Effect of Magnetic Field in Star Formation + Observational Visualization Kohji Tomisaka ( 富阪幸治 ) Division of Theoretical Astronomy / Center for Computational

Effect of Magnetic Field in Effect of Magnetic Field in Star Formation + Star Formation +

Observational VisualizationObservational Visualization

Kohji Tomisaka (Kohji Tomisaka ( 富阪幸治富阪幸治 ))Division of Theoretical Astronomy / Center for ComputaDivision of Theoretical Astronomy / Center for Computa

tional Astrophysicstional AstrophysicsNational Astronomical Observatory JapanNational Astronomical Observatory JapanNational Institutes of Natural SciencesNational Institutes of Natural Sciences

「星形成における「星形成における磁場の役割」磁場の役割」

(Effect of Magnetic Field in S(Effect of Magnetic Field in S

tar Formation)tar Formation)

天文月報Astronomical Heraldfrom Astronomical Society ofJapan in Japanese

Purpose of this reading was to demonstrate the importance to observe the magnetic field to ALMA(-J) people.

Condition of Cloud CollapseCondition of Cloud Collapse

Super-criticalCloud

Sub-criticalCloud

Cloud

plasma drift /ambipolar diffusion

magnetic braking

Quasistatic Evolution

Magnetic flux loss fromthe central part of the cloud

10 ff crM M

crM McrM M

Dynamical Contractionff

0.17 / / 2B BcrM G GpF F; ;

3/22 4

0 1/2 3/2 1/20

0.17( , , ) 1.39 1

/s

cc c

crc

M T B pG B G Ps

-é ùæ öê ú÷ç ÷= - çê ú÷ç ÷çè øê úë û

Zeeman

C.F.Upper limit

log( )MMcr

Heiles & Crutcher (2005)

magnetohydrostatic configuration is possible if M<Mcr

4

3/2 1/20

when sJcr

cM M

G P? :

Observationally,

Theoretically,

clouds are foundnear the critical state

critical mass formula

Mouschovias & Spitzer 76

Tomisaka et al 88

Molecular Outflow H CO+13

1400AU = 10"

Saito, Kawabe, Kitamura&Sunada 19

96 L1551 IRS5

Optical Jets

105 AU

12 1 0CO J

Snell, Loren, &Plambeck 1980 A Part of Gravitational Energy is Converted to Kinetic Energy in the Contraction

ProtostarOutflow from Protostar

Molecular Core

Magnetically Driven Outflow / Wind

Jets and Molecular Outflows

1/ 2f f ~ ( )G

1st, 2nd Core, Protostar Formation

prestellar phase protostellar phase

Spherical Collapse Spherical Collapse

• isothermal = 1 <A=10-13 g cm-3

run-away collapsefirst collapse

• adiabatic A << B= 5.6 10-8 g cm-3 　first coreoutflowfragmentation

• H2 dissociation = 1.1 B C= 2.

0 10-3g cm-3 　　second collapse

　　

Gas ( ) contracting under the self-gravity

Masunaga & Inutsuka (2000)

Second Collapse γ= 1.10

B

A

C

First Collapse γ= 1

0, 0 BLarson (1969)

Temp-density relation of IS gas.(Tohline 1982)

B

Initial Condition

periodic boundary

axisymmetric perturbation nonaxisymmetric perturbation

Magnetically supercritical cylindrical cloud.

=most unstablemode Jeans instability of a cylinder.

The cloud is in a (magneto)hydrostatic balance in r-direction.

Gc ccs2cparameters

Method: Nested Grid + 2D axisymmetric ideal MHD

prestellar runaway collapse phase

ƒrƒfƒI ƒNƒŠƒbƒv

Outflow is ejected (1) by the magnetic force made by rotation motion (2) after the first core is formed ( protostellar phase).

L8

Two Types of OutflowsTwo Types of Outflows

1 0.1

0.01

2 20 / 4 s cB c

strong Bstrong B wide opening angle wide opening angle U-typeU-type magnetocentrifugal windmagnetocentrifugal wind

weak Bweak B narrow opening angle narrow opening angle I-typeI-type magnetic pressure gradientmagnetic pressure gradient

1/ 20 /(4 ) 1cG Three cloud has the same rotation rate

but different magnetic field strength

Blandford & Payne (1982)

consistent with jet’s simulation from Kepler disk (Uchida & Shibata 1985)

““Angular Momentum Problem”Angular Momentum Problem”• Specific Angular Momentum of Spin Motion of PMS StarSpecific Angular Momentum of Spin Motion of PMS Star

• Orbital Specific Angular Momentum of BinaryOrbital Specific Angular Momentum of Binary

• Specific Angular Momentum of Parents Cloud CoreSpecific Angular Momentum of Parents Cloud Core

• Centrifugal RadiusCentrifugal Radius

2 -1

16 2 -1** 6 10 cm s

2 10day

R Pj

R

8

jR

cl -1 -12 -1

pc kms pccm s

FHG

IKJFHG

IKJ5 10

0 1 421

2

.

