AST3020. Lecture 09 Theory of transitional and debris disks The roles of radiation pressure Beta Pictoris as a young solar system Some observed examples and their non-symmetric morphology Possible mechanisms of structure formation: artifacts or background objects planets and stars internal disk dynamics: local dust release + avalanche intrinsic disk instabilities (optically thick disks)

Radiative blow-out of grains (  -meteoroids, gamma meteoroids) Dust avalanches Radiation pressure on dust grains in disks Neutral (grey) scattering from s> grains Repels ISM dust Disks = Nature, not nurture! Enhanced erosion; shortened dust lifetime Orbits of stable  - meteoroids are elliptical Dust migrates, forms axisymmetric rings, gaps (in disks with gas) Short disk lifetime Size spectrum of dust has lower cutoff Weak/no PAH emission Quasi-spiral structure Instabilities (in disks) Age paradox Color effects Limit on f IR in gas-free disks

Structure in transitional and debris disks - very common - visibly non-axisymmetric

AB Aur : disk or no disk? Fukugawa et al. (2004) another “Pleiades”-type star no disk

Hubble Space Telescope/ NICMOS infrared camera

HD A is a Herbig emission star >2 x solar mass, >10 x solar luminosity, Emission lines of H are double, because they come from a rotating inner gas disk. CO gas has also been found at r = 90 AU. Observations by Hubble Space Telescope (NICMOS near-IR camera). Age ~ 5 Myr, a transitional disk Gap-opening PLANET ? So far out?? R_gap ~350AU dR ~ 0.1 R_gap

HD 14169A disk gap confirmed by new observations (HST/ACS)

HD BC in V bandHD141569A deprojected HST/ACS Clampin et al.

The danger of overinterpretation of structure Are the PLANETS responsible for EVERYTHING we see? Are they in EVERY system? Or are they like the Ptolemy’s epicycles, added each time we need to explain a new observation?

FEATURES in disks: (9) blobs, clumps ￭ streaks, feathers ￭ rings (axisymm) ￭ rings (off-centered) ￭ inner/outer edges ￭ disk gaps ￭ warps ￭ spirals, quasi-spirals ￭ tails, extensions ￭ ORIGIN: (10) ￭ instrumental artifacts, variable PSF, noise, deconvolution etc. ￭ background/foreground obj. ￭ planets (gravity) ￭ stellar companions, flybys ￭ dust migration in gas ￭ dust blowout, avalanches ￭ episodic release of dust ￭ ISM (interstellar wind) ￭ stellar UV, wind, magnetism ￭ collective eff. (selfgravity)

FEATURES in disks: blobs, clumps ￭ streaks, feathers ￭ rings (axisymm) ￭ rings (off-centered) ￭ inner/outer edges ￭ disk gaps ￭ warps ￭ spirals, quasi-spirals ￭ tails, extensions ￭ ORIGIN: ￭ instrumental artifacts, variable PSF, noise, deconvolution etc.

FEATURES in disks: blobs, clumps ￭ streaks, feathers ￭ rings (axisymm) ￭ rings (off-centered) ￭ inner/outer edges ￭ disk gaps ￭ warps ￭ spirals, quasi-spirals ￭ tails, extensions ￭ ORIGIN: ￭ background/ foreground objects

Source: P. Kalas ?

AU Microscopii and its less inclined cousin This is a coincidentally(!) aligned background galaxy

FEATURES in disks: blobs, clumps ￭ streaks, feathers ￭ rings (axisymm) ￭ rings (off-centered) ￭ inner/outer edges ￭ disk gaps ￭ warps ￭ spirals, quasi-spirals ￭ tails, extensions ￭ ORIGIN: ￭ stellar companions, flybys Stellar and planetary perturbations => interesting prospect of finding planets by their imprint on dust

Kalas and Larwood initially thought they detected ripples on one side of the Beta Pic disk. Later, evidence for the reality of most ripples disappeared.

