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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. - PowerPoint PPT Presentation
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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)
Pathway to (giant) planets
Essentially all processes depend on the gas dynamics of protoplanetary disks.
μm cm km 103km 105km
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?
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)
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)
What drives accretion?
Radial (viscous) transport by: Vertical transport by:
(Balbus & Hawley, 1991)
Magneto-rotational instability Magneto-centrifugal wind
(Blandord & Payne, 1982)
(turbulence generated by) (with large-scale external B-field)
angular momentum
PPDs are extremely weakly ionized
cosmic raythermal 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.
Non-ideal MHD effects in weakly ionized gas
DenseWeak B
SparseStrong B
Ohmic Hall Ambipolarinductive
Induction equation (no grain):
In the absence of magnetic field:
In the presence of magnetic field:
midplane region of the inner disk
inner disk surfaceand outer disk
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
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.
Vast majority Poorly studied before
Zero net vertical magnetic flux
With net vertical magnetic flux
The importance of magnetic field geometry
βz0=Pgas,mid/Pmag,net
Inner disk: simulations with Ohmic+AD+Hall
(Bai & Stone, 2013b, Bai 2013,2014)
By default, we consider βz0=105
Ohmic resistivity ONLY Ohmic + ambipolar diffusion
azimuthal
radial
color: field strength
(Bai & Stone, 2013b)At 1 AU
Ohmic + ambipolar diffusion
azimuthal
radial
color: velocity magnitude
Magnetocentrifugal outflow!
Wrong geometry?
(Bai & Stone, 2013b)
Symmetry and strong current layer
Physical wind geometryUnphysical wind geometry
Br
Bϕ
Bz
Br
Bϕ
Bz
strong current layer
flipped horizontal
field
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.
wea
ker f
ield
Adding the Hall effect (1AU)
BΩBΩ
(Bai, 2014, submitted)
BΩ>0BΩ<0
Adding the Hall effect: range of stability
BΩBΩ
(Bai, 2014, submitted)
BΩ<0 BΩ>0
Outer disk: simulations with Hall + AD
(Bai & Stone, 2014, in prep)
Gas dynamics in the outer disk (15-60 AU)30 AU, weak vertical field β0=105
FUV layer (ideal MHD)
ambipolar diffusion
Hall
FUV layer (ideal MHD)
MRI turbulent,
disk outflow
MRI turbulent,
disk outflow
Aligned/anti-aligned field has stronger/weaker midplane magnetic activities compared with the Hall-free case.
BΩ>0
BΩ<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.BrBϕ
Gas dynamics in the outer disk (15-60 AU)
“dead zone”?
30 AU, weak vertical field β0=105
MRI turbulent,
disk outflow
MRI turbulent,
disk outflow
BΩ>0
BΩ<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)
Summary: a new paradigm
(Bai, 2013)
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.
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.