太陽質量程度の星の形成過程

Contraction of Magnetized Rotating Clouds and

Outflows

Kohji Tomisaka

with collaborators: M. N. Machida (Kyoto U.), K.

with collaborators: M. N. Machida (Kyoto U.), K.

Saigo

Saigo (NAOJ), T. Matsumoto ((NAOJ), T. Matsumoto (HoseiHosei U.), U.), Hanawa (Chiba U.)

Hanawa (Chiba U.)

星形成における磁場について---ＡＬＭＡに向けて

太陽質量程度の星の形成過程

分子雲 高密度コア コアの動的な収縮

前主系列星段階 (T Tau型星)

光、近赤外線源 主系列星段階

水素核融合

収縮する星の 重力エネルギー

降着するガスの 重力エネルギー

赤外線源 原始星段階

≈ 10⁵ yr

≈ 10¹⁰ yr

≈ 10⁷yr

星なしコア

星形成の概念図

1

2 2

2

2 0

d I

dt = (T − T )+ Μ + W

ビリアル定理

•

•

•

ρ ρ φ

π

∂

∂ + ⋅∇

F HG I

KJ

u u u B B

t ( ) p 1 ( )

4

r

星形成の条件 ^{ビリアル定理}

•

•

•

•

•

I =

z

T =

F

H I

K

z

1 2

3 2 ρ 2

T P_th dS P V

S cl

0 0

3

=

z

Μ

Φ Φ

= + ⋅ ⋅ − ⋅

≈ −

≈

F

HG I

KJ

z z z

z

B dV dS B

dS B B

dV R R

S S

B B

2 2

2

0 2

2

2 2

0

8 8

8

1 6

π π

π π

(r B B n) r n

W dV a GM

= −

z

2

P R

P₀

Φ_B = πR B₀² ₀

R₀

B₀

星形成の条件 ^{ビリアル定理}

Ｂ＝０の場合（ジーンズ質量）

•

•

•

•

4 4 3

5 0

3

0 3

πPR πP R a GM2

− − R =

P c c M

s s R

= ² = ² 3 ₃ ρ 4

π

P c M R

aGM R

s 0

2 3

2 4

3 4

3

= − 20

π π

R P

安定 不安定

P c

G M

s 0

8

3 2

,max = 3 15.

M M c

G P

J

< = 1 77 s

4 3 2

0

. _/ 1 2_/

1

2 2

2

2 0

d I

dt = (T −T )+ W

P R

P₀

星形成の条件 ^{ビリアル定理}

磁場が存在する場合

•

•

•

•

Φ_B ≡ B R₀

π

GM R

2 B

2 2

z

1

2 2

2

2 0

d I

dt = (T − T )+ Μ + W

4 4 3

5 0

3

0

3 2 2

π PR πP R G

R M M

− −

c

h

3

5 3

2 2

2

GM

R R

Φ = ΦB

π

星形成の条件 ^{ビリアル定理}

•

•

•

•

P P c

G M

M M

s

0 0

8

3 2

2 3

3 15 1

< = −

F

H I

L K

NM O

QP

−

,max . ^Φ

M M c

G P M M

cr

< = s

1 77 −

1

4 3 2

0

1 2 2 3 2

.

/ / /

b

g

R P

安定 不安定

P_0,max

M < M_Φ

M > M_Φ M < M_Φ

M M M M_cr

>

RS

T

M_Φ < M < M_cr

星形成の条件 ^{ビリアル定理}

(M > M_Φ)

/ _B 5 / 3 0.24

G M Φ c π =

臨界雲 M

G M R B

Φ = 1 ΦB ≈

3

5 55 0 2 100

2

π

e

j e

j

磁気静水圧平衡

R₀

B₀

P₀

磁束管内の質量と角運動量を保存 平衡形状

≈プラズマの閉じ込め

星形成の条件 ^{磁気静水圧平衡}

Mass Loading Angular Momentum Loading

中心密度の異なる一連の解（外圧、磁束＝一定）

β = 1 β = 0 02 .

