Understanding the
extrasolar planetary systems:
observations & theories
of disks and planets
Pawel Artymowicz
U of Toronto
1. Beta Pictoris and other dusty disks in planetary systems
2. Planet formation: are there really still two scenarios?
3. Discovery of the first 160+ planetary systems
4. Migration type I-III
5. Origin of structure in the dust and gas disks
How to find this talk online: either google up “pawel”, or get directly
planets.utsc.utoronto.ca/~pawel/UofA.ppt
Stellar
Astrophysics
Gen.Rel.
Astrophysics
of planetary atmosph.
Dynamics incl. systems
materials
Hydrodynamics
and statics
radioisotopes
Radiation transfer
High energ
physics.
Nuclear
physics
Thermodynamics of gas
Geochem
meteoritics
IDPs
& zodiacal disk
Astronomy:observations
of circumstellar disks
Astrophysics
atmosph
Stellar
of planetary
Dynamics,
Astrophysics
systems
materials
hydrodynamics
and hydrostatics
Gen.Rel.
radioisotopes
Radiation transfer
IDPs,
High ener.
Geozodiacal light disks
physics.
chem
Thermodynamics of gas
meteoritics
Nuclear
physics
Astronomy:observations
of circumstellar disks, radial
velocity exoplanets
First milestone in search for planetary
systems was detection of dust around normal
stars :
Vega phenomenon
Chemistry/mineralogy/crystallinity of dust
Astrochemical unity of nature
Infrared excess stars (Vega phenomenon)
Beta Pictoris
thermal radiation imaging (10 um)
Lagage & Pantin (1993)
1984
1993
Beta Pictoris, visible scattered starlight
comparison with IR data yields a high albedo, A~0.4-0.5
(like Saturn’s rings but very much unlike the black particles of
cometary crust or Uranus’ rings).
Small dust is observed due to its large total area
Parent bodies like these (asteroids, comets) are the ultimate sources of
the dust, but remain invisible in images due to their small combined
area
Comet
Optical thickness:
  (r ) 
 eq ( r ) 
perpendicular to the disk
in the equatorial plane
(percentage of starlight scattered and absorbed, as
seen by the outside observer looking at the disk
edge-on, aproximately like we look through the
beta Pictoris disk)
What is the optical thickness
  (r ) ?
It is the fraction of the disk surface covered by dust:
here I this example it’s about 2e-1 (20%) - the disk is optically
thin ( = transparent, since it blocks only 20% of light)
picture of a small portion of
the disk seen from above
Examples: beta Pic disk at r=100 AU opt.thickness~3e-3
disk around Vega
opt.thickness~1e-4
zodiacal light disk (IDPs) solar system ~1e-7
STIS/Hubble imaging
(Heap et al 2000)
Modeling
(Artymowicz,unpubl.):
parametric, axisymmetric disk
cometary dust phase function
Vertical optical
thickness 
Radius r [AU]
Vertical
profile of
dust density
Height z [AU]
Dust processing: collisions
1. Collisional time formula
2. The analogy with the early solar system
(in the region of today’s TNOs =
trans-Neptunian objects, or in other words,
Kuiper belt objects, KBOs; these are asteroid-sized
bodies up to several hundred km radius)
t coll  Time between collisions (collisional lifetime) of a typical
meteoroid. Obviously, inversly proportional to
the optical thickness (doubling the optical depth results in
2-times shorter particle lifetime, because the rate of collision
doubles).
t coll  P /(8  )
P = orbital period, depends on radius as in Kepler’s III law.
This formula is written with a numerical coefficion of 1/8 so as to
reproduce the fact that a disk made of equal-sized particles needs to
have the optical thickness of about 1/4 to make every particle
traversing it vertically collide with some disk particle, on average.
The vertical piercing of the disk is done every one-half period, because
particles are on inclined orbits and do indeed cross the disk nearly
vertically, if on circular orbits. If the orbits are elliptic, a better
approximate formula has a coefficient of 12 replacing 8 in the above
equation.
How does the Vega-phenomenon relate to our Solar System
(Kuiper belt, or TNOs - transneptunian objects)
Evidence of planetesimals and planets
in the vicinity of beta Pictoris:
1. Lack of dust near the star (r<30AU)
2. Spectroscopy => Falling Evaporating Bodies
3. Something large (a planet) needed to perturb FEBs so
they approach the star gradually.
4. The disk is warped somewhat, like a rim of cowboy hat, which
requires the gravitational pull of a planet on an orbit inclined
by a few degrees to the plane of the disk.
