Lecture L23 ASTB23 1. Radiation pressure in action 2. Structures in dusty disks vs. possible reasons including planets 3. Dust avalanches, gas, and the classification of disks 4. Non-axisymmetric features without planets (dust avalanches) * * * 5. Pulsar planets 6. Radial velocity surveys: the ~170 planetary systems known 7. Clues about the origin of the exoplanets 8. Implications for the solar system origin

Summary of the various effects of radiation pressure of starlight on dust grains in disks: alpha particles = stable, orbiting particles on circular & elliptic orbits beta meteoroids = particles on hyperbolic orbits, escaping due to a large radiation pressure

Radiation pressure coefficient (radiation pressure/gravity force) of an Mg-rich pyroxene mineral, as a function of grain radius s. s

Above a certain beta value, a newly created dust particle, released on a circular orbit of its large parent body (beta=0) will escape to infinity along the parabolic orbit. What is the value of beta guaranteeing escape? It’s 0.5 (see problem 1 from set #5). We call the physical radius of the particle that has this critical beta parameter a blow-out radius of grains. From the previous slide we see that in the beta Pictoris disk, the blow-out radius is equal ~2 micrometers. Observations of scattered light, independent of this reasoning show that, indeed, the smallest size of observed grains is s~2 microns. Particles larger but not much larger than this limit will stay in the disk on rather eccentric orbit.

How radiation pressure induces large eccentricity: = F rad / F grav

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 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

Structure formation in dusty disks

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 types) blobs, clumps ￭ streaks, feathers ￭ rings (axisymm) ￭ rings (off-centered) ￭ inner/outer edges ￭ disk gaps ￭ warps ￭ spirals, quasi-spirals ￭ tails, extensions ￭ ORIGIN: (10 categories) ￭ 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 effects (radiation in opaque media, selfgravity) (Most features additionally depend on the viewing angle)

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

Source: P. Kalas ?

Hubble Space Telescope/ NICMOS infrared camera

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

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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 planet depends on all this. Beta = 0.01 (monodisp.)

Dangers of fitting planets to individual frames/observations: Vega has 0, 1, or 2 blobs, depending on bandpass. What about its planets? Are they wavelength- dependent too!? 850 microns

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

Outward migration of protoplanets to ~100AU or outward migration of dust to form rings and spirals may be required to explain the structure in transitional (5-10 Myr old) and older dust disks

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

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

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

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

In the protoplanetary disks (tau  ) dust follows gas. Sharp features due to associated companions: stars, brown dwarfs and planets. These optically thin transitional disks (tau <1) must have some gas even if it's hard to detect. Warning: Dust starts to move w.r.t. gas! Look for outer rings, inner rings, gaps with or without planets. These replenished dust disk are optically thin (tau<<1) and have very little gas. Sub-planetary & planetary bodies can be detected via spectroscopy, spatial distribution of dust, but do not normally expect sharp features. Extensive modeling including dust-dust collisions and radiation pressure needed Planetary systems: stages of decreasing dustiness  Pictoris 1 Myr 5 Myr Myr

Gas pressure force vgvg v=v K v vgvg

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

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 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

Dust avalanches and implications: -- upper limit on dustiness -- the division of disks into gas-rich, transitional and gas-poor

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

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 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 fir in gas-free disks

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 almost the most dusty, gas-poor disk, 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 reemitted thermally multiplication factor of debris in 1 collision (number of sub-blowout debris) Avalanche growth equation Solution of the avalanche growth equation

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

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

source: Inseok Song (2004)

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

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

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 x (3-5) ￭ spiral shape of the avalanche - a robust outcome ￭ strong dependence on material properties and certain other model assumptions

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 exponential multiplication 3. Morphology depends on the amount and distribution of gas, in particular on the presence of an outer initial disk edge

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 !

From: Diogenes Laertius,  (3rd cn. A.D.), IX.31 “The worlds come into being as follows: many bodies of all sorts and shapes move from the infinite into a great void; they come together there and produce a single whirl, in which, colliding with one another and revolving in all manner of ways, they begin to separate like to like.”Leucippus (Solar nebula of Kant & Laplace A.D ? Accretion disk?) “There are innumerable worlds which differ in size. In some worlds there is no Sun and Moon, in others they are larger than in our world, and in others more numerous. (...) in some parts they are arising, in others failing. They are destroyed by collision with one another. There are some worlds devoid of living creatures or plants or any moisture.” Democritus (Planets predicted: around pulsars, binary stars, close to stars ? ) There are infinite worlds both like and unlike this world of ours. For the atoms being infinite in number (...) there nowhere exists an obstacle to the infinite number od worlds. Epicurus ( B.C.)