ρ_c: 2 ⇒10³ ρ_c: 2 ⇒10³

星形成の条件 ^{磁気静水圧平衡}

最大質量

最大質量

ρ ρ

/

M

Φ

= const Φ

D

磁気静水圧平衡

星形成の条件

星間雲を貫く磁束

磁場は自己重力 を支えることがで きる

0

2

0 p_ext /(B / 8 )

β = π

pext^一定

t ≈

τ

t ≈10

τ

磁気雲の重力収縮

星形成の条件

/ _B 0.17 1/ 2

G M Φ c π

3 / 2

2 4

1/ 2 3 / 2 1/ 2

0

1.39 1 0.17

/

s cr

c c

M M c

G σ B G P

⎡ ⎛ ⎞ ⎤−

⎢ ⎜ ⎟⎟ ⎥

< = ⎢⎢⎣ −⎜⎜⎜⎝ ⎟⎟⎠ ⎥⎥⎦

Zeeman

Upper limit C.F.

1/ 2π

Heiles & Crutcher (2005)

13CO map of Taurus molecular cloud observed by Nagoya 4m radio telescope.

Taurus Molecular Cloud

CO

Star Formation in Molecular Cloud

T Tauri Stars

Protostars

Molecular Cores C O

C¹⁸O integrated intensity map of HLC2 in Taurus molecular cloud.

This shows the molecular cloud consists of many molecular cores.

H¹³CO integrated intensity map of prestellar (left) and protostellar (right) cores in Taurus molecular cloud observed by Nobayama 45m radio telescope

Cores with/without Protostars

IR Source

H¹³CO

Starless Core (prestellar core)

Protostellar Core

Molecular Cloud Cloud Cores Dynamical Contraction of Core

Pre-main-sequence Stars (T Tau. Stars)

Opt, Near IR Sources Main-sequence Stars

Hydrogen Nuclear Fusion

Gravitational Energy of Stars

Accretion Energy

IR Sources Protostars

≈ 10⁵yr

≈ 10¹⁰yr

≈ 10⁷ yr

Starless Cores

Star Formation of ~M stars

Spherical Collapse

• isothermal γ= 1 ρ<ρ_A=10^-13 g cm^-3

9run-away collapse 9first collapse

• adiabatic γ= 7/5 ρ_A <ρ< ρ_B^{= 5.6 10-8 g}

cm^-3

9first core 9outflow

9fragmentation

• H₂ dissociation γ= 1.1 ρ_B <ρ< ρ_C^{= 2.0}

10^-3g cm^-3

9second collapse

Gas ( ) contracting under the self-gravity

cf. Masunaga & Inutsuka (2000)

Second Collapse γ= 1.10

ρ_B

ρ_A

ρ_C

First Collapse γ= 1

0, 0

= Ω = B

Larson (1969)

Temp-density relation of IS gas.

(Tohline 1982)

log n_c (cm^-3)

First Core γ=7/5

10 s13

× 10 s13

× 10 s13

× 10 s13

×

10 s13

× 10 s13

×

logr

Runaway Collapse

Larson 1969, MNRAS, 145,271

(1) Convergence to a power-law structure

(2) Increase of central density in a finite time.

Isothermal spherical collapse shows:

半径

(3) Only a central part contracts.

( )r r 2

ρ ∝ ⁻

This is called

“runaway collapse.”

First core

log ρ

How about a Rotating Magnetized Cloud?

1. In case with B and Ω, a runaway contracting disk is made. As a consequence,

(a) A flat first core is born.

(b) Outflow is driven by a twisted B-field and a rotating disk.

(c) B-field transfers the angular momentum from the contracting disk to the envelope.

3. Star formation process is controlled by the rotation speed of the first core.

(a) A slow rotator evolves similarly to the B=Ω=0 cloud.

(b) A first core with Ω in a finite range,

(c) A fast rotator fragments, which leads to binary formation.

