al. 2014

Trace, clumpy CO gas (10-6/-7 MEarth) now detected in majority (18) of debris disks resolved by ALMA. Collisions between comets!

Moor et al. (2017), Matra et al. (2017b) Shamelessly borrowed from Sharon Montgomery's fabulous review talk at 2019 Lorentz Center Exocomets workshop: https://www.exocomets.org/wp-content/uploads/2019/05/Leiden-talk-newest4.pdf Detected in sample of 24 debris disks!

Shamelessly borrowed from Sharon Montgomery's fabulous review talk at 2019 Lorentz Center Exocomets workshop: https://www.exocomets.org/wp-content/uploads/2019/05/Leiden-talk-newest4.pdf Resonant structures due to planets

Mark Wyatt

Cambridge University What is the effect of a planet on the debris disk structure?

Effect of planet's gravity on the orbits of planetesimals and dust in a debris disk which causes structures.

The effect of a planet’s gravity can be divided into two groups (e.g., Murray & Dermott 1999)

• Secular Perturbations • Resonant Perturbations

2 Both are the consequence of Newton’s F=GMdustMpl/r law of gravitation Secular perturbations explain some disks, e.g. Beta Pic

Are the long term effect of the planet’s gravity and act on all disk material over >0.1 Myr timescales

Cause the disk to be:

• Offset e.g., lobe brightness asymmetry in if the planet has HR4796 disk (Wyatt et al. 1999; Telesco et al. 2000) an eccentric orbit

• Warped e.g., warp in β Pictoris disk (Heap et al. 2000; if the planet has an Augereau et al. 2001) inclined orbit Resonant perturbations • Affect only material at specific locations in the disk where the dust or planetesimals orbit the star with a period which is a ratio of two integers times the orbital period of the planet…

Pres = Pplanet *(p+q)/p …which from Kepler’s law gives 2/3 ares = aplanet *[(p+q)/p]

• Resonant material receives periodic kicks from the planet which always occur at the same place(s) in its orbit, which can be a good or a bad thing!

Cause the disk to contain: • Gaps • Clumpy Rings How does material move into the resonances? While some resonances are very stable, they occupy a small region of parameter space

Resonances are filled for two reasons: • Inward migration of dust Dust spirals in toward the star Resonance due to P-R drag and resonances Star Pl temporarily halt inward migration

• Outward migration of planet Resonance Planet migrates out and Star Pl planetesimals are swept into the planet’s resonances

Resonant filling causes a ring to form along the planet’s orbit Dust migration into resonance with Earth and Neptune

Dust created in the asteroid belt spirals in toward Dust created in the Kuiper Belt also migrates the Sun over 50 Myr, but resonant forces halt the inward because of P-R drag and an equivalent inward migration… ring is predicted to form along Neptune’s orbit

Semimajor axis, AU

Time Kuiper Belt dust distribution

…causing a ring Sun Earth to form along the ⊕ Earth’s orbit

With and Without Planets

Dermott et al. (1994) Liou & Zook (1999) Geometry of resonances

Each resonance has its own geometry so that, e.g., the pattern formed by material in 2:1 3:2

2:1 is one clump 3:2 is two clumps 4:3 and 5:3 is three clumps

which follow(s) the planet around its orbit

4:3 5:3 The clumpy patterns of extrasolar resonant rings are determined by the extent to which different resonances are filled Paths of resonant orbits at equal timesteps in frame rotating with the planet (X) for e=0.3 Resonances are the only way to explain debris disk clumps

Observations show that many debris disks are characterized by clumpy rings.

Vega Fomalhaut ε Eridani

Diameter of Solar System

Holland et al. (1998) Holland et al. (2003) Greaves et al. (1998)

The only viable explanations for this clumpiness involve planetary resonances Resonance dust migration structures

Kuchner & Holman (2003) summarized the four types of dust structure expected when dust migrates into the resonances of high/low mass planets that are on eccentric/circular orbits:

I low mass, low eccentricity II high mass, low eccentricity e.g., Dermott et al. (1994), e.g., Ozernoy et al. (2000) Vega Ozernoy et al. (2000) ε Eri

III low mass, high eccentricity IV high mass, high eccentricity e.g., Wilner et al. (2002), Moran et al. (2004) e.g., Quillen & Thorndike (2002) Vega: Evidence of Planet Migration

• Wyatt (2003) explained Vega’s two asymmetric clumps by the

migration of a 17Mearth planet from 40-65AU in 56 Myr Observed

• Most planetesimals end up in the planet’s 2:1(u) and 3:2 resonances

Model

Orbit Distribution Spatial Distribution Emission Distribution This also happened in our own solar system! Nice model for our own solar system

Early Middle Late

Dark blue: Neptune, light blue Uranus, Orange: Saturn, green: Jupiter Gomes et al. 2005

-Giant planets initially formed at 5.5-17 AU - Jupiter and Saturn reach 2:1 resonance - After 600-800 Myr, Uranus, Neptune and Saturn move outward, Jupter slightly inward; note Neptune-Uranus swapping - Planetesimals ejected Small dust from 3:2 resonant planetesimals

• Small dust grains, as soon as they are created, see a less massive star due to radiation pressure, which changes their orbital period

• Numerical simulations have shown that: • large particles stay in resonance, but one with an increased libration width, hence smearing out the clumps • small particles fall out of resonance

• For the 3:2 resonance: 0.5 βmin = 0.02 (Mpl/Mstar) Small dust from 2:1 resonant planetesimals

• The result is similar for dust from planetesimals in the 2:1 resonance

• The effect of clump smearing, then falling out of resonance, for smaller grains, is still the same:

Star Pl

Planetesimals Large Dust Medium Dust Small Dust Implications for Vega’s clumpy disk

Question: what size of grains are we seeing toward Vega?