122

21 2 -10.06pc

5 10 cm sc

j j MR

GM M

8

R Rc *

j jcl *

1/21/ 219 2 -1bin

bin 4 10 cm s100AU

R Mj

M

8

cl binj j

bincR RTomisaka 2000 ApJL 528 L41--L44

““Angular momentum problem” can be Angular momentum problem” can be reconciled by the outflow driven by reconciled by the outflow driven by B+B+. . • In outflows driven by magnetic fields:In outflows driven by magnetic fields:

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

– If 10 % of inflowing mass is outflowed with havIf 10 % of inflowing mass is outflowed with having 99.9% of angular momentum, ing 99.9% of angular momentum, jj** would be would be reduced to 10reduced to 10-3-3 jjclcl. . Outflow

Disk

B-FieldsOutflow

MassInflow star Outflow

Ang.Mom.

separation between mass M and angular momentum J

Fragmentation and Binary Fragmentation and Binary FormationFormation

0.1

0.03 800yr 2000yr

Saigo, Matsumoto, Tomisaka 2008 ApJ 674, 997

Initial ConditionInitial Condition

• An isothermal cylindrical cloudAn isothermal cylindrical cloud– in hydrostatic balance (Stodin hydrostatic balance (Stod

olkiewicz 1963)olkiewicz 1963)• •

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

• Add non-axisymmetric perturbatAdd non-axisymmetric perturbation m=2 as well as axisymmetrion m=2 as well as axisymmetric m=0 modeic m=0 mode

• Parameters:Parameters:– B-field strength and angular rotB-field strength and angular rot

ation speed: ation speed: AA, ,

1/ 2 1/ 4; B

X

Z

Y

rotate

H=～ 106 　 [AU]M=～ 20 M

magnetic field line

// // FilamentΩ B

20

20

/ 4c

s c

B

c

1/ 2

04 cG

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

Typical EvolutionTypical Evolution

0.01, 0.1 0.5, 0.01 0.5, 1

Non-Fragmentation Disk FragmentationDisk Spiral Fragments

Bar Fragmentation

M.N.Machida, T. + M. 04M.N.Machida, M., H. + T. 05M.N.Machida, M. T. + H. 05M.N.Machida, M.,H., + T. 06T=Tomisaka, M=T.Matsumoto, H=Hanawa

(Am2, )=(0.2, 1, 0.5)

Initial state=102 cm-3

L=1

=103 cm-3

L=1

=107 cm-3

L=6=109 cm-3

L=9=1010 cm-3

L=11=1011cm-3

L=12

=104 cm-3

L=2=105 cm-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 3.Results

isothermal phase adiabatic phase

Typical Model(Am2, )=(0.01, 0.01, 0.5)


L=1

=103 cm-3

L=1

=107 cm-3

L=6=109 cm-3

L=9=1010 cm-3

L=10=1010cm-3

L=10

=104 cm-3

L=2=105 cm-3

L=3 Pole-on view

z=0 plane

Side view

x=0 plane

Model with weak magnetic field and high rotation speed



L=1

=103 cm-3

L=1

=107 cm-3

L=6=109 cm-3

L=9=1010 cm-3

L=11=1011cm-3

L=12

=104 cm-3

L=2=105 cm-3

L=3


Core Model(Am2, )=(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, 0.5A 0.01, 0.01, 0.5A

Ring Fragmentation

0.01, 1, 0.1A Non-Fragmentation

0.01, 0.1, 0.1A Non-Fragmentation

B-B- Flux-Spin Flux-Spin Relation Relation --Evolutionary Path--

Magnetic braking2 / 3/ constc cB r ;2 / 3/c crW ] J-loss

/c cB W Z

( ) ( )1/ 2 1/ 228 4c s c c cB c Gp r p r- W

Support deficient. Spherical collapse.