5. Large reservoir of parent (unseen) bodies of dust needed,
of order 100 Earth masses of rock/ice. Otherwise the dust
would disappear quickly, on the collisional time scale
This is how disks look a decade later - much better quality data, fewer
artifacts, disks appear smoother.
HST/WFPC2 camera
a fantastic large-scale
view of beta Pictoris
out to r ~800 AU
B Pic b(?) sky?
Beta Pictoris
Evidence of large bodies (planetesimals, comets?)
11 micron image analysis
converting observed flux
to dust area
(Lagage & Pantin 1994)
FEB = Falling Evaporating Bodies hypothesis in Beta Pictoris
FEB
star
H & K calcium absorption lines
are located in the center of
a stellar rotation-broadened line
absorption line(s) that
move on the time scale
of days as the FEBs
cross the line of sight
Microstructure of circumstellar
disks: identical with IDPs
(interplanetary dust particles)
mostly Fe+Mg silicates
(Mg,Fe)SiO3
(Mg,Fe)2SiO4
A rock
is a rock
is a rock…
which one is
from the Earth?
Mars?
Beta Pic?
It’s hard to tell from remote spectroscopy or even
by looking under a microscope!
EQUILIBRIUM COOLING SEQUENCE
Chemical unity
of nature… and it’s
thanks to
stellar nucleosynthesis!
T(K)
What minerals will
precipitate from a
solar-composition,
cooling gas? Mainly
Mg/Fe-rich silicates and
water ice. Planets are
made of precisely these
things.
Silicates
silicates
ices
Crystallinity of minerals
Recently, for the first time observations showed the difference
in the degree of crystallinity of minerals in the inner vs. the outer disk
parts. This was done by comparing IR spectra obtained with single dish
telescopes with those obtained while combining several such telescopes
into an interferometric array (this technique, long practiced by radio
astronomers, allows us to achieve very good, low-angular resolution,
observations).
In the following 2 slides, you will see some “inner” and
“outer” disk spectra - notice the differences, telling us about the different
structure of materials:
amorphous silicates = typical dust grains precipitating from gas,
for instance in the interstellar medium, no regular crystal structure
crystalline grains= same chemical composition, but forming a regular
crystal structure, thought to be derived from amorphous grains by
some heating (annealing) effect at temperatures up to ~1000 K.
~90% amorphous
compare
~60% amorphous
~45% amorphous
Beta Pic,
~95% crystalline
That was good, but people wanted PLANETS
Direct imaging
Transits
Indirect but
almost direct:
periodic, Keplerian
red+blueshifts
in stellar spectra,
or timing of pulsars
Structures
in dusty disks
(footprints
in the sand)
Pulsar planets: PSR 1257+12 B
2 Earth-mass planets and one Moon-sizes one
found around a millisecond pulsar
First extrasolar planets discovered by Alex Wolszczan
[pron.: Volshchan] in 1991, announced 1992, confirmed 1994
Name:
M.sin
PSR 1257+12 A PSR 1257+12 B
0.020 ± 0.002 ME 4.3 ± 0.2 ME
Semi-major axis:
P(days):
0.19 AU
0.36 AU
25.262±0.003, 66.5419± 0.0001,
PSR 1257+12 C
3.9 ± 0.2 ME
0.46 AU
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!
Pulsar planets: PSR 1257+12 B
2 Earth-mass planets and one Moon-sizes one
found around a millisecond pulsar
First extrasolar planets discovered by Alex Wolszczan
[pron.: Volshchan] in 1991, announced 1992, confirmed 1994
+comets ??
A
m: 0.020 ME
B
C
4.3 ME
3.9
ME
a: 0.19 AU 0.36 AU 0.46AU
e:
0
O: 0.0
0.0186
250.4
0.0252
108.3
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)
Radial migration
Hot jupiters
These planets were found
via Doppler spectroscopy
of the host’s starlight.
Precision of measurement:
~3 m/s
Like us?
NOT REALLY
Marcy and Butler (2003)
2005
~2003
m sin i vs.
a
Zones of
avoidance?
multiple
single
m sin i vs.
a
Zones of
avoidance?
