1. From magnetized cores to protoplanetary disks
Susana Lizano
CRyA, UNAM
219 AAS meeting, Austin, Tx January 8-12,2012

2. Collaborators: Fred Adams (UMich) Antony Allen (ASIAA)
Mike Cai (ASIAA)
Daniele Galli (OAArcetri)
Pat Diamond (UCSD)
Al Glassgold (UCB)
Frank Shu (UCSD)

3. Dense cores in molecular clouds are the cradles of new stars in the Galaxy. Low efficiency of SF ~2-5%
e.g., Evans 2011.
Cores of low-mass stars have: sizes ~ 0.1 pc, T~ 10K, masses ~ few Msun , W ~ few km s-1 pc-1 ,and snt < a
e.g., Lada et al. 2008, Frau et al
Rebull et al. 2011

4. It is under debate if the origin of these dense cores is controlled by magnetic fields or by fast turbulent compression (e.g., Nakamura & Li 2008; Adams & Shu 2010 ; Ballesteos-Paredes et al. 2007; McKee & Ostriker 2007).
Zeeman splitting observations of OH and CN give Bl.o.s. ~10 – 300 mG at gas densities n~3x x105 cm-3. These fields can provide support against gravitational collapse and there are difficult to get rid off (e.g., Troland & Crutcher 2008; Falgarone et al. 2008).

5. l >1 is necessary for instability.
<n(H2)> ≈ 3.2x103 cm-3
<Blos> ≈ 8.2±2.2 mG
<l> ≈ 4.8 (2)
The mass-to-magnetic flux ratio determines the relevance of magnetic support in cloud cores
l=2p G1/2M/F
l >1 is necessary for instability.
After geometric corrections => l~1-4
CN (Falgarone et al. 2008)
<n(H2)> ≈ 4.5x105 cm-3
<Btot> ≈ 0.56 mG
<l> ≈ 2±0.2; ( 1-4 )
log lobs
(Falgarone et al. 2008).
OH (Troland & Crutcher 2008)
log N(H)/cm-2
Crutcher (2005), updated

6. Polarization maps of dust continuum
NIR polarimetry of background starlight
Strong fields not distorted by supersonic turbulent flows
Well ordered magnetic fields.
JHK polariztionearly stage of cluster formation 260 pc
Serpens South (Sugitani et al. 2011)

7. Polarized dust emission:
NGC 1333 IRAS4
(low mass)
IRAS 4A
Girart, Rao & Marrone (2006)
400 AU
Rao et al. 2009: IRAS 16293
1.5”

8. Massive stars W51 G31: 2.5” G31.41+0.31 W51: 2.5” 0.1pc 3 x 105 Lo
Girart et al. (2009)
Tang et al. (2009)

9. Outline
During the gravitational collapse of a magnetized dense core, a frozen B produces a catastrophic magnetic braking that prevents the formation of a rotationally supported disk => magnetic field dissipation must take place to form the observed disks.
The magnetic field dragged into the disk during the gravitational collapse causes sub-keplerian rotation which makes the ejection of cold disk winds difficult and produces faster planet migration.
B field increases the disk stability.

10. Magnetic flux problem for collapse with field-freezing
F * ≈ 1/4 Fcore
M* ≈ 1/2 Mcore
=> l* ≈ 2 lcore (B*~MG)!!
Observationally
l* ≈ (B*~KG)
(Mestel & Spitzer 1956).
Fcore F*
Mcore M*
=> field dissipation must occur during the gravitational collapse of the dense core

11. Magnetic braking in hot molecular core G31. 41+0. 31 (Girart et al
Magnetic braking: torsional Alfven waves in twisted field lines carry away angular momentum
e.g., Mestel (1985); Mouschovias & Ciolek (1999).

12. Collapse of magnetized rotating core did not form a rotationally supported disk
Allen et al. (2003).

13. Gravitational collapse => B trapped in the central star creates a split monopole with Br ~ a3t /(G1/2 r2)
(Krasnopolsky & Konigl 2002; Galli et al. 2006)
streamlines and fieldlines
split monopole
side view
top view

14. => catastrophic magnetic braking
Galli et al. 2006

15. no B field (l = ∞)
with B field (l = 3), in ideal MHD
Price & Bate (2007)

16. no B field (l = ∞)
Fromang et al. (2006)
centrifugal disk
with B field (l = 2)
magnetic pseudo-disk (not supported centrifugally)
top view
side view

