ANGULAR MOMENTUM TRANSPORT In T TAURI ACCRETION DISKS: WHERE IS THE DISK MRI-ACTIVE?

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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)

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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). I O H A. (Wardle 1999; Balbus & Terquem 2001; Kunz & Balbus 2004). - PowerPoint PPT Presentation

Transcript of ANGULAR MOMENTUM TRANSPORT In T TAURI ACCRETION DISKS: WHERE IS THE DISK MRI-ACTIVE?

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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)

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(Wardle 1999; Balbus & Terquem 2001; Kunz & Balbus 2004)

I O H A

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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)

1/2

(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

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Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)

0.7 Msun

MMSN

0.1 um grains

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Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)

0.7 Msun

MMSN

10 um grains

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Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)

0.1 Msun

MMSN

0.1 um grains

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Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)

0.1 Msun

MMSN

10 um grains

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Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)

0.1 Msun

Σ r ∝ -1

Md M∝ *2

0.1 um grains

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Mohanty & Ercolano in prep. (Disk models by P. D’Alessio)

0.1 Msun

Σ r ∝ -1

Md M∝ *2

10 um grains

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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

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THE END