Structure from stellar encounter Doesn’t work in case of beta Pic (despite claim by Kalas and Larwood ca. 2001): model was oversimplified no radiation pressure on dust, no size distribution pure N-body unlikely if single passage P~1e-6 binary => ok, but repeated encounters delete structure rings an artifact of a sharp edge in initial distribution of particles

No ring features in more accurate simulations (Jeneskog, B.Sc. Thesis 2003)

Augereau and Papaloizou (2003) Stellar flyby (of an elliptic-obit companion) explains some features of HD A Application to Beta Pictoris less certain...

Resonant pileup of dust due to planets

Some models of structure in dusty disks rely on too limited a physics: ideally one needs to follow: full spatial distribution, velocity distribution, and size distribution of a collisional system subject to various external forces like radiation and gas drag -- that’s very tough to do! Resultant planets depend on all this. Beta = 0.01 (monodispersed) Vega

Warp from inclined planet (model of beta Pictoris), Wyatt; Augereau & Paploizou.

The danger of overinterpretation of structure Are the PLANETS responsible for EVERYTHING we see? Are they in EVERY system? Or are they like the Ptolemy’s epicycles, added each time we need to explain a new observation?

FEATURES in disks: blobs, clumps ￭ streaks, feathers ￭ rings (axisymm) ￭ rings (off-centered) ￭ inner/outer edges ￭ disk gaps ￭ warps ￭ spirals, quasi-spirals ￭ tails, extensions ￭ ORIGIN: ￭ dust migration in gas

Type 0 (gas drag + radiation pressure) Gas drag: Keplerian circular orbital velocity of solids, slightly subkeplerian rotation of gas in disk (pressure gradients) headwind, orbital decay (inward) (Adachi 1976, Weidenschilling 1977,...) Gas drag + radiation pressure: strongly subkeplerian orbital speed of solids affected by stellar radiation pressure back-wind, fast outward migration (Takeuchi&Artymowicz 2001, Lin & Klahr 2002, Thebault, Lecavelier, …)

Migration: Type 0 n Dusty disks: structure from gas-dust coupling (Takeuchi & Artymowicz 2001) n theory will help determine gas distribution Gas disk tapers off here Predicted dust distribution: axisymmetric ring

Dust avalanches and implications: -- upper limit on dustiness -- the division of disks into gas-rich, transitional and gas-poor -- non-axisymmetry ! Other reasons: ISM sandblasting radiative instabilities

Radiative blow-out of grains (  -meteoroids, gamma meteoroids) Dust avalanches Radiation pressure on dust grains in disks Neutral (grey) scattering from s> grains Repels ISM dust Disks = Nature, not nurture! Enhanced erosion; shortened dust lifetime Orbits of stable  - meteoroids are elliptical Dust migrates, forms axisymmetric rings, gaps (in disks with gas) Short disk lifetime Size spectrum of dust has lower cutoff Weak/no PAH emission Quasi-spiral structure Instabilities (in disks) Age paradox Color effects Limit on f IR in gas-free disks DUST AVALANCHES

FEATURES in disks: blobs, clumps ￭ streaks, feathers ￭ rings (axisymm) ￭ rings (off-centered) ￭ inner/outer edges ￭ disk gaps ￭ warps ￭ spirals, quasi-spirals ￭ tails, extensions ￭ ORIGIN: ￭ dust blowout avalanches, ￭ episodic/local dust release

Dust Avalanche (Artymowicz 1997) = disk particle, alpha meteoroid ( < 0.5) = sub-blowout debris, beta meteoroid ( > 0.5) Process powered by the energy of stellar radiation N ~ exp ( optical thickness of the disk * ) N

The above example is relevant to HD141569A, a prototype transitional disk with interesting quasi-spiral structure. Conclusion: Transitional disks MUST CONTAIN GAS or face self-destruction. Beta Pic is among the most dusty, gas-poor disks, possible. the midplane optical thickness Ratio of the infrared luminosity (IR excess radiation from dust) to the stellar luminosity; it gives the percentage of stellar flux absorbed, then re-emitted thermally multiplication factor of debris in 1 collision (number of sub-blowout debris) Simplified avalanche equation Solution of the simplified avalanche growth equation