2 / 3c cB rµ

2 / 3c crW µ

2 constcB RÜ =2 constcRÜ W =

/ constc cBW ;

1/ 2 1/ 2 1/ 6/ /c c c c cBr r rW µ µ

B-B- Flux-Spin Flux-Spin Relation Relation ( ) ( )

1/ 2 1/ 228 4c s c c cB c Gp r p r- W

Support sufficient. Radial collapsemove left-downmove slightly

Magnetic braking

/c cB W Z

--Evolutionary Path--

Support sufficientDisk formation

/ constc cB s ;/ constc csW ;

frozen-in

conserve J1/ 2/ constc cs r ; self-grav. disk

Radial collapse

constcB ;constcW ; cr Z

move left-down

move slightly

1. We know both the evolutionary path and fragmentation condition ob>3 or c/(4Gc)1/2>0.2.

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

Large symbolsinitial states

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

Fragmentation

No fragmentation

Small symbolsAdiabatic core

Evolutionary path

Magnetic field suppresses the fragmentation

To Fragment

11/ 27 -1 -10

1/ 2 10

3 10 yr G2 190ms

s

s

cG

B cm

--

-

æ öW ÷ç> ´ ÷ç ÷÷çè ø:

Prestellar core L1544-10.09km s @ 15000AUv rf =; Ohashi et al (1999)

-10.14km s @ 7000AUv rf =; Williams et al (1999)

6 -10 1.3 10 yr-Þ W ´;

6 -10 4.2 10 yr-Þ W ´;

Crutcher & Troland (2000)0 11 2 GB m+ ±; Zeeman splitting

7 -1 -10

0

(1.2 3.8) 10 yr GB

m-WÞ - ´:

Measurement both and B at the same density future forecast!

Marginal!!

Magnetic Field Suppress Magnetic Field Suppress

FragmentationFragmentation

Wolf et al (2003)

Alignment of Outflow and Magnetic Field

Polarization of thermal dust emission mapSCUBA 850m

???

Outflow

Magnetic field

Tamura et al (1995)

IRAS 16293-2422

L1551 IRS5

align

alignalign

1mm radio polarization

1800AU

BB

BB

BB

BBHow do the global and local magnetic field?

local B // Outflow but global B not // Outflow.

local B global B

B

j jAligned Rotator Misaligned Rotator

0 45

90

j

B

BE1.7 4 crM M M

0 0.5 0 0.02

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

1/ 2

B

24

G M

disk

outflow

Initial state

Spherical cloud

B-field

Matsumoto, Tomisaka 2004Matsumoto, Nakazato, Tomisaka 2006

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

x y

zGlobal J

Initial B

← 　 Three-dimensional structure46

00

AU

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

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

The outflow is well aligned with the polarization vector.

Reconstruction of Reconstruction of Polarization vectorsPolarization vectorsat 5000 AU scale (Bat 5000 AU scale (Baveave = 82.8 = 82.8G)G)

B0=18.6GMF45

Matsumoto et al. 2006 ApJ. 637, L105

yz xz xy

偏光度低偏光度高

Reconstruction of Polarization vectorsReconstruction of Polarization vectorsat 5000 AU scale (Bat 5000 AU scale (Baveave = 50.1 = 50.1G)G)

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 vectorRed : direction of the outflowColors: column density

B0=7.42GWF45

yz xz xy

B0=18.6GMF45 B0=7.42G

WF45

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

B

B

n

n

3D=53.5 deg.

3D=12.4 deg.

B ：Ｍａｇｎｅｔｉｃ　Ｆｉｅｌｄn: Disk normal

: Rotation Axis

Machida et al 2006

disk is perpendicular to J

disk is perpendicular to B

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

Target: B335 @ 250 pcResolution: 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=7.42GWF45

Observational Visualization Observational Visualization 観測的可視化観測的可視化

Texlow

Texhigh

Doppler blue-shifted

red-shifted

　　　　　　　 self-absorption, self-reversal

CO rotation transitionBlue Asymmetry

(ex.) Blue-enhanced Asymmetry(ex.) Blue-enhanced Asymmetry

ObserverRadio antenna

Star forming cloud

Observational VisualizationObservational Visualization• Spectrum/intensity expected for (magneto)hydro simulatiSpectrum/intensity expected for (magneto)hydro simulati

on can be compared with real observations by OV.on can be compared with real observations by OV.

• Observational visualization enables us to specify the paraObservational visualization enables us to specify the parameter of target objects. meter of target objects.

hydro simulation radiative transfer model obs. real obs.

Momosa et al. 1998C18O J1-0

L1551 IRS5

Intensity

Observational VisualizationObservational Visualization--NonLTE calculation--NonLTE calculation in Nested Grid Hierarchy-- in Nested Grid Hierarchy--

How is Outflow Observed?How is Outflow Observed?

K. Tomisaka

How is it observed?How is it observed?