, ≠ 0 B Ω

Tomisaka (1998) ApJ 502, L163-L167

Ω B

Initial Condition

periodic boundary

axisymmetric ρ perturbation nonaxisymmetric ρ perturbation

L=1

L=2 L=3

Nested grid Nested grid

Numerical Method

The coarsest grid Nested 4-times finer grid

Ω ρ Ω ρ

ビデオクリップ

Nested 2

-times finer grid

Ω ρ

density exceeds ρ_A (first core formation), outflow begins to blow.

(2) In this case, gas is accelerated by the

magnetocentrifugal wind mechanism.

(3) 10% of gas in mass is ejected with almost all the angular momentum.

Angular Momentum Redistribution in Dynamical Collapse

• In outflows driven by magnetic fields:

– The angular momentum is transferred effectively from the disk to the outflow.

– If 10 % of inflowing mass is outflowed with

having 99.9% of angular momentum, j

would

be reduced to 10

j

.

Disk

B-Fields Outflow

Mass

Inflow → star Outflow Ang.Mom.

Tomisaka (2000) ApJ 528 L41-L44

Angular Momentum Problem

• Specific Angular Momentum of a New-born Star

• Orbital Angular Momentum of a Binary System

• Specific Angular Momentum of a Parent Cloud Core

• Centrifugal Radius

2 -1

16 * 2 -1

* 6 10 cm s

2 10day

R P

j R

⎛ ⎞ ⎛ ⎞

≈ × ⎜ ⎟ ⎜ ⎟

⎝ ⎠

⎝ ⎠

j R

cl -1 -1

2 -1

pc kms pc cm s

≈ ×

F

HG I

KJ F

HG I

KJ

5 10 0 1 4

21

2

.

Ω

2 1 2

21 2 -1

0.06pc

5 10 cm s

c

j j M

R GM M

⎛ ⎞−

⎛ ⎞

= ≈ ⎜⎝ × ⎟ ⎜⎠ ⎝ ⎟⎠

R

>> R

j

>> j

1/ 2 1/2

19 bin 2 -1

bin 4 10 cm s

100AU

R M

j M

⎛ ⎞

⎛ ⎞

≈ × ⎜⎝ ⎟ ⎜⎠ ⎝ ⎟⎠

j

>> j

bin

R

>> R

Tomisaka 2000 ApJL 528 L41--L44

Angular Momentum Distribution

L ( ρ ρ ) ρ rv dV

ρ ρ

> ≡

>

z

1

1

M ( ρ ρ ) ρ dV

ρ ρ

> ≡

>

z

1

1

j M L

( ) M ( )

( )

< ≡ >

>

ρ ρ ρ ρ

(1) Mass measured from the center

(2) Angular momentum in

(3) Specific Angular momentum distribution

M(ρ ρ> ₁)

Angular Momentum Problem

Core Formation

7000 yr after Core Formation

Accumulated Mass Specific

Angular Momentum of gas <M

Initial

High-density region is formed by gases with small j.

Run-away Collapse

Magnetic torque brings the angular momentum from the disk to the outflow.

Outflow brings the angular momentum.

Accretion Stage

Angular Momentum Transfer

Molecular Outflow

1400AU = 10^"

Saito, Kawabe, Kitamura&Sunada

L1551 IRS5

Optical Jets

10⁵AU

12CO J = →1 0

Snell, Loren, &Plambeck 1980

Binary fraction is high.

Ghez et al 1993

Duquennoy & Mayor 2001 orbital period

Number

Binary: To understand Star Formation, study BINARY FORMATION.

Period distribution of nearby binaries

Gaussian around ~180yr

ΔK<2mag

if completely surveyed, bsd ~60%

Binary Fraction

Liu et al. 2003

(1) may depend on the mass of the stars

¾ Herbig/AeBe 68±11%

(SSB) (Baines et al. 06)

¾ similar to T Tau

local density binary fraction relative to that for field stars

(2) may be deferent between PMS and MS.

(3) may depend on the local stellar density

Ghez et al 1993 1

2

01 2 3 4

DM01 T Tau

MSS

1. Binary fraction is a decreasing function of local stellar density

Tau Oph

IC348

N2024 Trapezium This suggests binary/multiple systems are formed in early phase.