17. 1. Magnetic Braking and disk formation
B also seems to prevent cloud fragmentation (Hennebelle & Teyssier 2008; Duffin & Pudritz 2009 Commercon et al. 2011; Hennebelle et al. 2011).
1. Magnetic Braking and disk formation
Suppression of disk formation by catastrophic magnetic braking (Allen et al. 2003, Galli et al. 2006).
Disk formation with field-freezing possible only for clouds with l > 10-80, or l > 3 when the magnetic and rotation axis are perpendicular (Mellon & Li 2008; Hennebelle & Fromang 2007; Siefried et al. 2011; Hennebelle & Ciardi 2009).
But l ≈ 1-4 in molecular cloud
→ field-freezing must be violated
→ field dissipation, non-ideal MHD

18. Numerical simulations of gravitational collapse also show that B suppresses fragmentation for l < 20 unless initial density perturbations are large (50%).
e.g., Hennebelle & Teyssier 2008; Duffin & Pudritz 2009; Commercon et al. 2010, 2011.

19. Gravitational collapse with ohmic dissipation
Shu et al (2006)
uniform field for r <
split-monopole field for r >> rOhm
For Solar System, h ~1020 cm2 s-1 >> microscopic resistivity; rOhm~ 10AU (B in meteorites)

20. Gravitational collapse with ambipolar diffusion, Ohmic dissipation and Hall effect (Li et al. 2011).

21. 1. Summary
Recent numerical simulations of the collapse of rotating magnetized clouds to study magnetic field dissipation during the protostellar accretion phase find that:
one needs anomalous Ohmic resistivity;
AD alone cannot form rotationally supported disks;
iii) Hall effect can spin up the gas but sub-keplerian;
iv) disk could grow when envelope is depleted and magnetic braking becomes inefficient.
(Krasnopolsky et al. 2010; 2011; Li et al. 2011; Machida et al. 2011). Turbulent reconnection could help (Santos-Lima et al. 2010).

22. 2. Magnetized accretion disks
modifies the structure and dynamics of accretion disks
(Shu et al 2007).
Two diffusive processes:
Viscosity n → allows matter to accrete (MRI)
Resistivity h → allows matter to slip through the magnetic field Bz
disk z0
star BR
mass accretion
sink of mass (not flux/ang. mom.) R

23. Bend-pinch-disconnect-twist-reconnect-relax
Only possible in 3D!
Mixing length arguments:
Shu et al. 2007
=> the torque is
“turbulent”MRI viscosity n
In steady-state
(Lubow et al. 1994).

24. Disk B field dragged during the phase of gravitational collapse => sub-keplerian rotation
Sub-Keplerian rotation puts disk matter in a deeper potential well.
Thermal launching is not possible in cold disks.
Sufficient mass loading requires “super diffusion” (h ~ z0 a) which yields supersonic accretion => too short disk lifetimes.
Normal diffusion (h ~ m A z0 a) yields very light mass loading.
f ~ 0.7 for T Tauri disks.
to launch disk winds, they either have to be warm or have a dynamically fast diffusion that imply too short disk lifetimes (< 104 yr) (Shu et al. 2008; Konigl et al. 2009).

25. Planet migration I More than 700* exoplanets are known today.
There is a population of close orbit giant planets with a < 0.1 AU, the so-called ``hot Jupiters’’ (Udry et al. 2007).
This is explained by planet migration: planets and planitesimals form in the outer regions of the circumstellar disk and then migrate inwards because of the gravitational interaction with the disk (e. g., Papaloizou et al. 2007). * I 25

26. Migration type
Armitage I
Type I : a small protoplanet perturbs the disk producing density waves that carry away angular momentum.
Type II : : a massive planet opens a gap; the time evolution is set by the disk viscosity. 26

27. Planet migration in sub-keplerian disks
In sub-keplerian disks, embedded planets orbit with keplerian speeds. Thus, they experience a headwind from the slower gaseous disk. The velocity mismatch results in energy loss from the planet orbit and inward migration (Adams et al. 2009).
Time evolution of the semi-major axis: I
where
and

28. Migration time (Myr) and final planetary core mass( ) versus starting radius r0
Subkeplerian migration dominates over Type I migration inside ~1 AU. The mass accreted by the core is reduced.
Type I only
Type I + Type X
Type I + Type X

29. Dispersion relation for spiral waves
3. Stability of magnetized disks
Dispersion relation for spiral waves
magnetic tension dilutes gravity (ldisk ~ 4-20)
magnetic pressure replaces the sound speed for the magnetosonic speed
Lizano et al. 2010

30. For axisymmetric perturbations m=0, the modified Toomre Q parameter is
< 1 for instability
Sub-keplerian rotation:
=> competing effects :
Strong B enforce sub-keplerian flow:
Magnetic tension and pressure: QM QM

31. Stability of magnetized disks of Shu et al. (2007).
unstable
stable

32. Formation of giant planets via gravitational instability in magnetized disks.
Short cooling times:
Get rid of the magnetic flux:
Gammie 2001
These coupled constraints make it more difficult to form planets this way and limit their formation to take place at large radii.

