Magnetic Fields: Recent Progress and Future Tests Shantanu Basu The University of Western Ontario EPoS 2008, Ringberg Castle, Germany July 29, 2008.

Magnetic Fields: Recent Progress and Future Tests

Shantanu BasuThe University of Western Ontario

EPoS 2008, Ringberg Castle, GermanyJuly 29, 2008

Collaborators:

Glenn E. Ciolek (RPI, USA)Takahiro Kudoh (NAO, Japan) Eduard I. Vorobyov (ICA, Canada)Wolf Dapp (UWO)James Wurster (UWO)

Poster 02

Model for L1689B and magnetic field line curvature of OMC1

Many Thanks to

Molecular Clouds: Subcritical or Supercritical?

1/ 22 GB

1, 1, or 1 ?

Progenitors are H I CloudsHeiles & Troland (2008)

Column density

Blos

20 -210 cm

subcritical

supercritical

Flux freezing in HI gas Critical or supercritical MC formation requires significant accumulation of mass ALONG the magnetic field.

MC Accumulation Constraints

1/2 6 3

1

6 3 6

150 pc,2 1 3 10 G 1 cm

150 km/s.1 3 10 G 1 cm 10 yr

B B nL

G

L B n tv

t

Mestel (1999), Stellar Magnetism, and earlier papers quotes 103 above, not 150.

Bottom line: Highly supercritical MC and rapid formation time t is trouble!

GMC Fields align with Galactic B

H. Li et al. (2006)

Direction parallel to galactic plane

Goldsmith et al. (2008), 12CO emission

Striations of gas emission consistent with magnetically-dominated envelope.

Taurus Molecular CloudHeyer et al. (2008): Pol. maps → low plasma beta in envelope subcritical ? Most mass is in low density envelope (Goldsmith et al. 08), so probably, yes.

Pipe Nebula

Alves, Franco, & Girart (2008)

Magnetically regulated cloud formation?

Pipe (and Taurus) formed by flow or contraction along B?

Most mass is in the low density envelope

Kirk, Johnstone, & Di Francesco (2006)

Perseus Molecular Cloud

Subcritical common envelope? Also turbulent. Highly ionized?

Cores only at AV > 5 mag, threshold for shielding of UV?

Ambipolar Diffusion time in MC’s

2

2

21

2, where

1.4i

AD ni ni i iHA ni i H

mLn w

v m m

2 2 25

4 3 71.65 10 yr

0.1 pc 10 G 10 cm 10n i

AD

n xL B

For CR ionized regions

For UV ionized envelopes, xi is ~ 10-4 and AD is very long effective flux freezing.

Much larger than geometric cross sec. due to polarizability of H2

1 is interesting!

1/ 27 4 -310 10 cmi nx n

numbers from Ciolek & Basu (2006)

AD

0,g m

s

Z

c

0, 10g m

s

Z

c

ambipolar diffusion time

For CR ionized sheet, with half thickness Z0.

Magnetic Fields and Origin of the CMF/Massive Stars

Ciolek & Basu (2006)

22

, ,4g m g mM

Preferred fragmentation mass

can vary dramatically even with a narrow range of ,0

1/27

4 3

0.2

1010 cm

ni

i

nx

,0 0 flux freezingni

Standard value for CR ionized region

Magnetic Fields and Origin of the CMF/Massive Stars

Basu, Ciolek & Wurster (2008), arXiv: 0806.2482

0 1.1

0 2.0

0 0.5

Periodic isothermal thin-sheet model. Initial small amplitude perturbations. B is initially normal to sheet.

0' / (2 ), etc.x x Z

Column density and velocity vectors (unit 0.5 cs)Note irregular shapes with NO strong turbulence.

Narrow lognormal-like. High-mass slope much steeper than observed CMF/IMF.

“Core” = enclosed region with

.20, nn

Basu, Ciolek, & Wurster (2008)

Distributions peak at different values for each

CMF’s for fixed MTF

Magnetic Fields and Origin of the CMF/Massive Stars

Basu, Ciolek & Wurster (2008)

Data from Nutter & Ward-Thompson (2007)

Add results from a range of models with =0.5 to 0 = 2.0.

Cumulative histogram of 1524 cores from over 400 separate simulations

Get a broad distribution of core masses if 0 varies in a single cloud.

10 0 2

B

B

Critical Weak

Magnetic Field Line Curvature Reveals IC’s

Basu, Ciolek & Wurster (2008)

Modes of Subcritical Fragmentation

Basu, Ciolek, Dapp, & Wurster (2008)

standard quasistatic AD

flux freezing no collapse

Turbulence accelerated AD; Fatuzzo, Adams, Zweibel, Heitsch.

nonlinear flow accelerated AD; Li, Nakamura

These apply to CR ionized regions.

50 02 / 2 10 yrst Z c

Turbulent Fragmentation with B and Ambipolar DiffusionThin disk approximation Li & Nakamura (2004)

(a)-(e) subcritical (0.83model, (f)-(h) supercritical ( = 1.25model.

vk2~ k -4 spectrum – really a large-scale flow

note filamentarity and velocity vectors

time unit = 2 Myr; box width = 3.7 pc

3D Turbulent Fragmentation with B and AD

Kudoh & Basu (2008)

42 kvk

Nonlinear initial velocity field

rms amplitude

0 0.5

yr102 50 t

Gas density in midplane (z=0)

A vertical slice of gas density

Nonlinear IC

Linear IC

using 64 x 64 x 40 cells

allowed to decay

box width = 2.5 pc

3 Alfv c va s

trans-Alfvénic

3D Turbulent Fragmentation with B and AD

Kudoh & Basu (2008)

What’s really happening?

