Dust Dynamics in Debris Gaseous Disks Taku Takeuchi (Kobe Univ., Japan) 1.Dynamics of Dust - gas drag - radiation 2. Estimate of Gas Mass 3. Dust Disk Structure Formed by a Planet in a Gas Disk

Gas Drag on a Dust Grain Epstein drag law Stopping time

Small Grains: Due to strong gas drag, grains co-rotate with the gas, which orbits with sub- Keplerian velocity. sub-Kepler

Grains orbit with the Keplerian velocity, which is faster than the gas Large Grains: Kepler head-wind

Orbital Decay Rate As the gas mass decreases, –t min =const., but the size at t min decreases Even if the gas mass is as small as 0.01M earth, grains of  m rapidly fall Adachi et al. 1976; Weidenschilling 1977 at 100 AU t min t stop =t orb

Radiation Pressure (Optically thin disk) RP reduces the central star’s gravity Burns et al. 1979; Artymowicz 1988 reduction factor:

faster than gas headwind Direction of Grains’ Drift slower than gas fair-wind Takeuchi & Artymowicz 2001 Size segregation Dust clumping at the edge of the gas disk

Clumping Instability Gas temperature = Dust temperature Klahr & Lin 2005 Increase in the dust density radius pressure

Other Radiation Effects Poynting-Robertson drag –much smaller than gas drag Photophoresis (Krauss & Wurm 2005) hot cold 1AU10AU100AU Force Ratio (F ph / F RP ) MMSN model

Timescales In a gas disk with M g >M luna, gas drag dominates the dust evolution at 100 AU

Estimate of the Gas Mass (w/o planets)  Pic (Thébault & Augereau 2005) 100AU 1000AU Gas free disk Planetesimal disk dust disk

 Pic (Thébault & Augereau 2005) upper limit: M g <0.4M earth –H 2 emission (ISO): 50M earth (Thi et al. 2001) –H 2 absorption (FUSE): <0.1M earth (Lacavelier Des Etangs et al. 2001) –NaI emission : 0.1M earth (Brandeker et al. 2004) Gaseous disk (40M earth )

HD (Ardila et al. 2005) Scattered light from  meteoroids (s~1  m) M g <50M earth –Distribution of  meteoroids shows a spiral pattern, because it traces the distribution of planetesimals. CO emission: M g <60M earth (Zuckerman et al. 1995)  meteoroids Planetesimal disk Stellar flyby spiral wave

HR 4796 (Takeuchi & Artymowicz 2001) M g ~4M earth CII absorption: M g <1M earth (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 (Goldreich & Tremaine 1980) Timescale to form resonant structure (Weidenschilling & Davis 1985) j+1:j j+2:j+1

Gap Opening / Resonant Trapping Timescales Resonant trapping probably does not form prominent structure before gap opening 1M earth Timescale j j=10 1M Jupiter Timescale j j=3

Bryden et al Gas density Grain Accumulation at the Gap Edges

Spiral Waves Planet’s gravity and /or spiral waves may distort the dust rings. Lubow et al 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 M earth planet cannot open a gap in a turbulent disk (Nelson & Papaloizou 2004)

Type I Migration can be neglected –M p =30M earth, at 100AU, M g =30M earth, –t mig ~1Gyr (Tanaka et al. 2002)

Summary / Unresolved Questions Gas of a lunar mass can dominate the orbital 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?