1. DISK ACCRETION in YOUNG STARS & BROWN DWARFS: THEORY vs OBSERVATIONS
Subhanjoy Mohanty (Imperial College London)
Frank H. Shu (UC San Diego), Isabelle Baraffe (ENS Lyon)

2. HIGH SPECIFIC ANGULAR MOMENTUM KEPLERIAN DISK while
MAIN PROBLEMS:
1) HOW TO ACCRETE from
HIGH SPECIFIC ANGULAR MOMENTUM KEPLERIAN DISK
while
2) KEEPING CENTRAL PROTOSTAR SLOWLY ROTATING
and
3) SIMULTANEOUSLY DRIVE COLLIMATED OUTFLOWS
General Qualitative Picture
Jets/Outflows

3. General Problem
All current magnetospheric accretion models assume a dipolar stellar magnetic field.
However
Polarization studies: stellar surface field NOT dipolar.
Average field strengths: ~few kG (Zeeman)
Strong polarization in lines formed in accretion shock
 accretion occurs along ordered field lines
BUT
Accretion hot spots cover 0.1-5% of stellar surface
Net surface polarization ~ 0
 Complex multipolar surface fields

4. X-WIND MODEL: GENERAL STEADY-STATE SCHEMATIC
COROTATION RADIUS (RX)
MASS
MASS
ANG MOM
ANG MOM
Stellar Field
Shu et al. (1997)

5. GENERALIZED X-WIND MODEL
Trapped Flux at X-point: Φt
Fraction of trapped flux involved in accretion (funnel flow): Φt / 3
Same field lines flow into hot spot: (2π R*2) Fh Bh = Φt / 3
Angular momentum removed by trapped flux from funnel flow gas:
(1-f) MD (1-J*) RX2ΩX = ∮[r  (T • n) dS]  (Φt2 / RX)
Disk-locking: ΩX = Ω* = (GM*/RX3)1/2
 general: Fh R*2 Bh  (G M* MD / Ω*)1/2
dipole: R*3 Bh  (G M*5/3 MD / Ω*7/3)1/2 • ^ • •
Mohanty & Shu (2008)

6. Checking the Generalized Model...
DIPOLE X-WIND
DIPOLE X-WIND
CG98
VBJ93
GENERAL X-WIND
GENERAL X-WIND
Johns-Krull & Gaffford (2002)

7. The Cases of V2129 Oph & BP Tau
(Mdot, Fh, Bh directly measured simultaneously)
V2129 Oph:
M* = 1.35 M, R* = 2.4 R, Mdot = 1 X 10-8 M/yr
P* = 6.53 day  RCOROTATION (=RX) = 6.67 R*
Bh = 2 kG, Fh = 5%  measured FhBh = 100 G (Donati et al. 2007)
Multipole X-wind equation (with f = 1/3, ß = 1.21):
 predicted FhBh = 79 G
BP Tau:
M* = 0.8 M, R* = 1.95 R, Mdot = 3 X 10-8 M/yr
P* = 7.6 day  RCOROTATION (=RX) = 7.5 R*
Bh = 9 kG, Fh = 2%  measured FhBh = 180 G (Donati et al. 2008)
 predicted FhBh = 170 G

8. z/R*
/R*
z/R*
/R*
Mohanty & Shu (2008)

9. RX = 10 R* RX = 7.5 R* RX = 5 R* RX = 2 R*
Rescaled solution: RX = 7R*, hot spot latitude = 55°, dominant surface B: l = 1, 3, 5
Fh = 1%  Bh (with fiducial parameters M* = 0.5M, R* = 2R, Mdot = 10-8M/yr) = 8.8 kG
V2129 Oph & BP Tau: RX ~ R*, hot spot latitude ~ 70°, dominant surface B: l = 1, 3, 5
Fh = 2 - 5%, Bh = kG
Mohanty & Shu
(2008)

10. X-Wind Conclusions X-Wind theory: Main ingredient is trapped flux;
Dipole field not necessary; makes general unique prediction consistent with obs.
Multipole fields can match both the observational constraints on surface field and the X-point geometry
Requirement for flux trapping:
Field diffusivity (η) << Gas viscosity (ν)
 Prandtl # (= ν/η) >> 1
(consistent with Prandtl # from MRI analysis: Shu et al. 2007)