Narrow wind obs.

3D MHD Simulation of Rotating Magnetized Cloud Collapse

• Assume barotropic eq. state.

– mimicing the result of 1D RHD (eg. Masunaga, Inutsuka 2000).

• Ideal MHD

Isothermal phase

10 -3

5 10 cm ncrit = ×

Adiabatic phase

( ) 0,

,

( ) 0,

4 t

t p

t

G

ρ ρ

ρ ρ φ

φ π ρ

⎧ ∂ + ∇ ⋅ =

⎪ ∂

⎪ ⎛ ∂ ⎞

⎪ + ⋅∇ = −∇ − ∇

⎪ ⎜⎝ ∂ ⎟⎠

⎨⎪ ∂

⎪ + ∇× × =

⎪ ∂

⎪ Δ =

⎩

v v v v

B v B

( )^{7 / 5}

2 2

s s crit crit

p = c ρ + c ρ ρ ρ

2 7 / 5

( )

( )

s crit

crit

p c

K

ρ ρ ρ

ρ ρ ρ

⎧ ≤

≈ ⎨⎩ >

…

…

Log ρ

adiabatic

H2Dissoc.

isothermal 1st Core

2nd Core

log T

1 2 3 4

log ρ

Temp-density relation of IS gas.

(Tohline 1982)

Model and Numerical Method Model and Numerical Method

Machida, Tomisaka, Matsumoto 04 Machida, M.,H., Tomisaka, 05

Machida, M. Tomisaka, H. 05 Machida, M.,H., Tomisaka, 06

Numerical Method (cont.)

• Non-homologous Collapse

– Dynamic ranges of size and density scales are huge.

• “Nested Grid” Technique

– Coarser grid: covers global structure

– Finer grid: small-scale structure near the center.

• # of cells：128(x)×128(y)×32(z)×17 (level)

• equivalent to simulations

with～1.5×10²⁰ grids at the center.

• New Finer Grid is Generated to Guarantee the Jeans Condition (Truelove et al. 1997)

– To achieve physically correct answer:

– Simulations continues till the “Jeans Condition” is violated at the deepest level of grid (17th Level).

L=1

L=2 L=3

Nested grid Nested grid

2 -3

ISM 10 cm

ρ ^∼ ρ_{2ND CORE} ∼^{10 cm17 -3}

ISM 0.1pc

L ∼ L_{2ND CORE} ∼10 cm¹¹

1/ 2

J / 4 [(4 ) / _s] / 4

x λ π ρG c

Δ < =

L=17

Initial Condition

• An isothermal cylindrical cloud – in hydrostatic balance

(Stodolkiewicz 1963)

•

•

– Perturbations with the wavelength equal to the Jeans length is added.

• Add non-axisymmetric

perturbation m=2 as well as axisymmetric m=0 mode

• Parameters:

– B-field strength and angular rotation speed: Aφ,

1/ 2 1/ 4

;

B ∝ ρ Ω ∝ ρ

X Z

Y rotate

H=～10⁶ [AU]

M=～20 M

magnetic field line

// // Filament Ω B

2 0

2 0 c / 4

s c

B c α π

= ρ ω = Ω(4π ρG 0_c)^{−1/ 2}

Bonnor-Ebert Sphere with Rigid-body Rotation & Uniform B-Field Î Results in a Similar Result.

