Dead zones in protoplanetary discs Mark Wardle Macquarie University Raquel Salmeron (ANU) BP Pandey (Macquarie) Protoplanetary discs Magnetic fields Dead zones MRI and diffusion Modification to dead zones
Magnetic fields Magnetic fields are present in PPDs measured B in molecular clouds ==> B>1 mg in PPDs Zeeman, submm polarization Weak magnetic fields create turbulence subequipartition B and rotational shear ==> MHD turbulent torque magnetorotational instability (MRI) accretion, heating, stirring (chemistry, dust grains) disc evolution observational signatures planet formation planet migration (!) Accretion rates require B ~.1 1G at 1AU
Magnetorotational instability (MRI)! magnetic field couples different radii in disc" tension transfers angular momentum outwards" kh > 1 required to fit in disc, i.e. v A /c s < 1! resulting turbulence transports angular momentum outwards!
Flux freezing breaks down in PPDs high density and low ionisation drag on charged particles deeper layers shielded from ionising radiation for r < 5 AU x-ray attenuation column ~1 g/cm 2 cosmic ray attenuation column ~1 g/cm 2 dead zone near midplane (Gammie 1996)
MRI with! dead zone! Turner & Sano 28!
Magnetic diffusion Ideal MHD electrons, ions and neutrals tied to magnetic field Ambipolar diffusion neutrals decoupled Hall diffusion ions and neutrals decoupled Ohmic diffusion electrons, ions and neutrals decoupled
Ambipolar Hall
Wardle 27
2!! I ohmic + ambipolar diffusion!!! " II η P Ω / v A 2 1 stable I k k c k!! " k III k II III 2 1 1 2 s η H Ω / v A 2 k ideal MHD Wardle & Sameron 212
Charged particle abundances 6 M dust / M gas = 1 4 6 M dust / M gas = 1 2 log n / n H 1 14 18 M + e m + C + H 3 + He+ H + 7 Z 61 6 Z 51 8 Z 71 1 14 18 1 Z 1 Z = 11 Z 2 M + e m + C + H He+ + 3 H + 7 Z 61 6 Z 51 8 Z 71 5 Z 41 22 5 Z 41 22 9 Z 81 6 M dust / M gas = 1 M +, e log n / n H 14 m + 18 log ζ H (s 1 ) C + H 3 + He+ H + 22 1 2 3 4 5 z / h
Max growth rate: no dust 2.5 B z < 5 2.5 M dust / M gas = B z > 5 z (1 12 cm) z (1 12 cm) 2. 1.5 1..5. 2.5 2. 1.5 1. ohmic only 4 3 2 1 5 4 3 2 z / h z / h 2. 1.5 1..5.! / Ω.75.5.25 4 3 2 1.5 1. 1 3 1 2 1 1 1 1 1 1 2 B (G) Wardle & Sameron 212
Max growth rate: Mdust / Mgas = 1 2 2.5 5 B z < 2.5 M dust / M gas = 1 2 B z > 5 z (1 12 cm) 2. 1.5 1. 4 3 2 z / h 2. 1.5 1.! / Ω.75.5.25 4 3 2.5 1.5 1.. 2.5 ohmic only 5 2. 4 z (1 12 cm) 1.5 1. 3 2 z / h.5 1. 1 3 1 2 1 1 1 1 1 1 2 B (G) Wardle & Sameron 212
Column density of active layer! Wardle & Sameron 212
Column density of active layer! Wardle & Sameron 212
Summary & Discussion Ionisation levels determine extent of magnetically turbulent regions in protoplanetary discs dead zones: ~.3 3 AU from central star topped by magnetically active layers Hall diffusion modifies thickness of active layer by an order of magnitude dead zones: Bz < vs Bz > ; depends on magnitude of B can sustain accretion rates in these layers across radial extent of dead zone may drive undead zones more general geometries destabilise disk (Pandey & Wardle submitted) MHD simulations? linear analysis such as used here appears to be a good predictor of dead zone extent no MHD simulations with strong hall diffusion (yet) PS: simulations with non net flux are unrealistic