Result: a----m
Eccentricity of exoplanets vs. a and m sini
a
e ?
a
m
m, a, e somewhat correlated:
e ?
m
a
e ?
m
Eccentricity of exoplanets vs. a and m sini
a
e ?
a
m
m, a, e somewhat correlated:
e ?
m
a
e ?
m
Gravitational Instability
and the Giant Gaseous
Protoplanet hypothesis
Gravitational stability requirements
c
Q 
Safronov  Toomre number
G
Q 1
Q 1
Local stability of disk, spiral waves may grow
Local linear instability of waves, clumps form,
but their further evolution depends on equation of
state of the gas.
From: Laughlin & Bodenheimer (2001)
Disk in this SPH simulation
initially had Q ~ 1.5 > 1
The m-armed global
spiral modes of the form
exp[i (m   k dr  t )]
grow and compete with
each other.
But the waves in a stable
Q~2 disk stop growing
and do not form small
objects (GGPs).
Recently, Alan Boss revived the half-abandoned idea of
disk fragmentation
Clumps forming in
a gravitationally
unstable disk
(Q < 1)
GGPs?
Two examples of formally unstable disks not willing to form
objects immediately
Durisen et al. (2003)
Break-up of the disk depends on the equation of state of the gas,
and the treatment of boundary conditions.
Armitage and Rice (2003)
Simulations of self-gravitating objects
forming in the disk (with grid-based
hydrodynamics)
shows that rapid thermal cooling is crucial
Disk not allowed
to cool rapidly (cooling timescale > 1 P)
Disk allowed
to cool rapidly
(on dynamical
timescale,
<0.5 P)
Mayer, Quinn, Wadsley, Stadel (2003)
SPH =
Smoothed
Particle
Hydrodynamics
with 1 million
particles
Isothermal
(infinitely
rapid cooling)
GGP (Giant Gaseous Protoplanet) hypothesis
= disk fragmentation scenario (A. Cameron in the 1970s)
Main Advantages: forms giant planets quickly, avoids possible timescale paradox; planets
tend to form at large distances amenable to imaging.
MAIN DIFFICULTIES:
1. Non-axisymmetric and/or non-local spiral modes start developing not only
at Q<1 but already when Q decreases to Q~1.5…2
They redistribute mass and heat the disk => increase Q (stabilize disk).
2. Empirically, this self-regulation of the effects of gravity on disk is seen
in disk galaxies, all of which have Q~2 and yet don’t split into many baby gallaxies.
3. The only way to force the disk fragmentation is to lower Q~c/Sigma
by a factor of 2 in just one orbital period. This seems impossible.
4. Any clumps in disk (e.g. A. Boss’ clumps) may in fact shear and disappear
rather than form bound objects. Durisen et al. Have found that the equation of
state and the correct treatment of boundary conditions are crucial, but could
not confirm the fragmentation except in the isothermal E.O.S. case.
5. GGP is difficult to apply to Uranus and Neptune; final masses: Brown Dwarfs not GGPs
6. Does not easily explain core masses of planets and exoplanets, nor the chemical
correlations (to be discussed in lecture L23)
Video of density waves in a massive protoplanetary disk
The shocks at the surface are suggested as a way to heat solids
and form chondrules, small round grains inside meteorites.
Durisen and Boss (2005)
Envelope instability in protogiants
(nucleated gas accretion)
Comparison of gas and rock masses (in ME)
in giant planets and exoplanets (1980s)
envelope
(atmosphere)
Planet Core mass Atmosph. Total mass Radius
_________(rocks, ME )___(gas,_ME )____(ME )_______(RJ) _
Jupiter
0-10
~313
318
1.00
Saturn
15-20
~77
95
0.84
Uranus
11-13
2-4
14.6
0.36
Neptune
13-15
2-4
17.2
0.34
core
Comparison of gas and rock masses (in ME)
in giant planets and exoplanets (Oct. 2005)
envelope
(atmosphere)
core
Planet Core mass Atmosph. Total mass Radius
_________(rocks, ME )___(gas,_ME )____(ME )_______(RJ) _
Jupiter
0-10
~313
318
1.00
Saturn
15-20
~77
95
0.84
Uranus
11-13
2-4
14.6
0.36
Neptune
13-15
2-4
17.2
0.34
~0
~220
204-235
1.32 ± 0.05
~45
105-124
0.73 ± 0.03
HD 189733b ~10-20(?) ~350
351-380
1.26 ± 0.03
HD 209458b
?
(disc. 1999)
HD 149026b
~70
(disc. 7/2005)
(disc. 10/2005)
?
Standard Accumulation
Scenario
Two-stage accumulation of planets in disks
Planetesimal = solid
body >1 km
Mcore=10 ME(?) =>
contraction of the
atmosphere and inflow
of gas from the disk
(issues not addressed
in the standard theory
so far)
How many planetesimals formed in the solar nebula?
Core-atmosphere instability above a critical core mass
Mizuno (1980), Bodenheimer (1980s), Stevenson (1986)
Planetesimals supply heat of accretion L = GM/Rc (dM/dt)
Convection and radiation carry that luminosity away as
dictated by equations of stellar stucture.
Low-mass cores have tenuous hydrogen-helium dominated
envelopes that smoothly join the surrounding disk.
Opacity of the atmosphere and L have a major influence on
the envelope mass. When Mcore = Matm, the hydrostatic
equations of stellar structure no longer have solutions.
The critical core mass (above which no equilibrium
is possible) depends on opacity K and luminosity L as
Mcrit ~ (K L)^(- 3/4)
Mcrit ~ 8-20 ME in our solar system, perhaps different in others
Upsilon Andromedae
And the question of planet-planet vs. disk planet interaction
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
.
2

1
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.
0.8 Gyr integration of 2 planetary orbits
with 7th-8th order Runge-Kutta method
Initial conditions
not those
observed!
Orbit alignment angle
Upsilon And: The case of 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 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 interaction
a
m
e
X
(only medium)
planet-planet interaction
Xa
star-planet interaction
a
m
X
X
disk breakup
(fragmentation into GGP) a
m?
m
X X
yes
e
yes
e?
yes
e?
Metallicity no
X
X
This part of the lecture is more advanced and
optional (not required for the exam, for instance)
If you are skipping it, please go directly to the
last slide.
:
Disk-planet interaction
resonances and waves
in disks, orbital evolution
.
.
SPH (Smoothed Particle Hydrodynamics)
Jupiter in a solar nebula (z/r=0.02) launches waves at LRs.
The two views are (left) Cartesian, and (right) polar coordinates.
Inner and Outer Lindblad resonances in an SPH disk with a jupiter
Illustration of nominal positions of Lindblad resonances (obtained
by WKB approximation. The nominal positions coincide with the mean motion
resonances of the type m:(m+-1) in celestial mechanics, which doesn’t include
pressure.) Nominal radii converge toward the planet’s semi-major axis at high
azimuthal numbers m, causing problems with torque calculation (infinities!).
On the other hand, the pressure-shifted positions are the effective LR
positions, shown by the green arrows. They yield finite total LR torque.
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.
Eccentricity in type-I
situation is always
strongly damped.
--> m(z/r)
Conclusion about eccentricity:
As long as there is some gas in the corotational region
(say, +- 20% of orbital radius of a jupiter),
eccentricity is strongly damped.
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 to
be on eccentric orbits (Artymowicz 1992).
In practice, this may account for intermediate-e exoplanets.
For extremely high e’s we need N-body explanation:
perturbations by stars, or other planets.
Disk-planet interaction:
numerics
Mass flows through the gap
opened by a jupiter-class exoplanet
Mass flows despite
the gap. This result
explains the
possibility of
“superplanets”
with mass ~10 MJ
Migration explains
hot jupiters.
==> Superplanets can form
An example of modern Godunov (Riemann solver) code:
PPM VH1-PA. Mass flows through a wide and deep gap!
Surface density
Log(surface density)
Binary star on circular orbit
accreting from a circumbinary disk through a gap.
AMR PPM (Flash) simulation of a Jupiter in a standard solar nebula. 5 levels/subgrids.
What does the permeability of gaps teach us about
our own Jupiter:
- Jupiter was potentially able to grow to 5-10 mj,
if left accreting from a standard solar nebula for ~1 Myr
- the most likely reason why it didn’t:
the nebula was already disappearing and not enough mass
was available.
Variable-resolution
PPM (Piecewise
Parabolic Method)
[Artymowicz 1999]
Jupiter-mass planet,
fixed orbit a=1, e=0.
White oval = Roche
lobe, radius r_L= 0.07
Corotational region out
to x_CR = 0.17 from
the planet
disk
gap
(CR region)
disk
Outward
migration type III
of a Jupiter
Inviscid disk with an
inner clearing & peak
density of 3 x MMSN
Variable-resolution,
adaptive grid
(following the planet).
Lagrangian PPM.
Horizontal axis shows
radius in the range
(0.5-5) a
Full range of azimuths
on the vertical axis.
Time in units of initial
orbital period.
How can there be
ANY SURVIVORS of the rapid
type-III migration?!
Migration type III
Structure in the disk:
gradients od density,
edges, gaps, dead zones
Migration stops,
planet grows/survives
Edges or gradients in disks:
Magnetic
cavities around
the star
Dead zones
Unsolved problem of the Last Mohican scenario of
planet survival in the solar system:
Can the terrestial zone survive a passage of a giant planet?
 N-body simulations, N~1000 (Edgar & Artymowicz
2004)
 A quiet disk of sub-Earth mass bodies reacts to the
rapid passage of a much larger protoplanet (migration
speed = input parameter).
 Results show increase of velocity
dispersion/inclinations and limited reshuffling of
material in the terrestrial zone.
 Migration type III too fast to trap bodies in meanmotion resonances and push them toward the star
 Evidence of the passage can be obliterated by gas
drag on the time scale << Myr ---> passage of a prejupiter planet(s) not exluded dynamically.
1. Early dispersal of the primordial nebula ==> no material, no mobility
2. Late formation (including Last Mohican scenario)
Origin of structure in dusty disks:
HD107146
Source: P. Kalas
Disk of
Alpha Pisces
Austrini
(a PsA)
= Fomalhaut
a bright
southern star
type A
This is how disks
look when just
discovered
A new edgeon disk!
NICMOS/
HST
(Schneider
et al 2005)
near-IR band
(scattered
light)
HD 141569A is a Herbig emission star
>2 x solar mass, >10 x solar luminosity,
hydrogen emission lines 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??
TYPE III MIGRATION?
R_gap ~350AU
dR ~ 0.1 R_gap
HD 14169A disk gap confirmed by new observations
(HST/ACS)
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.
  0.5
  2m / 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:

= Frad / Fgrav
Weak/no PAH emission
Neutral (grey)
scattering from
s> grains
Size spectrum
of dust has lower cutoff
Repels ISM dust
Disks = Nature, not
nurture!
Radiative blow-out of grains
(-meteoroids, gamma meteoroids)
Instabilities
(in   1 disks)
Radiation pressure
on dust grains in disks
Dust
avalanches
Quasi-spiral
structure
Orbits of stable meteoroids elliptical
Color
effects
Enhanced erosion;
shortened dust lifetime
Dust migrates,
forms axisymmetric
rings, gaps
(in disks with gas)
Short disk lifetime
Age paradox
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)
ORIGIN: (10 categories)
blobs, clumps
￭
streaks, feathers
￭
rings (axisymm)
￭
rings (off-centered) ￭
inner/outer edges ￭
disk gaps
￭
warps
￭
spirals, quasi-spirals￭
tails, extensions
￭
￭ 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)
.
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 wavelengthdependent 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 ~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
HD141569+BC in V band
HST/ACS Clampin et al.
HD141569A deprojected
FEATURES in disks:
ORIGIN:
blobs, clumps
￭
streaks, feathers
￭
rings (axisymm)
￭
rings (off-centered) ￭
inner/outer edges ￭
disk gaps
￭
warps
￭
spirals, quasi-spirals￭
tails, extensions
￭
￭ stellar companions,
flybys
Best model, Ardila et al (2005)
involved a stellar fly-by &
5 MJ, e=0.6, a=100 AU
planet
Beta = 4
H/r = 0.1
Mgas = 50 M
HD 141569A
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
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 <1)
must have some gas even if it's hard to detect.
5 Myr
Warning: Dust starts to move w.r.t. gas!
Look for outer rings, inner rings, gaps
with or without planets.
Pictoris
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.
12-20
Myr
Extensive modeling including dust-dust collisions and radiation pressure needed
v=vK
vg
Gas pressure force
v
vg
Gas pressure force
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
Weak/no PAH emission
Neutral (grey)
scattering from
s> grains
Size spectrum
of dust has lower cutoff
Repels ISM dust
Disks = Nature, not
nurture!
Radiative blow-out of grains
(-meteoroids, gamma meteoroids)
Instabilities
(in   1 disks)
Radiation pressure
on dust grains in disks
Dust
avalanches
Quasi-spiral
structure
Orbits of stable meteoroids elliptical
Color
effects
Enhanced erosion;
shortened dust lifetime
Dust migrates,
forms axisymmetric
rings, gaps
(in disks with gas)
Short disk lifetime
Age paradox
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
Weak/no PAH emission
Neutral (grey)
scattering from
s> grains
Size spectrum
of dust has lower cutoff
Repels ISM dust
Disks = Nature, not
nurture!