Answer: using a model which fits the disk’s SED assuming a collisional cascade size distribution shows which grain sizes contribute to the flux in each waveband: 90% of the emission comes from grains of size

25 µm : <2-4 mm 60 µm : <2-4 mm 100 µm : <2-4 mm 450 µm : 160 µm – 8 cm 850 µm : 320 µm – 20 cm

Since the size cut-off for resonance is 300 µm – 2 mm, predict: sub-mm images will be clumpy; mid and far-IR images will be smooth Conclusions for small dust grains

• Small grains have different dynamics to large grains and so have different spatial distributions (with larger grains having clumpier distributions)

• Observations in different wavebands probe different grain sizes and therefore should see different structures, with a disk appearing smoother at shorter wavelengths

• By comparing observations in different wavelength regimes we can derive the size distribution and information about the planet mass Conclusions regarding resonant structures

If there are planets in disks, their resonances will affect the structure of the debris disks in a variety of ways: • gaps • within asteroid belts • along orbit of planet • clumpy rings • dust migration into resonance • resonance sweeping of planetesimals (KBOs) by planet migration • Modelling the observed structures can be used to identify the presence of a planet and set constraints on its location, mass and even evolutionary history • Multi-wavelength observations are particularly important for testing and constraining models Debris disks: other planetary systems?

B. Matthews et al. PPVI 1. Protoplanetary disk evolutionary stage #3: disk clearing 2. Debris disks & their evolution 3. Analyze Solar System's Kuiper Belt & Oort Cloud as preserved remnants of #1 & #2 The Solar System's Kuiper Belt (remnant debris disk)

Neptune

"Trans-Neptunian Objects" Our Solar System's debris disk stage: Kuiper Belt as seen from distance 23 µm simulation Face-on Viewed from Sun

Liou & Zook 1999 Spectral energy distribution solar system as template for debris disks

Hughes et al. 2018 What is the structure of Kuiper Belt?

▪ Swarm of small bodies beyond Neptune (30 AU) ▪ Now also called Trans Neptunian Objects (TNOs) ▪ Predicted by Edgeworth (1943, 1949) and Kuiper (1951) ▪ First KBO discovered in 1992 by Luu & Jewitt ▪ Now more than 1000 known, see http://www2.ess.ucla.edu/~jewitt/kb.html ▪ Most KBOs between 30 and 50 AU ▪ Distribution not uniform, but sculpted by gravitational influence giant planets

(What we just saw with debris disks) Types of KBOs ▪ Three distinct dynamical subgroups: ▪ Classical KBOs ▪ Resonant KBOs (Plutino’s and 2:1) ▪ Scattered KBOs ▪ Classical:Scattered:Plutino: 2:1 Resonant pop. ratios = 1.0 : 0.8 : 0.4 : 0.07 ▪ Population ratio corrected for known observational biases Classical KBOs

▪ Majority of known KBOs ▪ Semi-major axis 42 < a < 48 AU ▪ Small eccentricity: e~0.1 ▪ Perihelia q>35 AU ▪ Orbits immune to influence Neptune over Gyr timescale ▪ Large spread in e and i => orbits excited since formation ▪ Scattering by Earth-sized bodies in early solar system? ▪ Stellar encounter? Resonant KBOs

▪ Orbits have mean motion resonance with Neptune ▪ Ratio orbital period KBO/Neptune= ratio of integers ▪ Most densely populated resonance = 3:2 at 39.4 AU => Plutinos ▪ Most orbits are stable over age of solar system, but not all ▪ Supply of short period comets to inner solar system? ▪ Mean motion resonances probably populated by radial migration of giant planets (see later) Semimajor axis a vs eccentricity e and inclination i

Classical + Resonant KBOs Luu & Jewitt 2002 Scattered KBOs ▪ Large, highly eccentric and highly inclined orbits ▪ First evidence that population extends Neptune crossers beyond 50 AU ▪ Scattered by Uranus and Neptune to large distances during late stages of planet formation => Oort cloud and Scattered Kuiper Belt

Luu & Jewitt 2002 KBO Population characteristics ▪ Surface density: 1 KBO per square degree at mR~23.2 mag → faint! ▪ Increases by ~4 per magnitude ▪ Size distribution: n(R)dr=Γr-qdr +0.6 ▪ q=4.0 -0.5 ▪ N(r>1 km)~1010 ▪ N(r>50 km)~3 104 ▪ N(r>1000 km)~10 (most have now been found!)

