Protostellar Jet in the Collapsing Cloud Core

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3 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

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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 AU

Protostellar Jet in the

Collapsing Cloud Core

1000 times close
-
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

Protostar

outflow

jet

dark

cloud

protostar

Purpose of This Study


Understanding the driving mechanism of Jets / Outflows


Using the numerical simulation, we calculated the


cloud evolution
from the molecular cloud


(n=10
4

cm
-
3
, r~10
4

AU)

until
the protostar


(n~10
20

cm
-
3
, r ~ 1R
sun
)
formation

HH30, Pety et al. 2006

Dead region

B

dissipation

(10
12
cm
-
3
<n<10
15
cm
-
3
)

B

amplification

B

amplification

B

B

B

Log T (K)

Log n (cm
-
3
)

10
10

10
15

10
20

10
5

10

10
2

10
3

10
4

Isothermal Phase

Adiabatic Phase

Second Collapse &
Protostellar Phases

Adiabatic core

(First core)

Formation

H
2

dissociation

To MS

protostar

formation

Gas Temperature


1D Radiative Hydrodynamics

Spatial Scale (AU)

10
4

100

1

0.1

Larson (1969)

Tohline (1982)

Masunaga & Inutsuka (2000)

cloud core

Thermal Evolution in the Collapsing Cloud

Protostar

Magnetic Evolution

Resistivity

Magnetic Reynolds number

h
: resistivity

v: free fall velocity

L: Jeans Length



Magnetic Reynolds number

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<10
12

cm
-
3
)
:

Low ionization rate, but
well
-
coupled
due to
t
ff

>
t
col



Moderate density
(10
12
cm
-
3
<n < 10
16
cm
-
3
)


Ionization rate decreases as density increases




Dissipation of
B
by Ohmic dissipation



High density
(n>10
16

cm
-
3
)

Some metals are ionized,
Well
-
coupled

Cloud

Protostar

Cloud evolution

B

B

B


Basic equations

Gas sphere in hydrostatic
equilibrium


Critical Bonner
-
Ebert Sphere


+ Rotation + Magnetic Field








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



Parameters
: α, ω


α=B
c
2
/(4
pr
c
s
2
)
:magnetic field strength


(ratio of the magnetic to thermal pressure)



w
=
W
/(4
p
G
r
)
1/2

: angular velocity


normalized by freefall timescale



Initial Value


Number density

n=10
4

cm
-
3


Temperature

T=10K


Bonnor
-
Ebert Sphere


Rotation Axis

Magnetic Field Line

Ω

B

4.6x10
4

AU

L=4


(B
x,0
, B
y,0
, B
z,0
) = (0, 0,
(
a
4
pr
c
s
2
)
1/2

)


(
W
x,0
,
W
y,0
,
W
z,0
) =
(0, 0,
w
(
4
p
G
r
)
1/2

)




Cloud scale: 4.6x10
4


AU


Mass


M
tot

=14

M
sun

Initial Settings

同時刻、異なるグリッドスケール

L = 1

L = 2

L = 3

L = 31

L=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:

l
max
=31 (
l

: Grid Level)



Total grid number:

128 x 128 x 64 x 31




For uniform grid, (128x2x10
30
)x(128x2x10
30
)x(64x2x10
30
)





~ (10
30
)
3

cells are necessary


Grid generation:
Jeans Condition

l

=1: L
box

= 4 pc, n = 10
3

cm
-
3


(initial)

l

=31: L
box

= 0.2 R
sun
, n = 10
23

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

n
c
=10
4

cm
-
3

n
c
=10
9

cm
-
3

n
c
=10
11

cm
-
3

n
c
=10
13

cm
-
3

n
c
=10
15

cm
-
3

n
c
=10
17

cm
-
3

n
c
=10
21

cm
-
3

n
c
=10
22

cm
-
3

Initial State

Isothermal
Collapse

First Core
Formation

Adiabatic
Collapse

Outflow
Driving

Magnetic
Dissipation

Second
Collapse

Protostar & Jet



n= ~5x10
11

cm
-
3

:First core formation,
B

field begins to be twisted



10
11
cm
-
3

<n< 10
13
cm
-
3

:
B
field strongly twisted, outflow appears



10
13
cm
-
3

<n< 10
16
cm
-
3

:
B
Field is dissipated by the Ohmic dissipation (B
r
, B
f
)




The magnetic field lines are uncoiled (Bz becomes major component
)




10
16
cm
-
3

<n< 10
20
cm
-
3
: Second collapse,
B

is coupled with the neutral gas, amplified again



n>10
20
cm
-
3


:

Protostar formation,
B
r
,
B
f

increase 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 10
12
-
10
16

cm
-
3

Ideal MHD model

Resistive MHD model

Dissipation
by the

Ohmic Dissipation

Low
-
velocity Flow from First core

High
-
velocity flow from Protostar

~1000 times

close
-
up



of the central area

360 AU

0.35 AU


First Core

n~10
11

cm
-
3
, r~10
-
100 AU


Protostar

n~10
21

cm
-
3
, r~0.01 AU

Outflow and Jet Driving Phase

v
outflow
~ 5 km/s

v
Jet
~50 km/s

Two distinct flows appear

in the collapsing cloud!!

L=12

L=22


Adiabatic core (first and protostar

core) formation


t
rot

<
t
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

10
3
-
10
5

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

b
~1
-
10

b
>1000

First Core


Protostar


Forces



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


First core: ~0.01 M
sun
, ~1 AU


v
Kep
~ 5 km/s


v
max
= 5 km/s
(simulation)


Protostar: ~0.01 M
sun
, ~1 R
sun


v
Kep
~50 km/s


v
max
= 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 ~1M
sun


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=10
4

cm
-
3
)


until the protostar formation
(
n~10
23

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

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 Core

Bow shock, Cavity,
Turbulence

unsteady