Dust Dynamics in Debris Gaseous Disks

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

2. Gas Drag on a Dust Grain • Epstein drag law • Stopping time

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

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

5. at 100 AU tmin Orbital Decay Rate Adachi et al. 1976; Weidenschilling 1977 • As the gas mass decreases, • tmin=const., but the sizeat tmin decreases • Even if the gas mass is as small as 0.01Mearth, grains of 1-10mm rapidly fall tstop=torb

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

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

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

9. 100AU 10AU 1AU MMSN model Force Ratio (Fph / FRP) Other Radiation Effects • Poynting-Robertson drag • much smaller than gas drag • Photophoresis (Krauss & Wurm 2005) cold hot

10. at 100 AU Timescales • In a gas disk with Mg>Mluna, gas drag dominates the dust evolution

11. Gas free disk 1000AU 100AU Estimate of the Gas Mass (w/o planets) • b Pic (Thébault & Augereau 2005) dust disk Planetesimal disk

12. bPic(Thébault & Augereau 2005) • upper limit: Mg<0.4Mearth • H2 emission (ISO): 50Mearth (Thi et al. 2001) • H2 absorption (FUSE): <0.1Mearth (Lacavelier Des Etangs et al. 2001) • NaI emission : 0.1Mearth (Brandeker et al. 2004) Gaseous disk (40Mearth )

13. b meteoroids spiral wave HD 141569 (Ardila et al. 2005) • Scattered light from b meteoroids (s~1mm) • Mg<50Mearth • Distribution of b meteoroids shows a spiral pattern, because it traces the distribution of planetesimals. • CO emission: Mg<60Mearth(Zuckerman et al. 1995) Stellar flyby Planetesimal disk

14. gas disk planetesimal disk HR 4796 (Takeuchi & Artymowicz 2001) • Mg~4Mearth • CII absorption: Mg<1Mearth(Chen & Kamp 2004) Telesco et al. (2000)

15. 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.)

16. Complications by Gas Disturbances • Gap • Spiral waves • Turbulences Lubow et al. 1999

17. j+1:j j+2:j+1 Gap • Gap opening time at j+1:j LR (Goldreich & Tremaine 1980) • Timescale to form resonant structure (Weidenschilling & Davis 1985)

18. 1Mearth 1MJupiter Timescale Timescale j=10 j=3 j j Gap Opening / Resonant Trapping Timescales • Resonant trapping probably does not form prominent structure before gap opening

19. Gas density Bryden et al. 2000 Grain Accumulation at the Gap Edges

20. Spiral Waves • Planet’s gravity and /or spiral waves may distort the dust rings. clumps? Lubow et al. 1999

21. 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)

22. Type I Migration • can be neglected • Mp=30Mearth, at 100AU, Mg=30Mearth, • tmig~1Gyr (Tanaka et al. 2002)

23. 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?