33. The bulk of field dissipation occurs in accretion disks (lstar ≈ 102-103).
Conclusions
ldisk ≈ 4-16
lcloud ≈ 1-4
Magnetic field dissipation is needed to avoid catastrophic braking and form disks and normal stars.
B fields dragged in disks produce sub-keplerian rotation which affects the ejection of winds and planet migration.
B fields increase disk gravitational stability.
ALMA will be able to measure B and rotation curves with unprecedent spatial resolution and test these theories. BlAST-pol will measure B direction in molecular clouds.
CN 3mm, 1mm

34. Magnetic fields are dynamically important for star and planet formation.
Thank you!

36. Maximum disk mass (m=0).
To be stable to axisymmetric perturbations, the maximum mass a disk can have can be obtained by setting the surface density profile such that
Magnetic pressure and tension increase this maximum disk mass w.r.t. the non-magnetized disk by a factor ~ 2-8 => more massive disks stable!
Note that global stability to m=1 modes in B=0 disks require
Shu et al. (1990)

37. Disk truncation by stellar magnetosphere
In X-wind theory, the inner cutoff radius is given by
Planets cannot migrate inside the X-point through mechanisms involving disk torques because there is no disk material.
Extrasolar planets recently discovered have r ~ 0.02 AU. Planets could migrate to this very tight orbits during FU Ori outburst, when increases a factor of 25 (but short events).
Semimajor axis of
``hot Jupiters’’:
4-day orbits.

38. 1. OH Zeeman observations (Troland & Crutcher 2008)
OH lines probe densities cm-3 in molecular clouds
Previous observations: Crutcher (1999) with Arecibo (beam 3’ at n =1.666 GHz)
34 dark clouds, 9 detections
<n(H2)> ≈ 3.2x103 cm-3
<Blos> ≈ 8.2±2.2 mG
<l> ≈ 1.4

39. 2. CN Zeeman observations (Falgarone et al. 2008)
CN lines probe densities cm-3 in molecular clouds
Previous observations: Crutcher et al. (1996, 1999) at IRAM-30m (beam 23” at n =113 GHz)
14 cloud cores, 7 detections
<n(H2)> ≈ 4.5x105 cm-3
<Blos> ≈ 0.56 mG
<l> ≈ 2±0.2

40. 5. Test of ambipolar diffusion models (Crutcher, Hakobian & Troland 2008)
Ambipolar diffusion produces supercritical cores (l>1) surrounded by subcritical envelopes (l<1)
CHT performed OH Zeeman measurements to obtain the ratio of l between the envelopes and the cores of 4 clouds
Ciolek & Mouschovias (1994)

41. 7.8’ GBT beam
20’
3’ Arecibo beam

42. Cloud core
lcore /lenv
L1448CO
0.02 ± 0.36
B217-2
0.15 ± 0.43
L1544
0.42 ± 0.46 B1
0.41 ± 0.20
Mouschovias & Tassis (2008) criticism:
Inappropriate to average the 4 GBT measurements;
Inappropriate treatment of error propagation;
Inappropriate to treat non-detections as detections;
Data show field reversals in envelopes;

43. In steady-state, the inward dragging of field lines by accretion balanced by outward field diffusion. Consistency requires:
Viscosity n → mixing quantities on large scale R
Resistivity h → reconnection of BR across small scale z0
and

44. Theory vs. observations

45. Results object Mé dMé /dt age D Rd Md f (M8) (M8 yr-1) (yr) (AU)
T Tauri
0.5
1x10-8
3x106
10-2.5
300
0.03
0.66
Low-mass protostar
2x10-6
1x105 1
320
0.2
0.96
High-mass protostar 25
1x10-4
1500 10

46. QM > 1
Scale height parameter

47. Type I: a small protoplanet perturbs the disk producing density waves that carry away angular momentum. The back reaction produces planet migration depending on the net torque.
Type II: a massive planet opens a gap in the disk ending Type I migration . The time evolution is set by the disk viscosity.
(e.g., Papaloizou et al. 2007)
Type III: intermediate mass planets open a partial gap, corrotation torques can dominate over Linblad torques. 47