(A_m2, α, ω)=(0.2, 1, 0.5)

Initial state ρ=10²cm^-3 L=1

ρ=10³cm^-3 L=1

ρ=10⁷cm^-3 L=6

ρ=10⁹cm^-3 L=9

ρ=10¹⁰cm^-3 L=11

ρ=10¹¹cm^-3 L=12

ρ=10⁴cm^-3 L=2

ρ=10⁵cm^-3 L=3

Side view x=0 plane

Pole-on view z=0 plane

Only after the sufficiently thin disk is formed, the non-axisymmetric

perturbation can grow

Model with strong magnetic field and high rotation speed

3.Results

isothermal phase adiabatic phase

Typical Model

(A_m2, α, ω)=(0.01, 0.01, 0.5) Initial state

ρ=10²cm^-3 L=1

ρ=10³cm^-3 L=1

ρ=10⁷cm^-3 L=6

ρ=10⁹cm^-3 L=9

ρ=10¹⁰cm^-3 L=10

ρ=10¹⁰cm^-3 L=10

ρ=10⁴cm^-3 L=2

ρ=10⁵cm^-3

L=3 Pole-on view

z=0 plane

Side view x=0 plane Model with weak magnetic field and high rotation speed

isothermal phase adiabatic phase

Initial state ρ=10²cm^-3 L=1

ρ=10³cm^-3 L=1

ρ=10⁷cm^-3 L=6

ρ=10⁹cm^-3 L=9

ρ=10¹⁰cm^-3 L=11

ρ=10¹¹cm^-3 L=12

ρ=10⁴cm^-3 L=2

ρ=10⁵cm^-3 L=3

isothermal phase adiabatic phase

Core Model

(A_m2, α, ω)=(0.01, 1, 0.1)

This corresponds to strong B-field

& slow rotation.

Disk -->

Spherical core

In this model, the non-

axisymmetry hardly grows.

Core continues to contract.

Bar Fragmentation 0.2, 1, 0.5

A= α = ω = A= 0.01, 0.01, 0.5α = ω =

Ring Fragmentation

0.01, 1, 0.1 ANon-Fragmentation = α = ω =

0.01, 0.1, 0.1 ANon-Fragmentation = α = ω =

0.1 1.0 B_zc /(8πc_s²ρc)^1/2

0.01 0.1

Ωc /(4πGρc)1/2

n_c=5x10 ² [cm ^-3 ]: initial n_c=5x10 ⁴

n_c=5x10 ⁶ n_c=5x10 ⁸

π/4

α= 0.01 0.1 1.0

A B

C D

B-Ω Flux-Spin Relation

--Evolutionary Path--

Magnetic braking

2 / 3

/ const

c c

B ρ

2 / 3 c /ρc

Ω J-loss

c / c

B Ω

Support deficient.

Î Spherical collapse.

2 / 3

c c

B ∝ ρ

2 / 3

c ρc

Ω ∝

2 const B Rc

⇐ =

2 const

cR

⇐ Ω =

/ const

c Bc

Ω

1/ 2 1/ 2 1/ 6

/ /

c ρc Bc ρc ρc

Ω ∝ ∝

B_zc/(8πc_s²ρ_c)^1/2

Ω c/(4πGρ c)1/2

(

)

⁽

⁾

c s c c c

B π ρc −Ω π ρG

Machida et al. 2005a,b

0.1 1.0 B_zc /(8πc_s²ρc)^1/2

0.01 0.1

Ωc /(4πGρc)1/2

n_c=5x10 ² [cm ^-3 ]: initial n_c=5x10 ⁴

n_c=5x10 ⁶ n_c=5x10 ⁸

π/4

α= 0.01 0.1 1.0

A B

C D

B-Ω Flux-Spin Relation

(

)

⁽

⁾

c s c c c

B π ρc −Ω π ρG

Support sufficient.

ÎRadial collapseÆmove left-down Æ

m ov e sl ig h tl

Magnetic braking

c / c

B Ω

--Evolutionary Path--

Ω c/(4πGρ c)1/2

B_zc/(8πc_s²ρ_c)^1/2 Support sufficient

ÎDisk formation

/ const

c c

B σ

/ const

c σc

Ω

Ífrozen-in Íconserve J

/ 1/ 2 const

c c

σ ρ Íself-grav. disk

ÎRadial collapse const

Bc

const

Ωc ρ^c Æmove left-down

Æmove slightly

1/ 2 1/ 2 1/ 2

/ /

c ρc Bc ρc ρc⁻

Ω ∝ ∝

B-Ω Flux-Spin Relation

--Evolutionary Path--

• In the isothermal run-away collapse,

contraction proceeds self-similarly or solution converges to a family of self-similar solutions.

