Lecture L23 ASTB23 1. Radiation pressure in action 2. Structures in dusty disks vs. possible reasons including planets 3. Dust avalanches, gas, and the

Lecture L23 ASTB23

1. Radiation pressure in action2. Structures in dusty disks vs. possible reasons including planets3. Dust avalanches, gas, and the classification of disks4. Non-axisymmetric features without planets (dust avalanches) * * * 5. Pulsar planets6. Radial velocity surveys: the ~170 planetary systems known7. 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 radiationpressure

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

50.

sm / 2

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 thiscritical 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:

= Frad / Fgrav

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)1

Age paradox

Coloreffects

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 onthe 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:


ORIGIN:

￭ planets (gravity)

.

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 fittingplanets 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 141569A 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 ~100AUoroutward 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

HD141569+BC in V band HD141569A deprojected

HST/ACS Clampin et al.

FEATURES in disks:


ORIGIN:

￭ stellar companions, flybys

Beta = 4H/r = 0.1Mgas = 50 ME

Best model, Ardila et al (2005)involved a stellar fly-by &

HD 141569A

5 MJ, e=0.6, a=100 AUplanet

FEATURES in disks:


ORIGIN:

￭ dust migration in gas

In the protoplanetary disks (tau) dust follows gas.Sharp features due to associatedcompanions: 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, gapswith or without planets.

These replenished dust diskare 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

12-20 Myr

Gas pressure force

Gas pressure force

vgv=vK

v vg

Migration:

Type 0Dusty disks: structure

from gas-dust coupling (Takeuchi & Artymowicz 2001)

theory will help determine gas distribution

Gas disk tapersoff here

Predicted dust distribution: axisymmetric ring


Dust avalanches







(in disks with gas)

Short disk lifetime





Age paradox

Coloreffects

Dust avalanches and implications:

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

FEATURES in disks:


ORIGIN:

￭ dust blowout avalanches,￭ episodic/local dust release


Dust avalanches







(in disks with gas)

Short disk lifetime





Age paradox

Coloreffects

Limit on firin 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 * <#debris/collision>)

N

The above example is relevant to HD141569A, a prototype transitional disk (with interesting quasi-spiral structure.) Conclusion:

60

2

1

2

10~)20exp(~)exp(/

10~

2.0018.0)1.0(

)/(

)2/()/()/(

)2/()4/(2

NNN

NNdN

N

fzr

so

rdrzrdrs

rdrrrdrf

IR

IR

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

fIR =fd disk dustiness

OK!

Age paradox!

Gas-free modelingleads to a paradox==> gas required or episodic dust production

Bimodal histogram of fractionalIR luminosity fIR

predicted by diskavalanche 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

fd of beta Pic

-1.8

transitional systems 5-10 Myr age


Dust avalanches





Orbits of stable -meteoroids are elliptical


(in disks with gas)

Short disk lifetime





Age paradox

Coloreffects

Limit on fIRin 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 substantialgas 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. 1755-1776? 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 (341-270 B.C.)

Pulsar planets: PSR 1257+12 B2 Earth-mass planets and one Moon-sizes onefound around a millisecond pulsar

First extrasolar planets discovered by Alex Wolszczan [pronounced volsh-chan] in 1991, announced 1992

Name: PSR 1257+12 A PSR 1257+12 B PSR 1257+12 C M.sin 0.020 ± 0.002 ME 4.3 ± 0.2 ME 3.9 ± 0.2 ME

Semi-major axis: 0.19 AU 0.36 AU 0.46 AU

P(days): 25.262±0.003, 66.5419± 0.0001, 98.2114±0.0002

Eccentricity: 0.0 0.0186 ± 0.0002 0.0252 ± 0.0002

Omega (deg): 0.0 250.4 ± 6 108.3 ± 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 foundvia Doppler spectroscopyof the host’s starlight.

Precision of measurement:~3 m/s

Hot jupitersRadial 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)

~2003

2005

From Terquem & Papaloizou (2005)

Mass histogram semi-major axis distr.

Pileupofhotjupiters

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

Innersolarsystem(samescale)

.

1

2Definition 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 asto 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

ecce

ntr

icit

y

Orbit alignment angle

0.8 Gyr integration of 2 planetary orbitswith 7th-8th order Runge-Kutta method

Initial conditionsnot those observed!

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

unchanged

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 expectedand observed to be strong, and stabilizes the systemof two nearby, massive planets3. There are no mean motion resonances4. The present state lasted since formation period5. Eccentricities in inverse relation to masses, contrary to normal N-body trend tendency for equipartition.Alternative: a lost most massive planet - very unlikely6. Origin still studied, Lin et al. Developed first modelsinvolving time-dependent axisymmetric disk potential

Diversity of exoplanetary systems likely a result of: cores?

disk-planet interaction a m e (only medium) yes

planet-planet interaction a m? e yes

star-planet interaction a m e? yes

disk breakup (fragmentation into GGP) a m e? Metallicity no

X

XX X

X X

X

X

Wave excitation at Lindblad resonances (roughly speaking,places in disk in mean motion resonance, or commensurabilityof 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 isthus 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 numberk_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 andthe 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 thenear-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 gapopened by a jupiter-class exoplanet

==> Superplanets can form

Mass flows despitethe gap. This resultexplains the possibility of “superplanets” with mass ~10 MJ

Inward migrationexplains hot jupiters.

1. Early dispersal of the primordial nebula ==> no material, no mobility2. Late formation (including Last Mohican scenario)

Documents

Lecture L23 ASTB23 1. Radiation pressure in action 2. Structures in dusty disks vs. possible reasons including planets 3. Dust avalanches, gas, and the