High-resolution Imaging of Debris Disks Jane Greaves St Andrews University, Scotland.
ANGULAR MOMENTUM TRANSPORT In T TAURI ACCRETION DISKS: WHERE IS THE DISK MRI-ACTIVE?
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Transcript of ANGULAR MOMENTUM TRANSPORT In T TAURI ACCRETION DISKS: WHERE IS THE DISK MRI-ACTIVE?
ANGULAR MOMENTUM TRANSPORT
In T TAURI ACCRETION DISKS:
WHERE IS THE DISK MRI-ACTIVE?
Subhanjoy Mohanty (Imperial College London)
Barbara Ercolano (University of Exeter)
Neal Turner (JPL)
(Wardle 1999; Balbus & Terquem 2001; Kunz & Balbus 2004)
I O H A
1) vAz2 / ηOHM Ω > 1 : tangled field regenerated by MRI turbulence
[growth rate of fastest growing MRI-mode ( = k vA ~ Ω)
> the damping rate ( = k2η)]
2) vK2 / ηOHM Ω > 10 : toroidal field regenerated from seed radial fields
by orbital shear
1 + 2 ----- ACTIVE
2 ONLY ----- UNDEAD ZONE (no MRI, but field can be regen. by orbital shear)
NEITHER 1 NOR 2 ----- DEAD ZONE (no activity at all)
CONDITION 1: SUFFICIENT IONIZATION FRACTION
CONDITION 2: SUFFICIENT ION DENSITY
γinρi / Ω > 100 : sufficient # of ion-neutral collisions (otherwise MRI ang. mom.
transport nosedives)
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(Turner et al. 2009, Sano & Turner 2008)
(Kunz & Balbus 2004; Chiang & Murray-Clay 2007)
CONDITION 3: MAGNETIC PRESSURE
PB < Pgas : otherwise MRI ineffective
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DISK MODELS
2 STELLAR MASSES at 1 Myr conditions:
a) 0.7 M (with R* = 2 R and Teff = 4000 K)
b) 0.1 M (with R* = 1 R and Teff = 3000 K)
DISK IONIZATION by STELLAR X-RAYS:
LX / Lbol = constant, with LX = 1030 erg/s for 0.7 M (following median values of observations by Güdel et al. ‘07)
3 KEPLERIAN DISK MODELS:
a) Σ r ∝ -3/2 (i.e., standard MMSN), Md M∝ * , vertically isothermal
b) Σ r ∝ -1 (i.e., constant Mdot), Md M∝ * , vertically isothermal
•Σ r ∝ -1 (i.e., constant Mdot), Md M∝ *2 , midplane acc. with associated temperature structure (d’Alessio model)
NOTE 1: Disk outer radius Rout = 100 AU in all cases
NOTE 2: Disk mass Md normalized in all cases such that Md = 0.01 M for M* = 1 M .
As a result, the disk mass and structure of the 0.7 M star is very similar for the disk models (b) and (c),
except for small differences due to the inclusion of accretion-related temperature structure in (c). The disk of the 0.1 M star, on the other hand, is much less massive in (c) than in (b).
NOTE 3: PBz = Pgas_mid / 1000 , PB_TOT = 30 x PBz
(following results of ideal-MHD stratified shearing-box calculations: Miller & Stone 2000; Turner et al ‘09)
NOTE 4: The MMSN disk model (a) is supplied mainly for direct comparisons to Igea & Glassgold ‘99 and Turner et
al. ’08 and ‘09; it is possibly not the most realistic situation. The disk model (c), on the other hand, is
probably the most “realistic” of the models, within the context of an α parametrization.
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DISK MODELS (contd)
IONIZATION RATE: from LX , scaling from models of Ercolano et al. 2008, Monte Carlo MOCASSIN code
RECOMBINATION RATE: chemical network calculation:
e -, H+, H2+, H3
+, He+, C+, m+, M+, gr+, gr2+, gr -, gr2 -
3 IONIZATION FRACTION: IONIZATION RATE = RECOMBINATION RATE
RESISTIVITIES:
where
so
where
Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)
0.7 Msun
MMSN
0.1 um grains
Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)
0.7 Msun
MMSN
10 um grains
Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)
0.1 Msun
MMSN
0.1 um grains
Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)
0.1 Msun
MMSN
10 um grains
Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)
0.1 Msun
Σ r ∝ -1
Md M∝ *2
0.1 um grains
Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)
0.1 Msun
Σ r ∝ -1
Md M∝ *2
10 um grains
Conclusions
•Ambipolar Diffusion and grains is very important in disks;
•Depending on Lx & disk surface density (spectral type), can make active disk only a fraction of total disk mass
•In certain cases, *no* active channel exists to star:
(variable accretion?)
•Smaller dead-zone in M stars; also, outer as well as
inner pressure boundary between active / inactive zones
implications for planet formation
THE END