• All the models converge to a line as

• There exists a balance between B-field,

centrifugal force, thermal pressure and gravity.

2 2

2 2 2 1

(0.36) 8 (0.2) 4

c c

s c c

B

c G

π ρ π ρ

+ Ω = ^empirical

0.01 0.1 1 B_zc / (8πc_s²ρc)^1/2

0.01 0.1

Ωc / (4πGρc)1/2

A B

C D

initial

Ring Fragmentation Bar Fragmentation Both

No Fragmentation

n_c = 5x10¹⁰ cm^-3

Ring Fragmentation Bar Fragmentation No Fragmentation

Spherical Collapse Region Sph

Sph Sphheri

Vertical Collapse RegionRe

α = 0.001 0.01 0.1 1

nc,0 = 5x10⁴ cm^-3-3-3-3 nc,0 = 5x10⁶ cm^-3

~~~

~

0

nc,0 = 5x10⁶ cm^-3

1. We know both the evolutionary path and

fragmentation condition ε_ob>3 or Ω_c/(4πGρ_c)^1/2>0.2.

2. This gives a diagnosis of a cloud: fragments in the adiabatic stage or remains single ?

Large symbols initial states

For the adiabatic core to fragment, it must rotate fast enough.

Fragmentation No fragmentation

Small symbols Adiabatic core

Evolutionary path

Magnetic field suppresses the fragmentation

To Fragment

1/ 2 1

7 -1 -1

0

1/ 2 1

0

3 10 yr G

2 190ms

s s

c G

B c μ

−

−

−

⎛ ⎞

Ω > ∼ × ⎜⎜⎜⎝ ⎟⎟⎟⎟⎠

Prestellar core L1544

0.09km s @-1 15000AU

v_φ r = Ohashi et al (1999)

0.14km s @-1 7000AU

v_φ r = Williams et al (1999)

6 -1

0 1.3 10 yr⁻

⇒ Ω ×

6 -1

0 4.2 10 yr⁻

⇒ Ω ×

Crutcher & Troland (2000)

0 11 2 G

B + ± μ Zeeman splitting

7 -1 -1

0 0

(1.2 3.8) 10 yr G

B ⁻ μ

⇒ Ω ∼ − ×

Measurement both Ω and B at the same density Î future forecast!

Marginal!!

Misaligned case

J

Β

0.01, 0.01

α = ω = Evolution is understood by the spin-flux relation.

cp ˆ

B ≡ ⋅B n_disk Ω ≡ ⋅_cp Ω nˆ_disk

Ω cp/(4πGρ c)1/2

B_cp/(8πc_s²ρ_c)^1/2

B ˆ_disk

n

Machida, et al. (2006) ApJ. 645, 1227-1245

Effect of Magnetic Field ｓ Misaligned Rotators: B // J

• Promotion of disk formation

– A pseudo-disk extending

perpendicular to B is formed.

• Transfer the angular momentum if the cloud Î discourages disk formation

– Ω

– Ω

• Gravitational torque, Magnetic torque, Hydrodyn.

Torque

• Affect how Fragmentation Occurs

Ω

Ω

Matsumoto & Tomisaka 2004 Astrophysical Journal, 616, 266-282

Wolf et al (2003)

Alignment of Outflow and Magnetic Field

Polarization of thermal dust emission map SCUBA 850μm

???

Outflow

Magnetic field

Tamura et al (1995)

IRAS 16293-2422

L1551 IRS5

align

align align

1mm radio polarization

1800AU

Recent observations (1/2):

B-fields, optical jets, and disks in Taurus

Direction of magnetic fields inferred from polarized dust emission.

Direction of optical jets

Direction of disk normal

Menard & Duchene (2004)

CTTS are oriented

randomly with respect to local magnetic fields!

Taurus-Auriga region

L1551-IRS5

Angular Momentum

• Mechanism:

– Magnetic braking (disk -> magnetic torque -> redistribution of j along one magnetic field line)

– Molecular outflow ejected after the core formed. magneto-

centrifugal wind mechanism (disk -> magnetic torque -> wind ->

escape from the system)

– Mechanical (pressure and gravitational) torque

• 3D MHD simulation (Dorfi 1982)

