Great Migrations

1
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
2
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
3
Radiation pressure coefficient (radiation
pressure/gravity force) of an Mg-rich pyroxene
mineral, as a function of grain radius s.
s
4
Above a certain beta value, a newly created dust
particle, released on a circular orbit of its
large parent body (beta0) will escape to
infinity along the parabolic orbit. What is
the value of beta guaranteeing escape? Its 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
s2 microns. Particles larger but not much
larger than this limit will stay in the disk on
rather eccentric orbit.
5
How radiation pressure induces large eccentricity

Frad / Fgrav
6
Weak/no PAH emission
Neutral (grey) scattering from sgt? grains
Repels ISM dust Disks Nature, not nurture!
Size spectrum of dust has lower cutoff
Radiative blow-out of grains (??-meteoroids,
gamma meteoroids)
Radiation pressure on dust grains in disks
Instabilities (in disks)
Dust avalanches
Quasi-spiral structure
Orbits of stable ?-meteoroids elliptical
Dust migrates, forms axisymmetric rings, gaps
(in disks with gas)
Color effects
Enhanced erosion shortened dust lifetime
Short disk lifetime
Age paradox
7
Structure formation in dusty disks
8
The danger of overinterpretation of
structure Are the PLANETS responsible for
EVERYTHING we see? Are they in EVERY system? Or
are they like the Ptolemys epicycles, added
each time we need to explain a new
observation?
9
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)
10
AB Aur disk or no disk?
Fukugawa et al. (2004)
another Pleiades-type star
no disk
11
?
Source P. Kalas
12
Hubble Space Telescope/ NICMOS infrared camera
13
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)
14
.

15
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 -- thats
very tough to do! Resultant planet depends on all
this.
Beta 0.01 (monodisp.)
16
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
17
HD 141569A is a Herbig emission star gt2 x solar
mass, gt10 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
18
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
19
HD141569BC in V band
HD141569A deprojected
HST/ACS Clampin et al.
20
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
21
Best model, Ardila et al (2005) involved a
stellar fly-by
Beta 4 H/r 0.1 Mgas 50 ME
5 MJ, e0.6, a100 AU planet
HD 141569A
22
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
23
Planetary systems stages of decreasing
dustiness
In the protoplanetary disks (tau???) dust
follows gas. Sharp features due to
associated companions stars, brown dwarfs and
planets.
1 Myr
These optically thin transitional disks (tau lt1)
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.
5 Myr
??Pictoris
These replenished dust disk are optically thin
(taultlt1) and have very little gas.
12-20 Myr
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
24


vvK
vg
Gas pressure force


vg
v
Gas pressure force
25
Migration Type 0

• Dusty disks structure from gas-dust coupling
  (Takeuchi Artymowicz 2001)
• theory will help determine gas distribution

