Transcript Outflows from YSOs and the angular momentum of new

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 b>bcr.
• Angular Momentum Problem: j* << j cl
Specific angular momentum
of
a
new-born
-1
2
P
2 -1
star: j 6 1016 R*
cm s
*
2 Rthat 10
is much smaller than
of day
parent cloud:
I
F IF
J
H KG
H K
F R I F  Icm s
G
J
G
J
0.1pc KH
4 kms pc K
H
2
jcl 5 10
21
2 -1
-1
-1
Angular Momentum Transfer
>1: For supercritical clouds
• Magnetic Braking


2G

1/ 2
t B  

( 4G a )

B0
 2  a VA
 Column density
vA
Free-fall time in
ambient matter
Alfven Speed Longer than
 a Ambient density
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.
Inflow star
Outflow
B-Fields
Mass
Ang.Mom.
Disk
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
Outflow
Shu’s Inside-out Solution
Larson-Penston Solution
Numerical Method
• Ideal MHD + SelfGravity + Cylindrical
Symmetry
• Collapse: nonhomologous
• Large Dynamic Range is
attained by Nested Grid
Method.
– Coarse Grids: Global
Structure
– Fine Grids: Small-Scale
Structure Near the Core
1/4
1/2
1
L0 ~ L23
Initial Condition
• Cylindrical Isothermal
Clouds
lMGR
– Magnetohydrostatic
balance in r-direction
– uniform in z-direction
• Slowly rotating
(~ rigid-body
rotation)
• Added perturbation
• B-Fields
with l of the
Bz   , Br  B  0 gravitationally most
unstable mode lMGR.
parameters
Run-away Collapse Phase
t=0
0.6Myr
  1, 0  5 (L2)
1Myr
Accretion Phase
• High-density gas becomes adiabatic.
– The central core becomes optically thick for
thermal radiation from dusts.  > 1
10
-3
n

10
cm
– Critical density = crit
• An adiabatic core is formed.
• To simulate, a double polytrope is applied
– isothermal
– adaiabatic
p  cs 
2
p K

n ncrit
 = 7/5
 = 5/3
n ncrit
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
B0, 0
Accretion Phase
Core + Contracting Disk
PseudoDisk
Adiabatic
(the first)
Core
0 , B=0
Accretion Phase
A Ring Supported by
Centrifugal Force


z

Run-away Collapse Stage

Accretion Stage
Accretion Phase
1,5
B0, 0
300AU
L10
Run-away Collapse Stage
1000yr
B0, 0
Accretion Phase
Why Does the Outflow Begin in
the Accretion Stage?
Rotation Speed
Run-away
Accretion
Collapse
stage
v v
v  v r

r
Toroidal B-Field B  B pol
d
 c / 2G
Rotation Angle
B  B pol
c
i
much
0.2 
0.4
Angle
B-Fields
between 60 – 70 deg
and
10 – 30 deg
a
disk
Magneto-Centrifugal Wind
Blandford & Peyne 82
Mass Accretion Rate
Angular Momentum Problem
Angular Momentum Distribution
(1) Mass measured from
the center
(2) Angular
momentum in
M( 1 )
z
z
M (  1 ) 
dV
 1
L(  1 ) 
rv dV
 1
(3) Specific Angular
momentum distribution
j (M ) 
L(   1 )
M (   1 )
Specific
Run-away Collapse Angular
Momentum
High-density region
is formed by gases
with small j.
Angular Momentum Problem
Initial
Core Formation
Accretion Stage
Magnetic torque
brings the angular
momentum from the
disk to the outflow.
7000 yr after
Core Formation
Outflow brings the
angular momentum.
Mass
Magnetic Torque, Angular Momentum
Inflow/Outflow Rate
Accretion
Phase
Inflow
Torque
Core
Formation
Inflow
Torque
Initial
Inflow
Outflow
Torque
Mass
Ambipolar Diffusion?
• In weakly ionized plasma, neutral
molecules have only indirect coupling with
the B-fields through ionized ions.
200yr
• Neutral-ion collision time  K n
• When  ni  dyn , ambipolar diffusion is
important.
 ni  rot
GM
GM
j


(
0
.
1

0
.
25
)
• Assuming
(on
core
c
c
formation), rotation period of centrifugal
Fp I FM IF c I
400 yr
radius:  2p GM
H
H
H
c
0.1K
0.1MK
190 ms K
ni
s
1/ 2
i
5 8
s

3
3
3
rot
s
3
s

1
Molecular Outflow
L1551 IRS5
12
C O J 1  0
5
10 AU
Edge of Hole made
by Molecular Outflow
Optical Jets
Optical Jets
Jets and Outflows
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
Temperature-Density Relation
• Optical jets are formed just outside the
second core?
Temperature-Density Relation
15 2nd Core
5 Log ｎ 10
4
1st Core
3
Log T
Outflows
Jets?
2
1
Log 
Tohline 1982
Jets and Outflows
2nd Runaway 1 0
Collapse
Outflow
L8
z
L16
c=1019H2cm-3

