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

2. Pathway to (giant) planets Essentially all processes depend on the gas dynamics of protoplanetary disks. μm cm km10 3 km10 5 km Grain growth Planetesimal formation Planetesimal growth to cores growth/accretion to gas giants Planet migration Aerodynamic coupling Gravitational coupling Most importantly, what are the structure and level of turbulence in PPDs?

3. Observational facts Typical mass: 10 -3 -10 -1 M . Lifetime: 10 6 -10 7 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? Radial (viscous) transport by: Vertical transport by: (Balbus & Hawley, 1991) Magneto-rotational instabilityMagneto-centrifugal wind (Blandord & Payne, 1982) (turbulence generated by) (with large-scale external B-field) angular momentum

6. PPDs are extremely weakly ionized cosmic ray thermal ionization Umibayashi & Nakano (1981) Igea & Glassgold (1999) Perez-Becker & Chiang (2011b) far UV stellar X-ray (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 Dense Weak B Sparse Strong B Induction equation (no grain): In the absence of magnetic field: In the presence of magnetic field: midplane region of the inner disk inner disk surface and outer disk

8. Dead zone: resistive quenching of the MRI Active layer: resistivity negligible Conventional picture of layered accretion Armitage 2011, ARA&A 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). Gammie, 1996

9. Athena MHD code (fully conservative) Local shearing box simulations with orbital advection scheme (Gardiner & Stone, 2010) More realistic simulations x y z (Stone et al., 2008) 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. Vast majorityPoorly studied before Zero net vertical magnetic flux With net vertical magnetic flux The importance of magnetic field geometry β z0 =P gas,mid /P mag,net

11. Inner disk: simulations with Ohmic+AD+Hall (Bai & Stone, 2013b, Bai 2013,2014) By default, we consider β z0 =10 5

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

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

14. Symmetry and strong current layer Physical wind geometry Unphysical wind geometry BrBr BϕBϕ BzBz BrBr BϕBϕ BzBz strong current layer flipped horizontal field

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

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

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

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 β 0 =10 5 FUV layer (ideal MHD) ambipolar diffusion Hall FUV layer (ideal MHD) MRI turbulent, disk outflow Aligned/anti-aligned field has stronger/weaker midplane magnetic activities compared with the Hall-free case. B  Ω>0 B  Ω<0 No Hall Disk outflow can also play a role, but its contribution is uncertain based on local simulations. MRI in the FUV layer sufficient to drive rapid accretion. BrBϕBrBϕ

20. Gas dynamics in the outer disk (15-60 AU) “dead zone”? 30 AU, weak vertical field β 0 =10 5 MRI turbulent, disk outflow B  Ω>0 B  Ω<0 No Hall Aligned field geometry has weakest midplane turbulence: suppressed by stronger magnetic field. Anti-aligned field geometry has reduced midplane turbulence: MRI is suppressed in the midplane. FUV layer (ideal MHD) ambipolar diffusion Hall FUV layer (ideal MHD)

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.