Dust Dynamics in Debris Gaseous Disks

Taku Takeuchi (Kobe Univ., Japan)

1. Dynamics of Dust- gas drag- radiation

2. Estimate of Gas Mass3. Dust Disk Structure Formed by a Planet in a

Gas Disk

Gas Drag on a Dust Grain• Epstein drag law

• Stopping time

11 )(

orbgdd

gdrag tvvsa

orbg

d

drag

gdstop st

a

vvt

||

||

gd vv a

0 gd vv

stopt

timeorbital :

density gas :

sizegrain :

orb

g

t

s

Small Grains:• Due to strong gas drag, grains co-rotate

with the gas, which orbits with sub-Keplerian velocity.

orbstop tt

svr

1 svaaa rdragcentgrav sub-Kepler

gravacentadraga

centgrav aa

• Grains orbit with the Keplerian velocity, which is faster than the gas

Large Grains: orbstop tt

1 sadragKepler

head-wind

1 svr

Orbital Decay Rate• As the gas mass decreases,

– tmin=const., but the size at tmin decreases

• Even if the gas mass is as small as 0.01Mearth, grains of m rapidly fall

Adachi et al. 1976; Weidenschilling 1977

at 100 AU

tmintstop=torb

Radiation Pressure (Optically thin disk)

• RP reduces the central star’s gravity

grava rada

grav

radgraveff

a

aaa

)1(

grav

rad

a

a

Burns et al. 1979; Artymowicz 1988

reduction factor:

faster than gas

headwind

Direction of Grains’ Drift

Kd vv 2/1, )1( :Dust

Kg vv 2/1, )1( :Gas

slower than gas

fair-wind

Takeuchi & Artymowicz 2001

• Size segregation• Dust clumping at the edge of the gas

disk

Clumping Instability

• Gas temperature = Dust temperatureKlahr & Lin 2005

)0( dgasT

Increase in the dust density

d

radius

pres

sure

gasT d

Other Radiation Effects• Poynting-Robertson drag

– much smaller than gas drag

• Photophoresis (Krauss & Wurm 2005)

hot

cold

1AU10AU100AU

For

ce R

atio

(F

ph /

FR

P)

MMSN model

Timescales

• In a gas disk with Mg>Mluna, gas drag dominates the dust evolution

orbcol tt 1

orbK

PR tc

vt

11

at 100 AU

Estimate of the Gas Mass (w/o planets)

• Pic (Thébault & Augereau 2005)

100AU

1000AUGas free disk

Planetesimal disk

dust disk

Pic (Thébault & Augereau 2005)

• upper limit: Mg<0.4Mearth

– H2 emission (ISO): 50Mearth (Thi et al. 2001)

– H2 absorption (FUSE): <0.1Mearth (Lacavelier Des Etangs e

t al. 2001)

– NaI emission : 0.1Mearth (Brandeker et al. 2004)Gaseous disk (40Mearth )

HD 141569 (Ardila et al. 2005)

• Scattered light from meteoroids (s~1m)

• Mg<50Mearth

– Distribution of meteoroids shows a spiral pattern, because it traces the distribution of planetesimals.

• CO emission: Mg<60Mearth (Zuckerman et al. 1995)

meteoroids

Planetesimal disk

Stellar flyby

spiral wave

HR 4796 (Takeuchi & Artymowicz 2001)

• Mg~4Mearth

• CII absorption: Mg<1Mearth (Chen & Kamp 2004)

gas disk

planetesimal disk

Telesco et al. (2000)

Gas + Planets• Resonant trapping

– large grains (orbit faster than the gas):• drift inward• trapped at exterior resonances (Weidenschilling & Davis 1985)

– small grains (orbit slower than the gas):• drift outward• trapped at interior resonances

(Doi & Takeuchi, in prep.)

Complications by Gas Disturbances• Gap

• Spiral waves

• Turbulences

Lubow et al. 1999

Gap• Gap opening time at j+1:j LR (Goldreic

h & Tremaine 1980)

• Timescale to form resonant structure (Weidenschilling & Davis 1985)

orbpopen tMMjt 2*

6 )/(

j+1:j

j+2:j+1orbp

res

tMMj

vrt2/11

*2/3

max,drift

)/(

/

max,driftdrift vv max,driftdrift vv

Gap Opening / Resonant Trapping Timescales

• Resonant trapping probably does not form prominent structure before gap opening

1Mearth

Tim

esca

le

jj=10

6 jtopen

2/3 jtres

1MJupiter

Tim

esca

le

jj=3

6 jtopen

2/3 jtres

Bryden et al. 2000

Gas

den

sity

Grain Accumulation at the Gap Edges

Spiral Waves

• Planet’s gravity and /or spiral waves may distort the dust rings.

Lubow et al. 1999

clumps?

Turbulence• Optically thin disks are probably unstable

against MRI (Sano et al. 2000) • Turbulence inhibits planets from opening a gap• Can resonant trapping occur in turbulent disks?

A 30 Mearth planet cannot open a gap in a turbulent disk (Nelson & Papaloizou 2004)

Type I Migration

• can be neglected – Mp=30Mearth, at 100AU, Mg=30Mearth,

– tmig~1Gyr (Tanaka et al. 2002)

Summary / Unresolved Questions• Gas of a lunar mass can dominate the orbit

al evolution of the dust

• Gas drag can form structure in dust disks without any planets or companions

• Gas mass can be estimated from the structure of the dust disk (if there is no planet)

• What structure does a planet form in a gas disk?