Masahiro Machida 　 (Kyoto Univ.) Shu-ichiro Inutsuka (Kyoto Univ.), Tomoaki Matsumoto (Hosei Univ.)

Outflow jet

first core protostar

v~5 km/s v~50 km/s

360 A

U

Protostellar Jet in the Protostellar Jet in the Collapsing Cloud CoreCollapsing Cloud Core

1000 times clo

se-up

?Star Formation and Jet / Outflow

Before the star formation Just after the star formation

Molecular Cloud Core Hirano et al. (2006)Jet from protostar

Stars born in the molecular cloud core

Jet / Outflow always appears in the star formation process

Jet / Outflow plays crucial roles in the star formation

They are closely related to the stellar mass

They transport the angular momentum from the cloud core

・・・・

(Nagoya Univ.)

We cannot observe

Jet /outflow driving phase

Protostellar Outflows and Jets

Velusamy et al. 2007

In star-forming regions, there are two distinct flows: Outflows and Jets

◆Molecular Outflow ： low velocity (~10 km/s), wide opening angle

◆Optical Jet: high velocity (~100 km/s), well-collimated structure

Optical Jet is enclosed by Molecular Outflow

But, Mechanism is still unknown outflow

jet

protostella

r disk

Protostar

outflow

jet

dark cloud

protostar

Purpose of This StudyUnderstanding the driving mechanism of Jets / Outflows

Using the numerical simulation, we calculated the cloud evolution from the molecular cloud (n=104 cm-3, r~104 AU) until the protostar (n~1020 cm-3, r ~ 1Rsun) formation

HH30, Pety et al. 2006

Dead regionB dissipation(1012cm-3<n<1015cm-3)

B amplification B amplification

B BB

Lo

g T

(K

)

Log n (cm-3)

1010 1015 1020105

10

102

103

104

Isothermal Phase Adiabatic Phase Second Collapse & Protostellar Phases

Adiabatic core(First core)Formation

H2 dissociation

To MS

protostarformation

Gas Temperature

1D Radiative Hydrodynamics

Spatial Scale (AU)

104 100 1 0.1

Larson (1969)Tohline (1982)Masunaga & Inutsuka (2000)

cloud core

Thermal Evolution in the Collapsing CloudProtostar

Magnetic EvolutionR

esis

tivi

ty

Mag

netic R

eyno

lds n

um

ber : resistivity

v: free fall velocityL: Jeans Length

◆　Magnetic Reynolds number

L

R Me

v,

Ohmic dissipation

Well-Coupled Well-Coupled

◆　Resistivity is fitted as a function of n and T

　　　　　　　　　　　　　　　　　(Nakano　et　al.　2002)

Coupling between the magnetic field and neutral gas (weakly-ionized plasma)

Low density (n<1012 cm-3): Low ionization rate, but well-coupled due to ff > col

Moderate density (1012cm-3<n < 1016cm-3) ： Ionization rate decreases as density increases　　　　　　　　　　　　　　　　　　　　　　　　　　⇒ Dissipation of B by Ohmic dissipation

High density (n>1016 cm-3) ： Some metals are ionized, Well-coupled

Resistivity

Reynolds number Re

Cloud ProtostarCloud evolutionCloud evolution

B B

B

◆Basic equations

),( Tn

Gas sphere in hydrostatic equilibrium Critical Bonner-Ebert Sphere

+ Rotation + Magnetic Field

Magnetic field lines are parallel to the rotation axis: B//

　Parameters:　α,　ω

α=Bc2/(4cs) :magnetic　field　strength

　　　　(ratio　of　the　magnetic　to　thermal　pressure)

=/(4G)1/2 :　angular　velocity　　　　　　　　normalized　by　freefall　timescale

　　Initial ValueNumber density ： n=104 cm-3

Temperature ： T=10K

Bonnor-Ebert Sphere

Rotation Axis

Mag

net

ic F

ield

Lin

e

Ω

B

4.6x104 AU

L=4

(Bx,0, By,0, Bz,0) = (0, 0, (4cs)1/2 )

(x,0,　y,0,　z,0)　=　(0, 0, (4G)1/2　)

Cloud scale: 4.6x104 AU

Mass ： Mtot =14 Msun

Initial Settings

同時刻、異なるグリッドスケール

L = 1

L = 2L = 3

L = 31L=4

Schematic view of Nested Grid

At the same epoch but different spatial scales

Example of Nested Grid

3D Resistive MHD Nested Grid Method Grid size: 128 x 128 x 64 (z-mirror sym.) Grid level: lmax=31 (l　: Grid Level) Total grid number: 128 x 128 x 64 x 31 　

For uniform grid, (128x2x1030)x(128x2x1030)x(64x2x1030) 　

　

~ (1030)3 cells are necessaryGrid generation: Jeans Condition

l　=1: Lbox = 4 pc, n = 103 cm-3 　 (initial)l　=31: Lbox = 0.2 Rsun, n = 1023 cm-3 (final)

10 orders of magnitude in spatial scale 20 orders of magnitude in density contrast