– shows that component of J perpendicular to B is largely removed in the isothermal run-away collapse phase.

• Is a disk perpendicular to B or J?

– Disk perpendicular to B is formed.

Magnetic

Torque

B

j j

Aligned Rotator Misaligned Rotator

θ = 0 θ ⁼ 45 θ ⁼ ₉₀

θ j B

1.7 BE 4 _cr M = M = M

0 0.5

α =

0 0.02 β =

• Disk perpendicular to not J but B-field (!) is formed.

1/ 2

B

2πG M ₌ 4 Φ

disk

outflow Initial state

Spherical cloud

B-field

L4 L9 L12

L11

Cut A

Cut A Cut B

MF45 θ = 45

Local B-Field at the center Global J

Disk perpto local B

outflow

Axisymmetric!!

x16

x16

Disk, B Field and Rotation in Different Scales (Final state)

Global J

Disk oriantation, local B, and local J change their directions according to the scale.

Initial B

Convergence

B_g

j B_c

1. Loci of local B_c, local J_c, disk normal

vector n_c are plotted viewing from the direction of global J_g (z-axis).

2. Precession or

oscillation appears.

3. Finally, they

converges to one direction.

4. Angle between Bc and Bg is ~30 deg.

B_c B_g J_c

J_g n_c

core formation Explanation of precession.

(a) B-Field changes its direction owing to the rotation.

(b) Angular rotation vector inclines toward B-vector by the magnetic braking.

Case of large θ (angle between J

and B

)

θ=70 deg and θ=80 deg

θ=70 deg θ=80 deg

Local B_c, J_c, and disk normal direction are converged!!

B-Field removes the perpendicular component of J to B.

Perpendicular rotator

Even in this case, the outflow is ejected in the

direction of B-field.

J_c // B_c θ=90 deg

J_c

B_c

B_c B_c

J_c J_c

n_c n_c

θ~35 deg between B_c and B_g

J_g J_g

Magnetic Braking and

Angular Momentum of ρ >0.1ρ

• Angular

momentum is effectively

transferred by the magnetic braking.

• Especially model of θ = 90deg, J is effectively

removed from the central part.

B=0

θ = 0° θ = 45°

θ = 90°

ring

outflow

ρ_cr

logρρ_maxmax

log J/M2 （spec. ang. mom./mass）

Amb. Diff?

← Three-dimensional structure

4600AU

Tree-dimensional angle between magnetic field and outflow is 12.4 deg.

Green : mean direction of polarization vector Red : direction of the outflow (50AU scale B) Colors: column density

The outflow is well aligned with the polarization vector.

Reconstruction of Polarization vectors at 5000 AU scale (B

= 82.8 μ G)

B₀=18.6μG MF45

Matsumoto et al. 2006 ApJ. 637, L105

yz xz xy

偏光度 低 偏光度 高

Reconstruction of Polarization vectors at 5000 AU scale (B

= 50.1μG)

The alignment depends on the line of sight Three-dimensional angle between magnetic field and outflow is 53.5 deg.

Green : mean direction of polarization vector Red : direction of the outflow

Colors: column density

B₀=7.42μG WF45

B₀=18.6μG

MF45 B₀=7.42μG

WF45

Directions of B, Ω, and disk normal vectors: variation in scale.

B

B

Ω

Ω n

n

Φ_3D=53.5 deg.

Φ_3D=12.4 deg.

Can we infer the central magnetic field near future? … by ALMA?

Target: B335 @ 250 pc Resolution: 0.1” (25 AU)

Yes, we can resolve the magnetic fields around the protostar.

The outflow traces the direction of magnetic field at the cloud center.

B₀=7.42μG WF45