• Optically thin Optically thin – emissivity emissivity is given as a function of is given as a function of nn and and TT

• not necessarily thinnot necessarily thin– radiation field is absorbedradiation field is absorbed– radiation transferradiation transfer– Local Thermo dynamicsLocal Thermo dynamics

• Radiation field affectRadiation field affect– nonLocalnonLocal

( ( ), ( ))T n ds x x cooling function

i 1i 2i

d

dII

ds

( , ), = ( , )T n T n ,

emissionabs

s

, , , , , ,( ) ( )n n m n n m cell n m m m n m m n cell m m jm n m n m n m n

B Bn A n J d C n A n J d n Cn nf n n n f n n n¥ ¥

< ¹ > ¹- ¥ - ¥

é ù é ùê ú ê ú+ - + = + - +ê ú ê úê ú ê úë û ë û

å å å åò ò

Radiative Transfer based on Monte Carlo method

from level n

spontaneousemission

radiative excitation

collisional excitation

to level n

mean intensity1

4J I d

n

collisionradiation

Non-LTE Detailed balance is solved being coupled with the radiative transfer.

(i,j,k)dI

I jds

0 ( ) ( )4 l lu u ul cellh n B n B

0 ( )4ul

u ul cellhj n A

I, ulj

, ulj , ulj

transfer equation

n n

(1) 　 On a randomly chosen line, is calculated byI

(2) Specific intensity1

Ray

J IN

intensity

absorption coefficient

emissivity

until self-consistent solutionis obtained

L=0

L=1

L=0

boundary ~CMB

from Intensity given by L0

Proper boundary condition for nested grid

simple grid nested grid

Simultaneous equation for N elements: 3G LevelN N N

GN 1D grid number

LevelN depth of nested grid

detailed balance + nonLTE radiation transfer is separately solved for each level. 3GN N

3 9 3) G LevelN N NΟ(

9Level GN N

nested gridnested grid

emissivity+absorption coeffiecientsare known


1800

AU

axisymmetric MHD axisymmetric MHD symulation datasymulation data

3D Cartesian Grid3D Cartesian Grid

J=3-2 J=3-2

J=7-6 J=7-6

excitationtemperature

Level 5

exCS T

extracting only L=5 nested grid L=1,2,…5

The difference looks small.

2000

AU


J=1-0 J=1-0

J=6-5 J=6-5

opticallythickline

opticallythinline

integrated intensity

intensityweightedvelocity

large difference

relatively smalldifference

2000

AU

Pole-on View for a prestellar CorePole-on View for a prestellar Core

(1) 2-component(2) Asymmetry Blue > Red

10K

0K

redblue

-1.5km/s 1.5km/s

self-absorption featureself-absorption feature

Blueshift

redshift

Redshiftemission from the diskis absorbed by low-Texenvelope

Blueshiftemission from the diskis not absorbed andobserved.

Blue redI I

CS J=3-2

60

z z

zz

line-of-sight

departingfar-side

60

z z

zz

line-of-sight

departingfar-side

CS J=7-6

“Nested” velocity structure

positive Vr in lower side

negative Vr in upper side

positive Vr

negative Vr

uppe

r par

tlo

wer

par

t

1M M 8

19 31.415 10 g cm 4 17

0 10 AU 1.5 10 cmR

1D Finite element HD + Radiation Transfer (Masunaga & Inutsuka 2000)

12 310 g cmc

11 310 g cm

10 310 g cm

9 310 g cm

8 310 g cm

Snapshot Snapshot -T distribution-T distribution

early

late

barotropy

(1) Accretion shock generates entropy. (1) Accretion shock generates entropy. (2) The amount of this excess entropy increases with time, since infall speed(2) The amount of this excess entropy increases with time, since infall speedis accelerated.is accelerated.

Snapshot Snapshot -T distribution-T distributionSPH + Radiation Transfer (Stamatellos + 2007)SPH + Radiation Transfer (Stamatellos + 2007)

c cT

Masunaga & Inutsuka 2000

SummarySummary

• In star formation process, magnetic In star formation process, magnetic fields play an important role.fields play an important role.

• Comparison of observation with the Comparison of observation with the observational visualization of observational visualization of simulation gives us a tool to simulation gives us a tool to understand the physics.understand the physics.– observation of polarization (magnetic field)observation of polarization (magnetic field)– observation of molecular rotational linesobservation of molecular rotational lines

• To go to radiation MHD is essential. To go to radiation MHD is essential.