Numerical Methods

Cloud Evolution from Molecular Cloud to Protostar

nc=104 cm-3 nc=109 cm-3 nc=1011 cm-3 nc=1013 cm-3

nc=1015 cm-3 nc=1017 cm-3 nc=1021 cm-3 nc=1022 cm-3

Initial State Isothermal Collapse

First Core Formation

Adiabatic Collapse

Outflow Driving

Magnetic Dissipation

Second Collapse

Protostar & Jet

n= ~5x10n= ~5x101111 cm cm-3-3 :First core formation, B field begins to be twisted

101011 11 cmcm-3-3 <n< 10 <n< 1013 13 cmcm-3-3 : B field strongly twisted, outflow appears

101013 13 cmcm-3-3 <n< 10 <n< 1016 16 cmcm-3-3 : B Field is dissipated by the Ohmic dissipation (Br, B) The magnetic field lines are uncoiled (Bz becomes major component⇒ )

101016 16 cmcm-3-3 <n< 10 <n< 1020 20 cmcm-3 -3 : Second collapse, B is coupled with the neutral gas, amplified again

n>10n>1020 20 cmcm-3-3 : Protostar formation, Br, Bincrease again

100

AU

Evolution of the Magnetic field at center of the cloud

Grid level L =14 (Side on view)Magnetic flux against the central density

Magnetic flux is largely removed from the first core for 1012-1016 cm-3

Ideal MHD model

Resistive MHD model

Dissipation by the Ohmic Dissipation

Low-velocity Flow from First core High-velocity flow from Protostar

~1

00

0 tim

es

c

los

e-

up

of th

e c

en

tral a

rea

360 AU 0.35 AU

First Core ： n~1011 cm-3, r~10-100 AU

Protostar ： n~1021 cm-3, r~0.01 AU

Outflow and Jet Driving Phase

voutflow~ 5 km/s vJet~50 km/s

Two distinct flows appear in the collapsing cloud!!

L=12 L=22

Adiabatic core (first and protostar core) formation ⇒ rot < collapse

Magnetic field lines are twisted ⇒ ⇒ 　 Flow driving

Each core has different scale and different magnetic field strength

First Core does not experience the Ohmic dissipation: Strong field, hourglass 　

Protostar experiences the Ohmic dissipation: Weak field, straight lines

Driving Phase of Each Flow

1000 times close-up

103-105 yr

Different degrees of the collimation are caused by different driving mechanisms

Around First Core (Outflow)　 Lorenz Centrifugal Thermal Pressure ≒ ≒ (inflow)

Around Protostar (Jet)　 Centrifugal Thermal Pressure >> ≒ Lorentz (inflow)

Magnetocentrifugal wind First core, Outflow⇒

Driving Mechanism

Magnetic pressure gradient wind　 + MRI 　　　⇒　 Protostar, Jet

Disk Wind

Strong B

Wide Opening Angle

B gradient

Weak B

Narrow Opening Angle

・ Strong B・ flow along B lines・ hourglass B

・ weak B・ Flow along rotation axis・ straight B

Collimation

~1-10 >1000

First Core Protostar

Forces

Flow speed is determined by gravitational potential of each core (Kepler speed)

First core: ~0.01 Msun, ~1 AU v⇒ Kep~ 5 km/s ⇔ vmax= 5 km/s (simulation)

Protostar: ~0.01 Msun, ~1 Rsun v⇒ Kep~50 km/s ⇔ vmax= 50 km/s (simulation)

We calculated the very early phase of the star formation

Flow speeds increases with core mass

The Kepler speed is proportional to M∝ 1/2

When the first core and protostar grow up to ~1Msun

Outflow v⇒ Kep~ 50 km/s

Jet v⇒ Kep~500 km/s

Flow Speed

20 AU

First core

Proto star

Driver Speed collimation Mechanism Configuration of B

Outflow First core Slow (~10km/s) △ Disk Wind Hourglass

Jet Protostar High (~100km/s) ◎ Mag. pressure Straight

Our simulation could naturally reproduce properties of outflows and jets

Properties of Outflow and Jet

Schematic View

Low-velocity outflow is enclosed by the high-velocity Jet

Summary To avoid artificial settings around the protostar, we calculated the 　 cloud evolution (or jet driving) from the molecular cloud (n=104 cm-3) until the protostar formation (n~1023 cm-3)

Outflow is directly driven from the first core (not entrainmented by jet)

Two distinct flows: Outflow from the first core, Jet from the protostar

Outflow: wide opening angle and slow speed

Jet: well-collimated structure and high speed

The differences between outflow and jet is caused by different strength of magnetic field, and different depth of gravitational potential

Different strength of magnetic field is caused by the Ohmic dissipation

Deferent depth of the gravitational potential is cause by the thermal evolution of the collapsing cloud

10000 AU

Outflow driving point (small scale)

Outflow propagation (middle scale)

Velusamy et al. (2007) 　 HH47

Interaction between outflow and molecular cloud

Interaction between outflow and host cloud (large scale)

500 AU

8000 AU

2000 AU Initial Molecular Cloud CoreBow shock, Cavity,

Turbulence

unsteady