Download - Dust Dynamics in Debris Gaseous Disks
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?