Theory of Magnetic Fields in

Star and Disk FormationSHANTANU BASUMagnetic Fields or Turbulence: What is the Critical Factor in

Star and Disk Formation, National Tsing Hua University,

Hsinchu, Taiwan

06 Feb 2018

Magnetic Field Can Affect

➢Turbulence

➢Cloud Formation

➢Core/Filament Formation

➢Star Formation Rate/Efficiency

➢Disk Formation

➢Outflow Launching

➢Protostar Formation

➢Accretion Process

My MT thermometer:

0.1

Turbulent ICs from Expanding

Shells

Mol Cloud Progenitors are subcritical H I

Clouds Heiles & Troland (2008)

Column density

Blos

20 -210 cm

subcritical

supercritical

Flux freezing in HI gas Molecular clouds formed by HI

accumulation may have significant subcritical component.

Heiles & Troland (2005)

Can ambipolar diffusion create

supercritical m-t-f post shock?

➢ Inoue & Inutsuka (2008, 2009) conclude

AD in WNM not sufficient to allow MC

formation in flows unless they are largely

parallel to the ambient magnetic.

➢ See also Kortgen & Banerjee (2015),

Chen & Ostriker (2014), Inutsuka et al.

(2015)

Inutsuka et al. (2015)

Molecular Cloud 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) quotes 103 above, not 150.

Bottom line: Highly supercritical “initial” condition for MC is unlikely.

Cloud Initial Conditions

Hennebelle, Banerjee, Vazquez-

Semadeni+ 2008

Christie, Wu, Tan (2017) – GMC collisions with AD.See also Vazquez-Semadeni et

al. (2011), Heitsch et al. (2009)

➢ Collision of HI clouds can lead

to cloud formation

➢ Hennebelle et al. (2008) find

flat B-n relation for low

densities and B ~ n0.5 at

densities above 103 cm-3.

B- relation

But what is happening physically at

turnover region?

Crutcher et al. (2010)

0.65

Tritsis et al. (2015)

Basu (2000)

B

1/2

vB

Fit constant value of B at low

density, a turnover point, and

at densities above turnover. Best fit is virial relation

v Av

Model molecular data separated from

atomic data, and include horizontal

error bars.

in driven turbulence ideal MHD

0 16 0 1.6

Driven turbulence. Mach

number =10.

PS Li, McKee, Klein (2015)

1/2 00

0

2 GB

Moderate field model

Weak field model

0 ff1.6 : 0.62 0.11 at 0.57 ,

0.70 0.06.

t

0 16 : 0.57 0.05.

However Mocz et al. (2017)

find ~ 2/3 for weak field

model transitioning to ~ 1/2

for strong field model.

Important Questions

➢ How physically is subcritical to supercritical

transition accomplished? Does it require a

unique density?

➢ Does subcritical to supercritical transition take

place exactly when HI to H2 conversion takes

place?

➢ Or, is there a significant H2 envelope that is also

subcritical?

How to get to supercritical

collapse?

➢ Wait for flow along FLs to create supercritical m-t-f

Or, if cloud has inherited turbulence:➢ Turbulence accelerated fragmentation via

enhanced ambipolar diffusion (AD)

Or, if negligible turbulence:➢ Transcritical fragmentation (gravity-AD hybrid

mode)

➢ Subcritical fragmentation, inevitable win of gravity

due to AD

Transcritical Fragmentation➢ Related to ~ pc scale

clump formation?

➢ Massive prestellar

cores?

➢ Two-stage

fragmentation (Bailey

& Basu 2012, 2014)

2 p

c

Ciolek &

Basu (2006)

flux freezing

with AD

with AD

Ba

su,

Cio

lek, &

Wu

rste

r (2

009

)

Subcritical Fragmentation

➢ Occurs on classical AD timescale ~ 10 tff for

standard xi

➢ Subsonic infall motions

➢ Long gestation period

means subcritical cores

of moderate density

enhancement would

be visible

Basu, Ciolek, &

Wurster (2009)

Turbulence Accelerated AD (TAAD)

yr102 5

0 t

2 4 allowed to decaykv k

Kudoh & Basu (2008) – 3D model similar to thin sheet

models of Li & Nakamura (2004), Nakamura & Li (2005),

Basu, Ciolek, Dapp, & Wurster (2009).

0 00.5, .t Av v

Gas density in midplane (z = 0)

A vertical slice of gas density

Turbulence Accelerated AD

,0 0 0

1 if

3AD t Av v

0 0if .t Av v

Kudoh & Basu (2014)

Ambipolar diffusion time shortened in

predictable manner in oscillatory filamentary

evolution.

Filaments in Molecular Clouds

Is 0.1 pc a universal width?

Arzoumanian (2013)

Palmeirim et al.

(2012) – B

perpendicular to

massive filament

B211/213

Arzoumanian et al. (2011)

IC 5146

Ribbon Model Auddy, Basu, & Kudoh (2016)

Quasi-magnetohydrostatic ribbon

viewed at various viewing angles yields relatively flat observed width-N

correlation.