#) derivation:

Bimodal histogram of fractional IR luminosity f IR similar to that predicted by disk avalanche process

source: Inseok Song (2004) Bimodal histogram of fractional IR luminosity f IR similar to that predicted by disk avalanche process

ISO/ISOPHOT data on dustiness vs. time Dominik, Decin, Waters, Waelkens (2003) uncorrected ages corrected ages ISOPHOT ages, dot size ~ quality of age ISOPHOT + IRAS f d of beta Pic -1.8

transitional systems 5-10 Myr age

Grigorieva, Artymowicz and Thebault ( A&A, 2006 ) Comprehensive model of dusty debris disk (3D) with full treatment of collisions and particle dynamics. ￭ especially suitable to denser transitional disks supporting dust avalanches ￭ detailed treatment of grain-grain colisions, depending on material ￭ detailed treatment of radiation pressure and optics, depending on material ￭ localized dust injection (e.g., planetesimal collision) ￭ dust grains of similar properties and orbits grouped in “superparticles” ￭ physics: radiation pressure, gas drag, collisions Results: ￭ beta Pictoris avalanches multiply debris by up to 200! ￭ spiral OR blob-like shape of the avalanche ￭ km bodies must collide for observability in the innerb Pic disk, which isn’t very probable ￭ strong dependence on material properties and certain other model assumptions, but mostly on disk dustiness: 3 times larger than b Pic => planetesimal collisions likely!

f IR =f d disk dustiness OK! Age paradox! Gas-free modeling leads to a paradox ==> gas required or episodic dust production

Model of (simplified) collisional avalanche with substantial gas drag, corresponding to 10 Earth masses of gas in disk

Main results of modeling of collisional avalanches: 1. Strongly nonaxisymmetric, growing patterns 2. Substantial almost exponential multiplication 3. Morphology depends on the amount and distribution of gas, in particular on the presence of an outer initial disk edge

Beta = 4 H/r = 0.1 M gas = 50 M E Best model, Ardila et al (2005) HD A 5 M J, e=0.6, a=100 AU planet

Spontaneous axisymmetry breaking in optically thick disks results in structure resembling gravitational instability

In gas+dust disks which are optically thick in the radial direction there may be an interesting set of instabilities. Radiation pressure on a coupled gas+dust system that has a spiral density wave with wave numbers (k,m/r), is analogous in phase and sign to the force or self-gravity. The instability is linear, pseudo-gravitational, and can be obtained from a WKB local analysis. Forces of selfgravity Forces of radiation pressure in the inertial frame Forces of rad. pressure relative to those on the center of the arm

In gas+dust disks which are optically thick in the radial direction there may be an interesting set of instabilities. Radiation pressure on a coupled gas+dust system that has a spiral density wave with wave numbers (k,m/r), is analogous in phase and sign to the force or self-gravity.. effective coefficient for coupled gas+dust r (this profile results from dust migration)

Step function of r or constant (WKB) 2

Step function of r or constant (WKB) 2

r 1 Effective Q number (radiation+selfgravity) Analogies with gravitational instability ==> similar structures (?)

FEATURES in disks:(9 types) blobs, clumps ￭ (5) streaks, feathers ￭ (4) rings (axisymm) ￭ (2) rings (off-centered) ￭ (7) inner/outer edges ￭ (5) disk gaps ￭ (4) warps ￭ (7) spirals, quasi-spirals ￭ (8) tails, extensions ￭ (6) ORIGIN: (10 reasons) ￭ instrumental artifacts, variable PSF, noise, deconvolution etc. ￭ background/foreground obj. ￭ planets (gravity) ￭ stellar companions, flybys ￭ dust migration in gas ￭ dust blowout, avalanches ￭ episodic release of dust ￭ ISM (interstellar wind) ￭ stellar wind, magnetism ￭ collective eff. (self-gravity) Many (~50) possible connections !

Not only planets but also Gas + dust + radiation => non-axisymmetric features including regular m=1 spirals, conical sectors, and multi-armed wavelets, as well as blobs Conclusion: