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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)
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 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
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 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
HD 14169A disk gap confirmed by new observations
(HST/ACS)
HD141569+BC in V band
HST/ACS Clampin et al.
HD141569A deprojected
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)
ORIGIN: (10)
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 eff. (selfgravity)
FEATURES in disks:
ORIGIN:
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.
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:
ORIGIN:
blobs, clumps
￭
streaks, feathers
￭
rings (axisymm)
￭
rings (off-centered) ￭
inner/outer edges ￭
disk gaps
￭
warps
￭
spirals, quasi-spirals￭
tails, extensions
￭
￭ 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)
Stellar flyby (of an elliptic-obit companion) explains some features
of HD 141569A
Augereau and Papaloizou (2003)
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

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
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
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
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)
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, then re-emitted 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
Simplified avalanche equation
N / N 0  exp( N  ) ~ exp( 20) ~ 10
6
Solution of the simplified 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 among the most dusty, gas-poor disks, possible.
#) derivation:
f IR     2rdr /( 4r )     dr /( 2r )
2
   ( / s ) dr  ( r / z )   dr /( 2r )
so
  ( r / z ) f IR
  (0.1)  0.018  0.2
1
N  ~ 10
2
dN   N   N
N / N 0  exp( N   ) ~ exp(20) ~ 10
6
Bimodal histogram
of fractional
IR luminosity fIR
similar to that
predicted by disk
avalanche process
source: Inseok Song (2004)
Bimodal
histogram
of fractional
IR luminosity fI
similar to that
predicted by dis
avalanche
process
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
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
￭ 50-500 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!
OK!
Gas-free modeling
leads to a paradox
==> gas required
or
Age paradox!
episodic dust
production
fIR =fd
disk dustiness
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
Best model, Ardila et al (2005)
5 MJ, e=0.6, a=100 AU
planet
Beta = 4
H/r = 0.1
Mgas = 50 M
HD 141569A
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..
   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
 2   4 G 
   f
Poisson eq.
f  f1 exp(...)   f1  4 G 1
 ikf1  4 G 1
4 G 1
f1  i
k
(WKB)
  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
 2   4 G 
   f
Poisson eq.
f  f1 exp(...)   f1  4 G 1
 ikf1  4 G 1
4 G 1
f1  i
k
(WKB)
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, as well
as blobs