Tomisaka (2014):

Ribbon tends to

fragment along

length if line

mass to flux ratio above critical

value

Image of TAAD

scenario – Basu

et al. (2009).

Striations

Tritsis & Tassis (2016)

➢ Alfvén modes couple to

magnetosonic modes

➢ Density enhancements due

to magnetosonic modes

Density map

from 2D

simulation

with

spectrum of

Alfvén waves

initially

present.

CO integrated intensity

map of striations in

Taurus

Column Density PDFAuddy, Basu, & Kudoh (2018)Three distinct outcomes.

Supercritical fragmentation – Subcritical fragmentation – Turbulence Accelerated AD in subcritical cloud

Pure power laws of different slope in supercritical and subcritical fragmentation respectively.

For TAAD, a natural transition from lognormal pdf to power law at transition from subcritical to

supercritical gas.

Supercritical

contraction

consistent with

2.ln

dN

d

Effect of feedback – SFR/SFE

Federrath 2014

Wang, ZYLi, Abel, Nakamura (2010)

Add sink cells and protostellar outflow prescription to track long term

evolution.

Nakamura & Li (2008)

Subcritical cloud,

including AD

Supercritical clouds

Top to bottom: HD, +turbulence,

+MHD, +outflows

B is effective at spreading

outflow energy, keeps

cloud stirred up.

HD

+turbulence

+B

+outflow

Zoom in on Disk Formation

Magnetic Braking Catastrophe

Allen, Li, Shu (2001)

➢ 1990s: MB effective in subcritical

cloud, but ineffective in supercritical

prestellar core collapse: Tomisaka et

al. (1990), Basu & Mouschovias (1994)

➢ Allen, Li, & Shu (2001) – No! MB is

revitalized in protostellar phase, ideal

MHD

➢ MB catastrophe firmly established by

Mellon & Li 2008, 2009, Galli et al. 2006,

Hennebelle & Ciardi 2009

Magnetic Flux Loss in aligned rotator – enables

small class 0 disk within first core region

Tomida+ (2015)

used 3D

nonideal MHD

calculation to

find ~ 5 AU disk

at end of first

core phase

• Dashed lines are for flux-freezing model (no magnetic diffusion)extreme flaring of field lines long lever arm magnetic braking catastrophe

• Solid lines are for model with magnetic diffusion; field lines more relaxed (straight)

-4

0

-2

0

0

2

0

40

AU

Dapp, Basu & Kunz (2012)

– thin disk calculation

MB catastrophe

Centrifugal disk

Other causes of disk formation –

possibly large class 0 disks

➢ Misaligned rotation and magnetic axes (Hennebelle &

Ciardi 2009; Li, Krasnopolsky & Shang 2013)

➢ Magnetic flux loss due to turbulence induced

reconnection (Santos-Lima et al. 2012, 2013)

➢ Tangling of field lines due to turbulence leading to lower

efficiency of magnetic braking (Seifried et al. 2012, 2013)

➢ Enhanced magnetic flux loss due to pseudodisk warping

(Li et al. 2014)

3D nested grid resistive MHD

simulations: self consistent outflows

Outflows launched from

edge of first core

Machida et al. (2008)

and later papers

Jets launched

from just outside

second core

r zB B B

r zB B BSignificant Ohmic

resistivity within first

core region.Simulations typically

followed to early class 0

phase.

New insight into outflowsF. Alves, Girart, Caselli + 2017

➢ Class I object BHB07-11, in B59: outflow

launch site is ~ 100 AU from center

➢ Coincides with disk edge/centrifugal barrier

as revealed by gas kinematics

Velocity channel map

Magnetocentrifugal effect

at disk edge in late

accretion phase?

Alignment of B and J – Effect of the

Hall term

➢ Effect of an additional Hall current due to

e-i drift

➢ When B and J are parallel, the Hall effect

aids magnetic braking. When B and J

antiparallel, it weakens magnetic braking.

Can get bimodal disk size evolution

(Tsukamoto+2015, Wurster+2016, also

Braiding & Wardle 2012).

➢ In antiparallel case, can get a counter-

rotating envelope (Krasnopolsky et al.

2011, Tsukamoto et al. 2015, Wurster et al.

2016)Tsukamoto et al. (2015) – details

depend on value of Hall resistivity

Small

disk: B, J

parallel

Large

disk: B, J

anti-

parallel

Summary and Key Questions

➢ Exactly how/when is supercritical gas created? This

affects fragmentation mode, B-rho relation, column

density pdf

➢ Magnetic fields can explain ribbon-like and striation

features in molecular clouds

➢ Magnetic fields provide an efficient means of

spreading turbulent energy in clouds

➢ Disk and outflow formation depend sensitively on B

and non-ideal MHD. Are there self-regulation

mechanisms in play?