Predicted dust distribution axisymmetric ring
Gas disk tapers off here
26
Weak/no PAH emission
Neutral (grey) scattering from sgt? grains
Repels ISM dust Disks Nature, not nurture!
Size spectrum of dust has lower cutoff
Radiative blow-out of grains (??-meteoroids,
gamma meteoroids)
Radiation pressure on dust grains in disks
Instabilities (in disks)
Dust avalanches
Quasi-spiral structure
Orbits of stable ?-meteoroids elliptical
Dust migrates, forms axisymmetric rings, gaps
(in disks with gas)
Color effects
Enhanced erosion shortened dust lifetime
Short disk lifetime
Age paradox
27
Dust avalanches and implications -- upper
limit on dustiness -- the division of disks into
gas-rich, transitional and gas-poor
28
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
29
Weak/no PAH emission
Neutral (grey) scattering from sgt? grains
Repels ISM dust Disks Nature, not nurture!
Size spectrum of dust has lower cutoff
Radiative blow-out of grains (??-meteoroids,
gamma meteoroids)
Radiation pressure on dust grains in disks
Instabilities (in disks)
Dust avalanches
Quasi-spiral structure
Orbits of stable ?-meteoroids elliptical
Dust migrates, forms axisymmetric rings, gaps
(in disks with gas)
Limit on fir in gas-free disks
Color effects
Enhanced erosion shortened dust lifetime
Short disk lifetime
Age paradox
30
Dust Avalanche (Artymowicz 1997)
Process powered by the energy of stellar
radiation N exp (optical thickness of the disk
ltdebris/collisiongt)
N
disk particle, alpha meteoroid ( lt 0.5)
sub-blowout debris, beta meteoroid ( gt 0.5)
31
Ratio of the infrared luminosity (IR excess
radiation from dust) to the stellar
luminosity it gives the
percentage of stellar flux
absorbed reemitted thermally
the midplane optical thickness
multiplication factor of debris in 1 collision
(number of
sub-blowout debris)
Avalanche growth equation
Solution of the avalanche growth equation
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.
32
OK!
Gas-free modeling leads to a paradox gt gas
required or episodic dust production
Age paradox!
fIR fd disk dustiness
33
Bimodal histogram of fractional IR luminosity
fIR predicted by disk avalanche process
34
source Inseok Song (2004)
35
ISO/ISOPHOT data on dustiness vs. time
Dominik, Decin, Waters, Waelkens (2003)
uncorrected ages
corrected ages
-1.8
ISOPHOT ages, dot size quality of age
ISOPHOT IRAS
fd of beta Pic
36
transitional systems 5-10 Myr age
37
Weak/no PAH emission
Neutral (grey) scattering from sgt? grains
Repels ISM dust Disks Nature, not nurture!
Size spectrum of dust has lower cutoff
Radiative blow-out of grains (??-meteoroids,
gamma meteoroids)
Radiation pressure on dust grains in disks
Instabilities (in disks)
Dust avalanches
Orbits of stable ?-meteoroids are elliptical
Quasi-spiral structure
Dust migrates, forms axisymmetric rings, gaps
(in disks with gas)
Limit on fIR in gas-free disks
Color effects
Enhanced erosion shortened dust lifetime
Short disk lifetime
Age paradox
38
Grigorieva, Artymowicz and Thebault (AA
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
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Model of (simplified) collisional avalanche with
substantial gas drag, corresponding to 10 Earth
masses of gas in disk
41
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
42
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 !
43
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.)
44
Pulsar planets PSR 125712 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 125712 A PSR 125712 B PSR
125712 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) 25.2620.003,
66.5419 0.0001, 98.21140.0002 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!
45
Radial-velocity planets

• around normal stars

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-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.
48
Orbital radii masses of the extrasolar planets
(picture from 2003)
Radial migration
Hot jupiters
These planets were found via Doppler
spectroscopy of the hosts starlight. Precision
of measurement 3 m/s
49
Masset and Papaloizou (2000) Peale, Lee (2002)
Some pairs of exoplanets may be caught in a 21
or other mean-motion resonance
50
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Like us? NOT REALLY
52
Marcy and Butler (2003)
53
2005
2003
54
From Terquem Papaloizou (2005)
Mass histogram semi-major

axis distr.
Pileup of hot jupiters
55
M sin i vs. a
56
Eccentricity of exoplanets vs. a and m sini
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Metallicity of the star
59

• Upsilon Andromedae

60
The case of Upsilon And examined Stable or
unstable? Resonant? How, why?...
61
Upsilon Andromedaes two outer giant planets
have STRONG interactions
Inner solar system (same scale)
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Definition of logitude of pericenter (periapsis)
a.k.a. misalignment angle
.
64
Classical celestial mechanics
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.
65
0.8 Gyr integration of 2 planetary orbits with
7th-8th order Runge-Kutta method
Initial conditions not those observed!
eccentricity
Orbit alignment angle
66
Upsilon And The case of a very good alignment of
periapses orbital elements practically
unchanged for 2.18 Gyr
unchanged
unchanged
67
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
68
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
X
X
X
X
X
X
X
69
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, 2pi/k_r, becomes formally infinite
at LR.
70
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. (gt 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 es we need N-body
explanations perturbations by stars, or other
planets.
71
Mass flows despite the gap. This result explains
the possibility of superplanets with mass
10 MJ Inward migration explains hot jupiters.
Mass flows through the gap opened by a
jupiter-class exoplanet
gt Superplanets can form
72
1. Early dispersal of the primordial nebula gt
no material, no mobility 2. Late formation
(including Last Mohican scenario)