Outflows from YSOs and Angular Momentum Transfer

National Astronomical Observatory (NAOJ)

Kohji Tomisaka

Angular Momentum

• Fragmentation (binary formation) is much affected by the amount of angular momentum in rotation supported disk cr.

• Angular Momentum Problem: j* << j cl Specific angular momentum of a new-born star:

is much smaller than that of parent cloud:j RR

P*

* FH IKFHG IKJ6 102 10

162

daycm s

-12 -1

j Rcl -1 -1

2 -1

pc kms pccm s

FHG IKJ FHG IKJ5 100 1 4

212

.

Angular Momentum Transfer

• Magnetic Braking

tV

GB

GBa A

a

( ) /

2

2 40

1 2

a

vA

Alfven Speed

Ambient density

Column density Free-fall time in ambient matter

>1: For super-critical clouds

Longer than dynamical time

•B-Fields do not play a role in angular momentum transfer in a contracting cloud?

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 10-3 jcl.

Outflow

Disk

B-FieldsOutflow

MassInflow star Outflow

Ang.Mom.

Shu’s Inside-out SolutionLarson-Penston SolutionOutflow

What we have done.• Dynamical contraction of slowly rotating

magnetized clouds is studied by ideal MHD numerical simulations with cylindrical symmetry.

• Evolution is as follows: Run-away Collapse Increase in Central Density Formation of Adiabatic Core Accretion Phase

Numerical Method• Ideal MHD + Self-Gravity +

Cylindrical Symmetry• Collapse: nonhomologous• Large Dynamic Range is att

ained by Nested Grid Method.– Coarse Grids: Global Structur

e – Fine Grids: Small-Scale Struc

ture Near the Core

L0 L231

1/21/4

Initial Condition

• Cylindrical Isothermal Clouds– Magnetohydrostatic ba

lance in r-direction– uniform in z-direction

• B-FieldsB B Bz r , 0

• Slowly rotating (~ rigid-body rotation)

• Added perturbation with of the gravitationally most unstable mode MGR.

M

GR

parameters

1 50, (L2)

t=0 0.6Myr 1Myr

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Run-away Collapse Phase

Accretion Phase

• High-density gas becomes adiabatic.– The central core becomes optically thick for ther

mal radiation from dusts.– Critical density =

• An adiabatic core is formed.• To simulate, a double polytrope is applied

– isothermal– adaiabatic

1ncrit

-3cm 1010

p cs 2

p K

= 7 / 5 = 5 / 3

n n crit

n n crit

Accretion Phase (II)

• Collapse time-scale in the adiabatic core becomes much longer than the infall time.

• Inflowing gas accretes on to the nearly static core, which grows to a star.

• Outflow emerges in this phase.

Outflow

Core + Contracting Disk

Pseudo-Disk

Accretion Phase B0,

Adiabatic (the first) Core

A Ring Supported by Centrifugal Force

Run-away Collapse Stage Accretion Stage

Accretion Phase 0 , B=0

z

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Accretion Phase B0, 0

Run-away Collapse Stage 1000yr

L10

300A

U

ビデオ クリップ

ビデオ クリップ

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Why Does the Outflow Begin in the Accretion Stage?

Run- awayC ollapse

Accretionstage

Rotation Speed v vr

v v r

T oroidal B - F ield B B pol B B pol

Rotation Angle

c cG/

. .

20 2 0 4

d i

muchAngle betweenB- F ields and adisk

60 – 70 deg 10 – 30 deg

B0, 0Accretion Phase

Blandford & Peyne 82

Mass Accretion RateMagneto-Centrifugal Wind

Angular Momentum Distribution

L rv dV( )

z1

1

M dV( )

z1

1

j M LM

( ) ( )( )

1

1

(1) Mass measured from the center

(2) Angular momentum in

(3) Specific Angular momentum distribution

M( ) 1

Angular Momentum Problem

Core Formation

7000 yr afterCore Formation

Mass

Specific Angular Momentum

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 Problem

Magnetic Torque, Angular Momentum Inflow/Outflow Rate

Mass

Initial

Torque

Inflow Outflow

Accretion Phase Inflow

Torque

Core Formation

Inflow

Torque

• In weakly ionized plasma, neutral molecules have only indirect coupling with the B-fields through ionized ions.

• Neutral-ion collision time• When , ambipolar diffusion is import

ant.• Assuming (on core formatio

n), rotation period of centrifugal radius:

rot yrms

FHIKFH IKFH IK

2 4000 1 0 1 190

33

3

1

3

p GMc

p MM

c

s

s

. .

Ambipolar Diffusion?

niiK n

200yr

5 81 2/

j GMc

GMcs s

( . . )0 1 0 25

ni rot

ni dyn

Edge of Hole madeby Molecular Outflow

Molecular Outflow Optical Jets

L1551 IRS5 Optical Jets

105 AU

12 1 0CO J

Optical Jets

• Flow velocity: faster than molecular outflow.• The width is much smaller.

• These indicate ‘Optical jets are made and ejected from compact objects.’

• The first outflow is ejected just outside the adiabatic (first) core.

Jets and Outflows

• Optical jets are formed just outside the second core?