Pulsar planets: PSR B 2 Earth-mass planets and one Moon-sizes one found around a millisecond pulsar First extrasolar planets discovered by Alex Wolszczan [pronounced volsh-chan] in 1991, announced 1992 Name: PSR A PSR B PSR C M.sin ± M E 4.3 ± 0.2 M E 3.9 ± 0.2 M E Semi-major axis: 0.19 AU 0.36 AU 0.46 AU P(days): ±0.003, ± , ± Eccentricity: ± ± Omega (deg): ± ± 5 The pulsar timing is so exact, observers now suspect having detected a comet!

Radial-velocity planets around normal stars

-450: Extrasolar systems predicted (Leukippos, Demokritos). Formation in disks -325 Disproved by Aristoteles 1983: First dusty disks in exoplanetary systems discovered by IRAS 1992: First exoplanets found around a millisecond pulsar (Wolszczan & Dale) 1995: Radial Velocity Planets were found around normal, nearby stars, via the Doppler spectroscopy of the host starlight, starting with Mayor & Queloz, continuing wth Marcy & Butler, et al.

Orbital radii + masses of the extrasolar planets (picture from 2003) These planets were found via Doppler spectroscopy of the host’s starlight. Precision of measurement: ~3 m/s Hot jupiters Radial migration

Masset and Papaloizou (2000); Peale, Lee (2002) Some pairs of exoplanets may be caught in a 2:1 or other mean-motion resonance

Like us? NOT REALLY

Marcy and Butler (2003)

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From Terquem & Papaloizou (2005) Mass histogram semi-major axis distr. Pileup of hot jupiters

M sin i vs. a

Eccentricity of exoplanets vs. a and m sini

Metallicity of the star

Upsilon Andromedae

The case of Upsilon And examined: Stable or unstable? Resonant? How, why?...

Upsilon Andromedae’s two outer giant planets have STRONG interactions Inner solar system (same scale)

. Definition of logitude of pericenter (periapsis) a.k.a. misalignment angle

In the secular pertubation theory, semi-major axes (energies) are constant (as a result of averaging over time). Eccentricities and orbit misalignment vary, such as to conserve the angular momentum and energy of the system. We will show sets of thin theoretical curves for (e2, dw). [There are corresponding (e3, dw) curves, as well.] Thick lines are numerically computed full N-body trajectories. Classical celestial mechanics

eccentricity Orbit alignment angle 0.8 Gyr integration of 2 planetary orbits with 7th-8th order Runge-Kutta method Initial conditions not those observed!

Upsilon And: The case of a very good alignment of periapses: orbital elements practically unchanged for 2.18 Gyr unchanged

N-body (planet-planet) or disk-planet interaction? Conclusions from modeling Ups And 1. Secular perturbation theory and numerical calculations spanning 2 Gyr in agreement. 2. The apsidal “resonance” (co-evolution) is expected and observed to be strong, and stabilizes the system of two nearby, massive planets 3. There are no mean motion resonances 4. The present state lasted since formation period 5. Eccentricities in inverse relation to masses, contrary to normal N-body trend tendency for equipartition. Alternative: a lost most massive planet - very unlikely 6. Origin still studied, Lin et al. Developed first models involving time-dependent axisymmetric disk potential

Diversity of exoplanetary systems likely a result of: cores? disk-planet interactiona m e (only medium) yes planet-planet interactiona m? e yes star-planet interactiona m e? yes disk breakup (fragmentation into GGP) a m e? Metallicity no X X X X XX X X

Wave excitation at Lindblad resonances (roughly speaking, places in disk in mean motion resonance, or commensurability of periods, with the perturbing planet) is the basis of the calculation of torques (and energy transfer) between the perturber and the disk. Finding precise locations of LRs is thus a prerequisite for computing the orbital evolution of a satellite or planet interacting with a disk. LR locations can be found by setting radial wave number k_r = 0 in dispersion relation of small-amplitude, m-armed, waves in a disk. [Wave vector has radial component k_r and azimuthal component k_theta = m/r] This location corresponds to a boundary between the wavy and the evanescent regions of a disk. Radial wavelength, 2*pi/k_r, becomes formally infinite at LR.

Disks and the eccentricity of planets: As long as there is some gas in the corotational region (say, +- 20% of orbital radius of a jupiter), eccentricity is strongly damped by the disk. Only if and when the gap becomes so wide that the near-lying LRs are eliminated, eccentricity is excited. (==> planets larger than 10 m_jup were predicted in 1992 to be on eccentric orbits ). In practice, disks may account for intermediate-e exoplanets. For extremely high e’s we need N-body explanations: perturbations by stars, or other planets.

Mass flows through the gap opened by a jupiter-class exoplanet ==> Superplanets can form Mass flows despite the gap. This result explains the possibility of “superplanets” with mass ~10 M J Inward migration explains hot jupiters.

1. Early dispersal of the primordial nebula ==> no material, no mobility 2. Late formation (including Last Mohican scenario)