11. Disk Winds Requires fast (turbulent) diffusion, and Prandtl # ~ 1,
for sufficient mass-loading and flinging
 disk-gas radial velocity ~ sonic (e.g., Ferreira et al95)
 If disk-wind is primary accretion mechanism out to,
say, 300 AU (Td ~ 20K), then entire disk empties
onto star in ~ 5000 years
 If disk wind over small inner region of disk, then
inner regions of disk will be very optically thin
(e.g., Combet et al. ‘08). Does not appear consistent
with majority of CTTS (except perhaps transition disks)

13. Effect of accretion on evolutionary models
Assumptions: Phenomenological approach (Gallardo, Baraffe, Chabrier 2009)
Accretion through a disk or magnetospheric accretion (non spherical) ---> disturbs only a small portion  of the surface
Lphot=4πR2(1- )Teff -----> 0
Accreted matter brings internal energy: GMdotM/R ≤1
(accretion from a thin disk:  ≤ 0.5)
Fraction  absorbed by the central object
   
radiated away absorbed intrinsic mass increase

14. J. Gallardo, I. Baraffe, G. Chabrier 2009
=0 : accreting object contracts faster structure more compressed than non accreting counterpart Two important timescales: acc=M/M thermal =GM2/(RL) Structure affected if acc << thermal
Mdot=0
Mdot=10-8M/yr

15. Initial masses minit = 1 MJup - 0.1 M
Mdot = Myr-1 applied during t= yr
(=0)
0.1 M
0.05 M
0.01 M
5 Mjup
1 Mjup
log

16. Conclusion on accretion effects
Initial rates Mdot ≤ 10-6 Myr-1 produce small luminosity
scatter in HRD at ages of ~ Myr
A scenario based on very early stages of non steady accretion
(series of short episodes of vigorous accretion Mdot  10-4 Myr-1
of a few 100 yr):
- naturally produces a spread in the HRD at ages of a few Myr:
provides an explanation for the presence of underluminous objects in star formation regions which « look » significantly older
- Produces a significant radius spread as a function of Teff
- Consistent with recent observations of protostars and revised
lifetimes of class 0 - I

17. Conclusion on accretion effects
Concept of a birthline not valid: depends on the accretion history
IMF of very young (<~ few Myr) clusters/SFRs is elusive!!
Accretion effects cannot explain the objects that appear
significantly above the non-accreting tracks; possibly need to
invoke magnetic field effects on convection (a la 2M0535: young
eclipsing binary in ONC with Teff reversal: Mohanty et al. 2009).
This is further bad news for IMF determination in very young regions

19. THE END

20. Include viscous torque (if disk fields present);
FUTURE
X-wind theory:
Include viscous torque (if disk fields present);
Tilted Fields; Non-Axisymmetry;
Simulations:
non-dipole fields with flux-trapping
Disk + B-fields Theory:
understand disk viscosity vs. resistivity better
(require MRI simulations with global and non-zero fields)
Observations required!!!! :
Disk field strength + geometry,
Disk inner edge / jet field geometry,
Jet launch region (e.g., from rotation, vel., density…)

21. Why Important? End-game of star formation, IMF: Accretion + Outflow
+ Blowout of surrounding envelope by outflow
 Final mass of star
Injection of turbulence from combined outflows into cloud
 Regulated star formation
Disk accretion lifetime + disk physics
 planet formation timescale + formation/migration physics

22. Connection with Planet Formation
Mass accretion vs. Outflow rates
Size of stellar field / disk interaction region
Location and extent of jet launching region…
Efficiency of disk magneto-rotational instability (MRI)
Turbulent viscosity vs. Field diffusivity from MRI
Degree of disk ionization
Thickness of ionized surface vs. dead zone in interior
Stellar field geometry
Strength of stellar field vs. Global disk fields…
Efficiency of grain sedimentation & coagulation
Efficiency of core-accretion near ice line
Orbital migration & Eccentricity pumping…
SPECIFICS of
ACCRETION / OUTFLOW
DEPEND on: 
DISK PARAMETERS,
which also CONTROL: 
PLANET
FORMATION / MIGRATION