Temperature-Density RelationJets and Outflows

Temperature-Density Relation

adiab

atic

H 2 Disso

c.

isothermal

1st Core

2nd CoreLo

g T

Log

Outflows

Jets?Log 5 10 15

1

2

3

4

Tohline 1982

10 5

2 10 5

0 002.

zOutflow

Jetsz

zJets and Outflows

s=104H2cm-3

=1,

L8

L16

10AU

10Rc=1014.6H2cm-3

c=1019H2cm-3

c=1021.3.H2cm-3

H 2 D

issoc

.

10R

2nd RunawayCollapse

X256

ビデオ クリップ

Summary

• In dynamically collapsing clouds, the outflow emerges just after the core formation (yr).

• In the accretion phase, the centrifugal wind mechanism & magnetic pressure force work efficiently.

• In 7000 yr ( ), the outflow reaches 2000 AU. Maximum speed reaches

M M* . 0 2

v cc

ss

max-1

-1 km s m s

FH IK7 1 3190

. .

Summary(2)

• In the process, the angular momentum is transferred from the disk to the outflow and the outflow brings the excess j.

• This solves the angular momentum problem of new-born stars.

• The 2nd outflow outside the 2nd (atomic) core explains optical jets.

Runaway Collapse Accretion-associated Collapse

Den

sity

incr

ease

s inf

inite

lyInside-out CollapseHydrostatic Core

Larson 1969, Penston 1969, Hunter 1977,Whitworth & Summers 1985

Shu 1977

Dynamical Collapse

Parameters

• Angular Rotation Speed

• Magnetic to thermal pressure ratio

014

1 2

09 10100 5

FHG IKJ F

HGIKJ rad s

H cm-1

2-3

ns

/

( / ) / , .B p02 4 1 0 1th

vr

FH IKFHG IKJ2 79 10

014. km s

rad s 1pc-1

-1cl

Nest (Self-Similar) Structure

L5

L12

z

vzBz

z

2 1287

ビデオ クリップ

Run-away Collapse Phase

Along z-axis

Run-away Collapse

• Evolution characterized as self-similar 10AU

0 1. pc

Magnetocentrifugal Wind Model:Blandford & Peyne 1982

• Consider a particle rotating with rotation speed = Kepler velocity and assume is conserved moving along the B-fields.

• Along field lines withdeg the particle is accelerated. For deg decelerated.

Effective potential for a particle rotating with

Momentum Flux (Observation)• Low-Mass YSOs (Bontemps et al.1996)

Class0Class1

F L cbolCO /

Luminosity

Mom

entu

m

Angular Momentum

L rv dV( )

z1

1

M dV( )

z1

1

j M LM

( ) ( )( )

1

1

(1) Mass measured from the center

(2) Angular momentum in

(3) Specific Angular momentum distribution

j M( )

M( ) 1

Angular Momentum Problem

Effective Outflow Speed

V

dMVdt

dMdt

eff

Outflow Driving Mechanism

• Rotating Disk + Twisted Magnetic Fields– Centrifugal Wind +

• Pudritz & Norman 1983;• Uchida & Shibata 1985;• Shu et al.1994; • Ouyed & Pudritz 1997;• Kudoh & Shibata 1997

• Contraction vs Outflow?• When outflow begins?

• Condition?

Outflow

Disk

B-FieldsOutflow

Inflow

Accretion/Outflow Rate

• Inflow Rate is Much Larger than Shu’s Rate (1977).

• LP Solution: • Outflow/Inflow Mass

Ratio is Large ~ 50 %.• Source Point of Outflo

w Moves Outward.

m v ndS z

0 975 3. /c Gs

29 3c Gs /

10 5 M -1yr

mShu

6000yr2000yr 4000yr

1

2

3

4

Momentum Driving Rate

• Molecular Outflows (Class 0&1 Objects) show Momentum Outflow Rate (Bontemps et al.1996)

3 10 5 106 4 yr km s-1 -1M

dmvdt

v dSzz z 2

Upper / Lower

Boundaries

1 10 5 M yr km s-1 -1

6000yr2000yr 4000yr

2 10 5 M yr km s-1 -1

Weak Magnetic Fields (=0.1,)

0 yr 2000 yr 4000 yr ビデオ クリップ

B0, 0Accretion Phase

Effect of B-Field Strength

• In small model, toroidal B-fields become dominant against the poloidal ones.

• Poloidal B-fields are winding. • Small and slow rotation lead less effecti

ve acceleration.

B0, 0Accretion Phase

Angular Momentum Problem

• Typical specific angular momentum of T Tauri stars

• Angular momentum of typical molecular cores

• Centrifugal Radius

j RR

P*

* FH IKFHG IKJ6 102 10

162

daycm s

-12 -1

j Rcl -1 -1

2 -1

pc kms pccm s

FHG IKJ FHG IKJ5 100 1 4

212

.

R jGM

j MMc

FH IKFHIK

2 1

0 06. pc5 10 cm s21 2 -1

2

R Rc *

j jcl *

Angular Momentum Problem

Molecular Outflow H CO+13

1400AU = 10"

Saito, Kawabe, Kitamura&Sunada 1996 L1551 IRS5Optical Jets

105 AU

12 1 0CO J

Snell, Loren, &Plambeck 1980