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Gas Dynamics in Protoplanetary Disks

Hubble Fellow Symposium, STScI , 03/10/2014. Gas Dynamics in Protoplanetary Disks. Xuening Bai. Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics. Collaborator: Jim Stone (Princeton). Pathway to (giant) planets. Aerodynamic coupling. Gravitational coupling.

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Gas Dynamics in Protoplanetary Disks

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  1. Hubble Fellow Symposium, STScI, 03/10/2014 Gas Dynamics in Protoplanetary Disks Xuening Bai Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics Collaborator: Jim Stone (Princeton)

  2. Pathway to (giant) planets Aerodynamic coupling Gravitational coupling μm km 103km 105km cm Planetesimal formation Planetesimal growth to cores growth/accretion to gas giants Grain growth Essentially all processes depend on the gas dynamics of protoplanetary disks. Most importantly, what are the structure and level of turbulence in PPDs? Planet migration

  3. Observational facts • Typical mass: 10-3-10-1M. • Lifetime: 106-107 yr. • Typical accretion rate ~ 10-8 M yr -1. • Outflow is intimately connected to accretion: Sicilia-Aguila et al. (2005)

  4. Goal: • Understanding the gas dynamics in PPDs: • What is the radial and vertical structure of PPDs? • Which regions of PPDs are turbulent / laminar? • What drives accretion and outflow in PPDs? • The role of magnetic field: • Magneto-rotational instability (MRI) • Magneto-centrifugal wind (MCW) (Balbus & Hawley 1991) (Blandford & Payne 1982, Pudritz & Norman 1983)

  5. What drives accretion? angular momentum Radial (viscous) transport by: Vertical transport by: (turbulence generated by) (with large-scale external B-field) Magneto-rotational instability Magneto-centrifugal wind (Balbus & Hawley, 1991) (Blandord & Payne, 1982)

  6. PPDs are extremely weakly ionized cosmic ray thermal ionization far UV stellar X-ray Umibayashi & Nakano (1981) Igea & Glassgold (1999) Perez-Becker & Chiang (2011b) (Bai, 2011a) Ionization fraction rapidly decreases from surface to midplane. Including small grains further reduce disk ionization.

  7. Non-ideal MHD effects in weakly ionized gas In the absence of magnetic field: In the presence of magnetic field: inductive Ohmic Hall Ambipolar Induction equation (no grain): Dense Weak B Sparse Strong B midplane region of the inner disk inner disk surface and outer disk

  8. Conventional picture of layered accretion Armitage 2011, ARA&A Gammie, 1996 Dead zone: resistive quenching of the MRI Active layer: resistivity negligible • Semi-analytical studies already indicated that MRI is insufficient to drive rapid accretion when including the effect of ambipolar diffusion (Bai & Stone, 2011, Bai, 2011a,b, Perez-Becker & Chiang, 2011a,b).

  9. More realistic simulations • Athena MHD code (fully conservative) • Local shearing box simulations with orbital advection scheme (Gardiner & Stone, 2010) (Stone et al., 2008) z y x • Magnetic diffusion coefficients obtained by interpolating a pre-computed lookup table based on equilibrium chemistry. (Bai & Goodman 2009, Bai 2011a,b) • MMSN disk, CR, X-ray and FUV ionizations, 0.1μm grain abundance 10-4.

  10. The importance of magnetic field geometry Zero net vertical magnetic flux With net vertical magnetic flux Vast majority Poorly studied before βz0=Pgas,mid/Pmag,net

  11. Inner disk: simulations with Ohmic+AD+Hall (Bai & Stone, 2013b, Bai 2013,2014) By default, we consider βz0=105

  12. Ohmic resistivity ONLY Ohmic + ambipolar diffusion azimuthal radial color: field strength At 1 AU (Bai & Stone, 2013b)

  13. Ohmic + ambipolar diffusion Magnetocentrifugal outflow! azimuthal Wrong geometry? radial color: velocity magnitude (Bai & Stone, 2013b)

  14. Symmetry and strong current layer strong current layer Bϕ Bϕ Bz Bz Br Br flipped horizontal field Physical wind geometry Unphysical wind geometry

  15. Radial dependence (Ohmic + ambipolar) Weak MRI turbulence sets in beyond ~5-10 AU. MRI sets in the (upper) far-UV ionization layer due to weak field MRI sets in at midplane, where Ohmic-resistivity is no longer important at large radii weaker field Wind is still the dominant mode to drive accretion. (Bai, 2013)

  16. Adding the Hall effect (1AU) BΩ<0 BΩ>0 Ω Ω B B (Bai, 2014, submitted)

  17. Adding the Hall effect: range of stability BΩ<0 BΩ>0 Ω Ω B B (Bai, 2014, submitted)

  18. Outer disk: simulations with Hall + AD (Bai & Stone, 2014, in prep)

  19. Gas dynamics in the outer disk (15-60 AU) 30 AU, weak vertical field β0=105 Aligned/anti-aligned field has stronger/weaker midplane magnetic activities compared with the Hall-free case. FUV layer (ideal MHD) ambipolar diffusion FUV layer (ideal MHD) Hall BΩ>0 MRI in the FUV layer sufficient to drive rapid accretion. No Hall BrBϕ BΩ<0 Disk outflow can also play a role, but its contribution is uncertain based on local simulations. MRI turbulent, disk outflow MRI turbulent, disk outflow

  20. Gas dynamics in the outer disk (15-60 AU) 30 AU, weak vertical field β0=105 Anti-aligned field geometry has reduced midplane turbulence: MRI is suppressed in the midplane. FUV layer (ideal MHD) ambipolar diffusion FUV layer (ideal MHD) Hall BΩ>0 No Hall BΩ<0 Aligned field geometry has weakest midplane turbulence: suppressed by stronger magnetic field. MRI turbulent, disk outflow MRI turbulent, disk outflow “dead zone”?

  21. Summary: a new paradigm (Bai, 2013)

  22. Implications: planet formation & disk evolution • Grain growth and planetesimal formation • Planetesimal growth • Planet migration • Global disk evolution • Polarity dependent planet formation? Inner disk is the favorable site for planetesimal formation. Planetesimal growth does not suffer from turbulent excitation. Gap opening is much easier, may slow down type-I migration. Largely dictated by global magnetic flux distribution, heritage from star formation plus intrinsic magnetic flux transport within the disk.

  23. Conclusions and future work • Non-ideal MHD effects play a crucial role in PPDs • MHD from midplane to disk surface dominated by Ohmic, Hall and AD • The inner PPD is purely laminar, launching an MCW. • MRI suppressed by Ohmic and AD, external vertical field is essential. • Hall effect modestly modifies the wind solution, depending on field polarity. • Accretion proceeds through thin strong current layer. • The outer PPDs is likely to be turbulent with layered accretion. • MRI is most active in the surface FUV layer, midplane is weakly turbulent. • Global simulations with resolved microphysics is essential: • Issues with symmetry and strong current layer, kinematics of the wind • Interplay between disk evolution and magnetic flux transport.

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