23. Insights from Brown Dwarfs
Mohanty et al., 2009, in prep.

24. Truncation radius from rotation velocity:
Ω* = (GM*/RX3)1/2  (RX/R*) = (GM*/v*2R*)1/3
 CTTS: RX ~ 6--7 R* , BDs: RX ~ 4--5 R*
Remember: Fh Bh = f1/2 (G M* MD2 / R*5)1/4 (RX / R*)3/4
 in CTTS: FhBh ~ 77G , in BDs: FhBh ~ 17G
If Fh roughly same in both cases (few %),
 Bh in BDs ~ 1/5 Bh in CTTS
Bh in CTTS: ~ 2 kG  in BDs: ~ 500 G
Observationally true!!
(Reiners & Basri 2009, submitted)

25. Maybe expected:
Field VLMS/BDs: ~ few kG, 1/3 R*  young: few 100G
BUT WHY???
Why should field generation mechanism produce field strengths just right to truncate disk at about the same RX/R* in T Tauri stars and BDs, with vastly different masses and accretion rates???
Mystery thickens, or solution:
The RX/R* in CTTS (~6-7) and in BDs (~4-5) imply:
TDISK ~ 1200 K
 Minimum temperature for good field/disk coupling!!

26. ACCRETION DISKS + JETS AROUND YOUNG STARS:
REAL IMAGES

27. ACCRETION DISK AROUND A YOUNG STAR:
ARTIST’S IMPRESSION

28. BOUNDARY-LAYER X-WIND
EXTENDED DISK WIND
Blandford & Paine ‘82, Wardle & Königle ‘93
BOUNDARY-LAYER X-WIND
Hartmann & McGregor ‘82, Shu et al. ‘88
X-WIND
Ostriker & Shu ‘94, Shu et al. ’95, Mohanty & Shu ‘08
EXTENDED STAR-DISK INTERACTION
Ghosh & Lamb ‘79, Königle ‘91

29. CONSTANT of PROPORTIONALITY• •
With: f  MW / MD and   ∫01 ()d , where B = () u
(i.e., =mean magnetic field to mass flux ratio in X-wind)
Wind dynamics: Φt / 3 = 2  f1/2 (G M* MD2 RX3)1/4
Recall: (2π R*2) Fh Bh = Φt / 3 and ΩX = Ω* = [GM*/RX3]1/2
Fh Bh = f1/2Bnorm (RX / R*)3/4 where Bnorm  (G M* MD2 / R*5)1/4
FhR*2Bh = Φt / 6 = f1/2(GM*MD/Ω*)1/2
Angular momentum balance in X-region (entering = leaving):
MD RX2ΩX = (1-f) MD J*RX2ΩX + f MD JW RX2ΩX + 
 f = (1 - J* - ) / (JW - J*)
Assume: J* ≈ 0 ,  ≈ 0  JW ≈ 1 / f ; f = 1/3   = 1.21 (Cai et al. 2008) • • • • • •
Mohanty & Shu (2008)

30. (RX = 5 R*) X-WIND MODEL: DIPOLE FIELD Z Ostriker & Shu (1995) 25.0
22.5
20.0
X-WIND MODEL: DIPOLE FIELD
(RX = 5 R*)
17.5
15.0 Z
12.5
10.0
7.5
5.0
2.5
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
22.5
25.0
 (R/R*)

31. Observational Constraints on Surface Field
Low Net Surface Polarization
High Polarization within Accretion Flow
Small Hot-Spot Covering Fraction (~few %)

32. 2012 onwards..:
Average polarization direction of disk field
(toroidal or poloidal)
690 hrs ‘08-’12:
Inner disk
& surface fields
First data
coming in..
ESPaDOnS / CFHT
Cornell Caltech Atacama Telescope 
Sims by Bessolaz et al.’08
and Zanni et al. ‘07 
2012 onwards..:
Field strength + geometry in disk + jet
on 1 AU scales
ALMA