5
z
c=1014.6H2cm-3

2 1 0

5
10R
0 .002
z
Jets
c=1021.3.H2cm-3
10AU
s=104H2cm-3
=1, w1/2
10R
Summary
• In dynamically collapsing clouds, the
outflow emerges just after the core
formation (~1000yr).
• In the accretion phase, the centrifugal wind
mechanism & magnetic pressure force work
efficiently.
• In ~7000 yr (M 0.2 M), the outflow
reaches 2000 AU. Maximum speed reaches
*
vmax 7cs
c
F
I.
1.3 km 
s
H
190 m 
s K
-1
s
-1
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.
Larson 1969, Penston 1969,
Hunter 1977,
Whitworth & Summers 1985
Dynamical Collapse
Hydrostatic Core

Accretion-associated Collapse
Density increases infinitely
Runaway Collapse
Shu 1977
Inside-out Collapse
Parameters
• Angular Rotation Speed
F n I F  I
G
J
G
J
100 H cm K H5 K
H
1/ 2
 0  9  10
14
rad  s
-1
s
0
-3
2
v  2.7km  s
-1
F 
H
9  10 rad  s
• Magnetic to thermal pressure ratio
 ( B0 / 4 ) / pth 1, 0.1
2
0
14
r I
IF
G
J
K
1pc K
H
cl
-1
Run-away Collapse Phase
L12
Nest (Self-Similar)
Structure
Along z-axis

7
2 128
L5
vz
Bz
z
z
Run-away Collapse
• Evolution characterized as self-similar
10AU
0.1pc
Magnetocentrifugal Wind Model:
Blandford & Peyne 1982
• Consider a particle
rotating with rotation
speed w= Kepler
velocity and assume w
is conserved moving
along the B-fields.
• Along field lines with
<60deg the particle is
accelerated. For
>60deg decelerated.

Effective potential for a
particle rotating with w.
Momentum Flux (Observation)
Momentum
• Low-Mass YSOs (Bontemps et al.1996)
FCO  Lbol / c
Class0
l Class1
Luminosity
Angular Momentum Problem
Angular Momentum j(M)
(1) Mass measured from
the center
(2) Angular
momentum in
M( 1 )
z
z
M (  1 ) 
dV
 1
L(  1 ) 
rv dV
 1
(3) Specific Angular
momentum distribution
j (M ) 
L(   1 )
M (   1 )
dM V
Effective Outflow Speed
1
0.1
1
Veff  dt
5
1
dM
dt
5
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
B-Fields
• Contraction vs Outflow?
• When outflow begins?
• Condition?
Disk
Inflow
Accretion/Outflow Rate
z
 
  v 
m
ndS
2000yr 4000yr 6000yr

5
• Inflow Rate is Much
Larger than Shu’s
Rate 0 .9 7 5 c s3 / G (1977).
• LP Solution: 2 9 c s3 / G
• Outflow/Inflow Mass
Ratio is Large ~ 50 %.
• Source Point of
Outflow Moves
Outward.
10 Myr
-1
4
3
2
1
 Shu
m
Momentum Driving Rate
2000yr 4000yr 6000yr
• Molecular Outflows
(Class 0&1 Objects)
show Momentum
Outflow Rate
(Bontemps et al.1996)

6
3 10 5 10
dmvz
z

dt

5

4
-1
Myr km s
Upper / Lower
Boundaries
-1
2 10 Myr km 
s

5
-1
-1
1 10 Myr km 
s
-1
vz 2 dS
-1
B0, 0
Accretion Phase
Weak Magnetic Fields
(=0.1,5)
0 yr
2000 yr
4000 yr
Accretion Phase
B0, 0
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
effective acceleration.
Angular Momentum Problem
Angular Momentum Problem
• Typical specific angular momentum of T
-1
2
Tauri stars
R
P
F
I
F
I
j 6 10
cm s
G
J
H
2 RK
10day K
H
Angular momentum of typical molecular
F
I
cores
R I F 
j 5 10 G JG
cm s
J
0.1pc KH
4 kms pc K
H
16
2 -1
*
*
•

2
21
2 -1
cl
-1
• Centrifugal Radius
j
2
j cl  j*
F
H
j
Rc 
0.06 pc
21
2 -1
GM
5 10 cm s
-1
IFI
KH
MK
2
M

1
Rc  R*
Molecular Outflow
H CO
L1551 IRS5
Saito, Kawabe,
Kitamura&Sunada
1996
12
C O J 1  0
13
Optical Jets
5
10 AU
"
1400AU = 10
Snell, Loren, &Plambeck 1980
+