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)

IO H A (Wardle 1999; Balbus & Terquem 2001; Kunz & Balbus 2004)

CONDITION 1: SUFFICIENT IONIZATION FRACTION 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) 1/2 (Turner et al. 2009, Sano & Turner 2008) CONDITION 2: SUFFICIENT ION DENSITY γinρi / Ω > 100 : sufficient # of ion-neutral collisions (otherwise MRI ang. mom. transport nosedives) (Kunz & Balbus 2004; Chiang & Murray-Clay 2007) CONDITION 3: MAGNETIC PRESSURE PB < Pgas : otherwise MRI ineffective

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.

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

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

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