▪ Total mass = 0.08 MEarth -3 ▪ Assumes rmin=1 km, rmax=1000 km, ρ=1 g cm , albedo pR=0.07 ▪ Original mass probably much larger

Jewitt website

Planet Nine? Presence inferred from TNO/KBO orbits

Batygin & Brown 2016 How large is the Kuiper Belt?

▪ Surveys indicate that KBO surface density drops steeply near 50 AU ▪ Edge at 47±1 AU ▪ Possible explanations: ▪ Systematically lower albedos beyond 50 AU: no physical foundation (ice gives higher albedo) ▪ Decrease in rmax of KBOs: expect some effect based on planetesimal growth (Chapter 9), but too small to explain lack of detection ▪ Tidal truncation by a passing star with periapse at 150-200 AU Physical properties of KBOs

▪ Albedos: measured ▪ Pluto: 0.5-0.7 (atmosphere => frost) ▪ Charon: 0.4 ▪ 20,000 Varuna: 0.07 ▪ Albedos of KBOs which are too small to sustain atmosphere are expected to be very small ▪ Consistent with measurements of comets and Centaurs ▪ Water ice detected on several KBOs ▪ Colors show large diversity, some very red (e.g. Arrokoth, methanol ice-rich) ▪ Intrinsic compositional differences? ▪ Collisional resurfacing? Albedo vs diameter

Jewitt et al. 2001 Luu & Jewitt 2002 TNOs are cool!

T. Mueller 2013 Note large range in sizes and albedos Water ice on KBOs

Centaur

KBO

Luu & Jewitt 2002 KBO Internal structure

▪ KBOs are ice-rich but contain a significant component of refractory material ▪ Refractories include radioactive nuclei (K, Th, U) whose decay is source of heat ▪ Larger KBOs (>100 km) cannot conduct radiogenic heat on timescales of their age => temperature gradient ΔT=150 K => partial differentiation, outgassing, volcanism? Relation of KBOs to other Solar System bodies

▪ Pluto-Charon, Triton ▪ Pluto-Charon are the two largest known KBOs ▪ Triton is a captured KBO

▪ Comets, Centaurs ▪ Jupiter-family comets are comets whose orbits cross or approach Jupiter’s orbit. They likely originate from small size end of the Kuiper Belt. Since they have short lifetimes of 104-105 yr due to sublimation and dynamics, they must be replenished continuously ▪ Centaurs are objects on unstable planet-crossing orbits between Jupiter and Neptune. They likely originate in the Kuiper Belt and are now in transition to the inner solar system ▪ Most comets are likely collision fragments of larger KBOs Centaurs

Dave Jewitt website Formation of Kuiper Belt

▪ Kuiper Belt is processed remnant of protoplanetary disk of our Sun

▪ Kenyon & Luu model of KBO growth ▪ Follow evolution of planetesimal masses and velocities (see Lecture 9, Wetherill & Stewart) ▪ Start with 100m planetesimals in annulus with width Da=6 AU at 35 AU around Sun ▪ Allow for fragmentation during accretion ▪ Follow for ~108 yr, when Neptune expected to form ▪ Neptune excites orbits KBOs and inhibits further growth Formation (continued)

▪ Results Kenyon & Luu model

8 ▪ Can form Kuiper Belt in 10 yr if initial mass is 3-30 MEarth, 30-300 times larger than current mass but consistent with Hayashi minimum mass solar nebula (see Lecture 8) ▪ Final size distribution determined by competition growth and fragmentation. Find broken power- law with different indices for small and large objects. Several Pluto-sized bodies naturally produced ▪ Fragmentation limits maximum size to 3000 km (depending on tensile strength) ▪ Most of initial mass ends up in small (0.1-10 km) objects that can be collisionally depleted Size + velocity distribution

Kenyon & Luu Initial mass 10 MEarth Summary history Kuiper Belt

▪ Planetesimals originally have low relative velocities and nearly circular orbits => growth ▪ As planetesimals grow, velocity dispersion increases due to mutual scattering => stronger collisions, more debris => dusty trans-Neptunian belt. ▪ After ~107 yr, bodies large enough (300 km) to excite velocities of smaller planetesimals => more disruptive collisions => more dust ▪ After 108 yr, Neptune obtains final mass and begins to erode Kuiper Belt Solar system overview 1. Protoplanetary disk evolutionary stage #3: disk clearing 2. Debris disks & their evolution 3. Analyze Solar System's Kuiper Belt & Oort Cloud as preserved remnants of #1 & #2 Lecture 9 question round-up (1/2)

1) Movie that wouldn't load: 2) Roche lobe overﬂow stopping migration

Mass in Moves back out

Ang. mom. out

Armitage (2005): website below (movie linked in ﬁrst sentence) https://jila.colorado.edu/~pja/planet_migration.html Lammer et al. (2012) Lecture 9 question round-up (2/2)

3) Saturn currently forming new moon

https://science.nasa.gov/science-news/science-at-nasa/2014/14apr_newmoon

Credit: Science@NASA Appendix

▪ IR radiation from disk