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.

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effective coefficient for coupled gas+dust

r

(this profile results from outward dust migration;Chiang & Murray-Clay 2007;Dominik & Dullemond 2011did not consider coagulation)

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Step function of r or constant

)( tmkri (WKB)

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4exp(...).4

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Step function of r or constant

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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) !