NonLTE calculationNonLTE calculation in Nested Grid Hierarchy in Nested Grid Hierarchy

(1) prestellar and protostellar evolution(1) prestellar and protostellar evolution(2) contraction and outflow phases(2) contraction and outflow phases

, , , , , ,( ) ( )n n m n n m cell n m m m n m m n cell m m jm n m n m n m n

B Bn A n J d C n A n J d n Cn nf n n n f n n n¥ ¥

< ¹ > ¹- ¥ - ¥

é ù é ùê ú ê ú+ - + = + - +ê ú ê úê ú ê úë û ë û

å å å åò ò

Radiative Transfer based on Monte Carlo method

from level n

spontaneousemission

radiative excitation

collisional excitation

to level n

mean intensity1

4J I d

n

collisionradiation

Non-LTE Detailed balance is solved being coupled with the radiative transfer.

(i,j,k)dI

I jds

0 ( ) ( )4 l lu u ul cellh n B n B

0 ( )4ul

u ul cellhj n A

I, ulj

, ulj , ulj

transfer equation

n n

(1) 　 On a randomly chosen line, is calculated byI

(2) Specific intensity1

Ray

J IN

intensity

absorption coefficient

emissivity

L=0

L=1

L=0

boundary ~CMB

from Intensity given by L0

Proper boundary condition for nested grid

simple grid nested grid

Simultaneous equation for N elements: 3G LevelN N N

GN 1D grid number

LevelN depth of nested grid

detailed balance + nonLTE radiation transfer is separately solved for each level. 3GN N

3 6 3) G LevelN N NΟ(

6Level GN N

nested gridnested grid



1800

AU

axisymmetric MHD axisymmetric MHD symulation datasymulation data

3D Cartesian Grid3D Cartesian Grid

J=3-2 J=3-2

J=7-6 J=7-6

excitationtemperature

Level 5

exCS T


The difference looks small.

2000

AU


J=1-0 J=1-0

J=6-5 J=6-5

opticallythickline

opticallythinline

integrated intensity

intensityweightedvelocity

large difference

relatively smalldifference

2000

AU

prestellar spectra

CSJ=2-1

zline-of-sight

-1 -11kms 1kmsrV

max 10KBT

Blue>Red asymmetry

2000AU

infall motion


intensity weighted line-of-sight velocity ( )r r B r rV V T V dV I

integrated intensity ( )B r rI T V dV

CSJ=2-1

30 45

60 80

z z

zz

line-of-sight

reachingnear-side

departingfar-side

CSJ=7-6

30

60

z

z

line-of-sight

45

80

z

z


positive Vr in lower side

negative Vr in upper side

positive Vr

negative Vr

uppe

r par

tlo

wer

par

t

prestellar core protostellar core

30 30

60 60

Equation of State?Equation of State?SPH + Radiation Transfer (Whitehouse & Bate 2006)SPH + Radiation Transfer (Whitehouse & Bate 2006)

1.2M M 8

19 31.7 10 g cm 17

0 1.5 10 cmR

barotropy

c cT

gasT

radT

Is barotropy a good approximation?Is barotropy a good approximation?

1M M 8

19 31.415 10 g cm 4 17

0 10 AU 1.5 10 cmR

1D Finite element HD + Radiation Transfer (Masunaga & Inutsuka 2000)

12 310 g cmc

11 310 g cm

10 310 g cm

9 310 g cm

8 310 g cm

Snapshot Snapshot -T distribution-T distribution

early

late

barotropy

(1) Accretion shock generates entropy. (1) Accretion shock generates entropy. (2) The amount of this excess entropy increases with time, since infall speed(2) The amount of this excess entropy increases with time, since infall speedis accelerated.is accelerated.

Snapshot Snapshot -T distribution-T distributionSPH + Radiation Transfer (Stamatellos + 2007)SPH + Radiation Transfer (Stamatellos + 2007)

c cT

Masunaga & Inutsuka 2000

Radiation Magnetohydrodynamics Radiation Magnetohydrodynamics is needed.is needed.

SummarySummary

• In star formation process, magnetic In star formation process, magnetic fields play an important role.fields play an important role.

• Comparison of observation with the Comparison of observation with the observational visualization of observational visualization of simulation gives us a tool to simulation gives us a tool to understand the physics.understand the physics.– observation of polarization (magnetic field)observation of polarization (magnetic field)– observation of molecular rotational linesobservation of molecular rotational lines

• To go to radiation MHD is essential. To go to radiation MHD is essential.

Documents

Effect of Magnetic Field in Star Formation + Observational Visualization Kohji Tomisaka ( 富阪幸治 ) Division of Theoretical Astronomy / Center for Computational