Radiative blow-out of grains
(-meteoroids, gamma meteoroids)
Instabilities
(in   1 disks)
Radiation pressure
on dust grains in disks
Dust
avalanches
Limit
on fir
Quasi-spiral
structure
Orbits of stable meteoroids elliptical
in gas-free
disks
Enhanced erosion;
shortened dust lifetime
Color
effects
Dust migrates,
forms axisymmetric
rings, gaps
(in disks with gas)
Short disk lifetime
Age paradox
Dust Avalanche
(Artymowicz 1997)
Process powered by the energy of stellar radiation
N ~ exp (optical thickness of the disk * <#debris/collision>)
N
= disk particle, alpha meteoroid (  < 0.5)
= sub-blowout debris, beta meteoroid ( > 0.5)
  (r / z ) f IR
Ratio of the infrared luminosity
(IR excess radiation from dust) to the
stellar luminosity; it gives the
percentage of stellar flux
the midplane optical thickness
absorbed reemitted thermally
  (0.1)  0.018  0.2
1
N  ~ 10 2
multiplication factor of debris in 1 collision
(number of sub-blowout debris)
dN   N   N
Avalanche growth equation
N / N 0  exp( N  ) ~ exp( 20) ~ 106
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.
OK!
Gas-free modeling
leads to a paradox
==> gas required
or
Age paradox!
episodic dust
production
fIR =fd
disk dustiness
Bimodal histogram
of fractional
IR luminosity fIR
predicted by disk
avalanche process
source: Inseok Song (2004)
ISO/ISOPHOT data on dustiness vs. time
-1.8
Dominik, Decin, Waters, Waelkens (2003)
uncorrected ages
ISOPHOT ages, dot size ~ quality of age
fd of beta Pic
corrected ages
ISOPHOT + IRAS
transitional systems
5-10 Myr age
Weak/no PAH emission
Neutral (grey)
scattering from
s> grains
Repels ISM dust
DUST
AVALANCHES
Size spectrum
of dust has lower cutoff
Disks = Nature, not
nurture!
Radiative blow-out of grains
(-meteoroids, gamma meteoroids)
Instabilities
(in   1 disks)
Radiation pressure
on dust grains in disks
Dust
avalanches
Limit
on fIR
Quasi-spiral
structure
Orbits of stable meteoroids are
elliptical
in gas-free
disks
Enhanced erosion;
shortened dust lifetime
Color
effects
Dust migrates,
forms axisymmetric
rings, gaps
(in disks with gas)
Short disk lifetime
Age paradox
Grigorieva, Artymowicz and Thebault (to be subm. to A&A 2005)
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
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 thus pseudo-gravitational in nature
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. The instability is thus pseudo-gravitational in nature
and can be obtained from a WKB local analysis.
   0 exp(    dr )  0 exp(  )
 0  effective coefficient for coupled gas+dust
 0 ~ 0.1....10
   0  1 ei ( kr m t )

   0 (r ) 
r
1
ik
ei ( kr m t )
(this profile results from
dust migration)
  Step function of r or constant
1 i ( kr m t )
   0 (r ) 
e
ik
2
f rad   K r  0 e
f self  gravity
 0
i1 i ( kr m t )
(1 
e
)
k
i 4G1 i ( kr m  t )

e
k
(WKB)
 2   4 G  Poisson eq.
   f f  f1 exp(...)   f1  4 G 1
 ikf1  4 G 1
4 G 1
f1  i
k
  Step function of r or constant
1 i ( kr m t )
   0 (r ) 
e
ik
2
f rad   K r  0 e
f self  gravity
 0
i1 i ( kr m t )
(1 
e
)
k
i 4G1 i ( kr m  t )

e
k
(WKB)
 2   4 G  Poisson eq.
   f f  f1 exp(...)   f1  4 G 1
 ikf1  4 G 1
4 G 1
f1  i
k
G
Q 
;
Q 1  1  ( grav.) instability
 orb cs
G 1
1
Q 
 2  0 e  ( r )0 r 
 orb cs
G 1
 ( r )
1
Effective Q number
Q 
 2  0e
(r 0 / r )
(radiation+selfgravity)
 orb cs
1
0
0
 1
0 
 1
1
r
Analogies with gravitational instability ==> similar structures (?)
FEATURES in disks:(9 types)
ORIGIN: (10 reasons)
Many (~50) possible connections !
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)
￭ 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)
Conclusion:
Not only planets but also
Gas + dust + radiation =>
non-axisymmetric features
including regular m=1
spirals, conical sectors, and
multi-armed wavelets