.4

Bv Bnt

ni B B Bn

28 2csB

2 3/2 22

2 2 2L LL n i n

ADv B BniA

is a proxy for .

Early turbulent compression

5/2 quickly as L LAD Then, higher density region evolves with near vertical force balance

1/2 more slowlyAD

Rapid contraction when/where 1.

Thin Sheet vs. 3D

Bottom line: 3D nonideal MHD fragmentation simulations confirm basic features of thin sheet models: kinematics, fragment spacings, etc.

Kudoh, Basu, Ogata, & Yabe (2007) confirm gravitational fragmentation (small-amplitude) models of Basu & Ciolek (2004), Basu et al. (2008)

Kudoh & Basu (2008) confirm turbulent fragmentation models of Li & Nakamura (2004), Nakamura & Li (2005).

Super-Alfvénic Turbulence ↔ Highly Filamentary, Large Velocities

Basu, Ciolek, Dapp, & Wurster (2008)

subcritical mass-to-flux ratiotrans-Alfvénic turbulence

supercritical mtoflx ratiosuper-Alfvénic turbulence

Each compression leads to rapid, high velocity, efficient collapse (no rebound)

Decaying initial supersonic velocity perturbations in two thin-sheet models.

Velocity Fields Tell the Story

Conclusion 1: These differences are testable!

Conclusion 2: Highly turbulent Fourier space driving in periodic boxes is NOT the way to go. Models of turbulence require GLOBAL approach.

Future Trends – MC Formation

Black arrows are velocity vectors. B field initially along x-direction. Ambipolar diffusion not included.

Fabian Heitsch’s talk, and e.g. Heitsch et al. (2007)

Molecular cloud formation and evolution starting from converging H I flows. Not periodic. No Fourier space driving. Thermal instability (and other instabilities) occur.

Left: inclusion of B field; Hennebelle et al. (2008), Banerjee et al. (2008). See poster 01 by Robi Banerjee. Use AMR codes.

Cluster Forming Region with B

Price and Bate (2008)

SPH simulation of cluster forming region with supercritical flux-frozen magnetic field. Leads to lower star formation efficiency and creation of magnetically dominated “voids”.

time

Initi

al m

ag.

field

str

engt

h

Future Trends – Toward Global nonideal MHD Models

Nakamura & Li (2008)

turbulent diffuse halo

fragmented nearly critical sheet

supercritical dense cores

Magnetic field lines in orange

3D with ambipolar diffusion, in a patch of a larger cloud.

Future Trend - Observing Simulations

Observations

Simulations

1. Star Formation Taste Tests, Alyssa Goodman, Focus group, Thursday.

2. Helen Kirk’s talk today. “Observe’’ magnetic turbulent ambipolar diffusion simulations. Compare relation of core velocity dispersion to that of the surrounding region.

Focus on Single Objects Also Important

Ang

le (

degr

ees)

AU

Ang

le (

degr

ees)

Poster 02, Wolf Dapp & S. Basu

This massive star forming region fit by mildly supercritical model.

01.0 2.0

OMC-1 Schleuning (1998)

The Later Stage of Core Collapse

Girart, Rao, & Marrone (2006)

Catastrophic Magnetic Braking if Field is Frozen

Allen, Li, & Shu (2003)

No Keplerian disk forms.

Lever arm is relatively very BIG!

Disk Formation with Magnetic Field

Mellon & Li (2008)

Flux freezing disk forms only if ≥ 100 ! Shown on left.

Can such a highly supercritical region be achieved, and within 100 AU of protostar?

Black lines represent magnetic field. Centrifugal disk enclosed by white line.

Magnetic dissipation

Ambipolar diffusion

Ohmic Dissipation

2

2 2

1AD

A ni

L

v B

Neutral-ion colliison time. More generally, neutral-charged-grain collisions too. Grains in turn affect ion numbers. In AD, field does not decay but neutrals do not advect field fully.

2

4OD

cL

Resistivity. Depends on e-i and e-n collisions generally. A true decay of currents and magnetic field. Eventually more effective than AD in reducing central flux.

3D Nested Grid Simulation with Ohmic Dissipation

Machida et al. (2007)

Also, talk by Ralph Pudritz today

Calculation stops when central star mass ~ 0.01 solar mass. Mass to flux ratio > 100 times critical value within ~ 1 AU radius.

based on Nakano et al. (2002)

Thin Sheet collapse with Ambipolar D. & Ohmic D.

(

mtf

rat

io)

Tassis & Mouschovias (2007)

AD dominates OD dominates

Calculation stops when central star mass ~ 0.01 solar mass. Mass to flux ratio > 100 times critical value within ~ 1 AU radius.

Is B too strong in the late phases?

• How do observed disks form? Magnetic dissipation may not resolve MB catastrophe• Alternate explanations may be needed: outflow blows away envelope and eliminates angular momentum coupling? Main disk forms after outflow begins?• A 3D calculation with magnetic dissipation (microphysics can be tricky) that can model the full accretion phase is necessary for the future.

Role of B in the Early Phases

• Interplay of gravity, magnetic fields, and ambipolar diffusion yields a broad CMF, including massive cores. This process is independent but not mutually exclusive of competitive accretion and turbulent fragmentation.

• Magnetic field line curvature at core edges may be used as a proxy for measuring ambient mass-to-flux ratio

• Hard to avoid conclusion that overall cloud mass-to-flux ratios are close to critical value. Common envelope likely slightly subcritical but entire cluster forming regions (OMC1) may be supercritical

• Three-dimensional simulations confirm the mode of Turbulence Accelerated Magnetically Regulated Fragmentation. Formation of quiescent cores in ~106 yr

• Local (periodic) highly turbulent models predict very large infall and have other drawbacks. Future global approaches, including ambipolar diffusion.