Structures in illuminated, optically thick dust disks
Pawel Artymowicz, Jeffrey Fung
U of Toronto
1.Origin of the observed structure in disks2.Disks with structure but without planets
Signposts of Planets GSFC, 18 Oct. 2011
HD 141596
FEATURES in disks:(9)
blobs, clumps ■ (5)streaks, feathers ■ (4)rings (axisymm) ■ (2)rings (off-centered) ■ (7)inner/outer edges ■ (5)disk gaps ■ (4)warps, uneven wall ■ (7)spirals, quasi-spirals ■ (8)tails, extensions ■ (6)
THEIR ORIGIN:(11)
■ 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
or the tau > 1 instability
LOTS OF CONNECTIONS (~50) !
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)1
Age paradox
Coloreffects
Limit on fIRin gas-free disks
Structure in dusty disks
Overinterpreted observations
(noise, backgroundobjects)
Dust-gas interaction: axisym. rings (Takeuchi
and Artymowicz 2001) Create large gaps!
Dust avalanches,
optical thickness <<1but > ( LIR/L*. ~ 3e-3)
Optical thickness > 1non-axisymmetric
instabilities
Planetsand other perturbers
Outward Migration of Jupiter-like planet in a MMSN-like disk.
Outward migration type IIIof 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 showsradius in the range (0.5-5) a
Full range of azimuthson the vertical axis.
Time in units of initialorbital period.
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
fzrso
rdrzrdrs
rdrrrdrf
IR
IR
Transitional disks MUST CONTAIN GAS or face self-destruction.Beta Pic is among the most dusty, gas-poor disks, 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, then re-emitted thermally
multiplication factor of debris in 1 collision (number of sub-blowout debris)
Simplified avalanche equation
Solution of the simplified avalanche growth equation
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 = maximum dustiness of disks
-1.8
Grigorieva, Artymowicz and Thebault (A&A, 2007)Comprehensive model of dusty debris disk (3D) with full treatmentof collisions and particle dynamics.
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
Structure in dusty disks
Overinterpreted observations
(noise, backgroundobjects)
Dust-gas interaction: axisym. rings (Takeuchi
and Artymowicz 2001)
Dust avalanches,
optical thickness <<1but > ( LIR/L*. ~ 3e-3)
Optical thickness > 1non-axisymmetric
instabilities
Planetsand other perturbers
Theory of the tau>1 instability in disks.
Axisymmetric diskof opaque gas
or
dust w/shadowing
Point source of gravity
radiationpressure on gas/dust
Ingredients of the instability:
Isn’t it stable?..
Radiation pressureon 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 forceor self-gravity. The instability is thus pseudo-gravitational in natureand can be obtained from a WKB local analysis.
Forces of selfgravity Forces of radiation pressure in the
inertial frame (notice their gradient!)
Forces of rad. pressure relativeto those on the center of the arm
The instability is thus pseudo-gravitational in natureand can be obtained from a WKB local analysis.
ekGif
ek
ierf
eik
r
e
dr
gravityself
tmkriKrad
tmkri
tmkri
1
)(10
)(10
)(10
0
0
00
4
)1(
)(
10....1.0~
)exp()exp(
0
effective coefficient for coupled gas+dust
r
(this profile results from outward dust migration;Chiang & Murray-Clay 2007;Dominik & Dullemond 2011did not consider coagulation)
ekGif
ek
ierf
eik
r
e
dr
gravityself
tmkriKrad
tmkri
tmkri
1
)(10
)(10
)(10
0
0
00
4
)1(
)(
10....1.0~
)exp()exp(
0
Step function of r or constant
)( tmkri (WKB)
2
kGif
Gikf
GffffeqPoissonG
11
11
111
2
44
4exp(...).4
ekGif
ek
ierf
eik
r
e
dr
gravityself
tmkriKrad
tmkri
tmkri
1
)(10
)(10
)(10
0
0
00
4
)1(
)(
10....1.0~
)exp()exp(
0
Step function of r or constant
)( tmkri (WKB)
2
kGif
Gikf
GffffeqPoissonG
11
11
111
2
44
4exp(...).4
00
0)(2
11
,11
/)()(
.)(1;
0
rrdec
GQ
yinstabilitgravQc
GQ
r
sorb
sorb
r1
Effective Q number(selfgravity + radiation)
Analogies with gravitational instability ==> similar structures (?)
2
Previously just this inverse Safronov-Toomre number
Now:
tau = 2, beta = 0.2
0 180 deg 360 deg
radius
.7
1
1.6
azimuthal angle
Free particles casting shadows
tau = 4, beta = 0.2
0 180 deg 360 deg
radius
.7
1
1.6
azimuthal angle
Free particles casting shadows
tau = 12, beta = 0.2
0 180 deg 360 deg
radius
.7
1
1.6
azimuthal angle
Free particles casting shadows
Beta = 0.2
De Val Borro& Artymowicz(2008, unpubl.),
FLASH hydrocode
Beta = 0.2
Beta = 0.2
tau = 3beta = 0.075
PPM
gas disk density
soundspeed c/vk = 0.05
Navier-Stokesviscosity: alpha = 0
radius
Azi
mut
hal a
ngle
(0-3
60 d
eg)
1 2 3(2a)
tau = 4beta = 0.15
PPM
gas disk density
soundspeed c/vk = 0.05
Navier-Stokesviscosity: alpha = 0
radius
Azi
mut
hal a
ngle
(0-3
60 d
eg)
1 2 3(3a)
NOT
nVidia GeForcegraphics processors
CPU=Intel4-core
nVidia CUDA = extended C-language for GPU programmingup to 5 TFLOP/s using one computer
Cudak1 2 TFLOP, 484 coresCudak2 3 TFLOP , 724 coresCudak3 5+ TFLOP, 1444 cores all: max 10+ TFLOP, 2652 cores
PPM hydrodynamical simulation on GPU of a gas+embedded dust disk around with effective beta = 0.15 and total optical depth tau|| =15
Please see Jeffrey Fung’s poster on linear modal analysis which confirms that irradiated disks have a wide variety of unstable modes!
Not only planets but also
Gas + dust + radiation => non-axisymmetric features in gas-poor and gas-rich disks, & TIME VARIABILITY due to radial, azimuthal and vertical variations in them.
m=1 one armed spirals, conical sectors, blobs and warps (due to avalanching)m>1 multi-armed wavelets and vortices
(due to tau>1 radiation pressure instability)
+ many other possible causes
FEATURES in disks:(9)
blobs, clumps ■ (5)streaks, feathers ■ (4)rings (axisymm) ■ (2)rings (off-centered) ■ (7)inner/outer edges ■ (5)disk gaps ■ (4)warps,uneven walls ■ (7)spirals, quasi-spirals ■ (8)tails, extensions ■ (6)
THEIR ORIGIN:(11)
■ 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
or the tau > 1 instability
LOTS OF CONNECTIONS (~50) !
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