Excesses of Magnetic Flux and Angular Momentum in Stars

1
Excesses of Magnetic Flux and Angular Momentum in
Stars

• National Astronomical Observatory (NAOJ)
• Kohji Tomisaka

2
Angular Momentum

• Angular Momentum Problem j ltlt j cl Specific
  angular momentum of a new-born star
• is much smaller than that of parent cloud

3
Excess Magnetic Flux

• Magnetic Flux of Main Sequence Stars
• Magnetic Flux of Parents Cloud

4
Angular Momentum Transfer

• Magnetic Braking

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

5
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.

6
What we have done.
Shus Inside-out Solution Larson-Penston Solution

• Dynamical contraction of slowly rotating
  magnetized clouds is studied by ideal MHD
  numerical simulations with cylindrical symmetry
  with nested grid. (cf. AMR)
• Evolution
• Isothermal Run-away Collapse Phase
• Adiabatic Accretion Phase

Nested Grid Method
7
Larson 1969, Penston 1969, Hunter
1977, Whitworth Summers 1985
Dynamical Collapse
Runaway Collapse
Accretion-associated Collapse
Shu 1977
Density increases infinitely
Inside-out Collapse
Hydrostatic Core
8
Runaway Collapse

• In Isothermal regime, even for magnetized clouds
  the run-away collapse Self-similar collapse.
• UniversalityNakamura et al. 99
• Initial apmag/pth0.05-10
• Final
• 2pG1/2Sc/Bc1.1-1.3

9

• Evolution is as follows Run-away Collapse
  (isothermal G1) Increase in Central Density
  Formation of Adiabatic Core(1st core G7/5)
  Accretion Phase Dissociation of H2 Second
  Collapse (G1.1) Second Core(G5/3)
  (Larson 1969)

10
Angular Momentum

• OUTFLOW is formed just outside the 1st molecular
  core.
• Angular momentum is effectively transported by
  the outflow motion and the gas with less angular
  momentum falls into the core.

11
Run-away Collapse Phase

• t0 0.6Myr
  1Myr

12
Accretion Phase

• High-density gas becomes adiabatic.
• The central core becomes optically thick for
  thermal radiation from dusts.
• Critical density
• An adiabatic core is formed.
• To simulate, a double polytrope is applied
• isothermal
• adaiabatic

13
Accretion Phase
B¹0, W¹0
a1, W5
L10
300AU
Run-away Collapse Stage
t1000yr
14
Weak Magnetic Fields (a0.1,W5)
B¹0, W¹0
Accretion Phase
0 yr
2000 yr
4000 yr
15
Accretion/Outflow Rate

• Inflow Rate is Much Larger than Shus
  Rate (1977).
• LP Solution
• Outflow/Inflow Mass Ratio is Large 50 .
• Source Point of Outflow Moves Outward.

16
Specific Angular Momentum
Angular Momentum Problem
Initial
Core Formation
7000 yr after Core Formation
Mass
17
Molecular Outflow
Optical Jets
L1551 IRS5
18
Optical Jets
Jets and Outflows

• 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.

19
Temperature-Density Relation
Jets and Outflows

• Optical jets are formed just outside the second
  core?

Tohline 1982
20
Jets and Outflows
L16
rc1019H2cm-3
2nd Runaway Collapse
Outflow
H2 Dissoc.
L8
rc1014.6H2cm-3
10R
X256
Jets
rc1021.3.H2cm-3
10AU
rs104H2cm-3
a1, w1/2
10R
21
Case with a0.1 w0.3
22
Microjet around S106 FIR

• H2O maser observation
• Small scale expanding bow shocks?
• No bipolar molecular outflow.
• Prediction Two outflows with different scales

Maser spots
4AU
25-40km/s
25AU
25AU
Class0 protostar
23
Centrifugal Radius

• Specific angular momentum
• Mass
• Centrifugal radius

• For a slow rotator,
• No outflow outside the 1st core?
• Jet outside the 2nd core?

24
Flux Loss

• Induction Equation of B-Fields
• After
• Diffusion speed is larger than free-fall speed.
  Joule dissipation.

s
M
Log nH
Nakano, Umebayashi 1986
25
Flux Loss(II)
first core
Magnetic Flux in Mrec
second core
26
Further Accretion
(A)
(B)

• If , a
  star with has
• Or if dipolar B-fields are formed (B),
  accretion would not increase the magnetic flux
  further.

• The final magnetic flux can be determined as the
  magnetic flux when the X-point is formed.

27
Numerical Method

• Ideal MHD Self-Gravity 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

L0 L23
28
Initial Condition

• Cylindrical Isothermal Clouds
• Magnetohydrostatic balance in r-direction
• uniform in z-direction
• B-Fields

• Slowly rotating ( rigid-body
  rotation)
• Added perturbation with l of the gravitationally
  most unstable mode lMGR.

lMGR
parameters
29
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.

30
Core Contracting Disk
B¹0, W0
Accretion Phase
Pseudo- Disk
Adiabatic (the first) Core
31
A Ring Supported by Centrifugal Force
W¹0 , B0
Accretion Phase
r
r
W
W
Accretion Stage
Run-away Collapse Stage
32
Why Does the Outflow Begin in the Accretion Stage?
B¹0, W¹0
Accretion Phase
Blandford Peyne 82
Mass Accretion Rate
Magneto-Centrifugal Wind
33
Angular Momentum Distribution
Angular Momentum Problem
(1) Mass measured from the center
(2) Angular momentum in
(3) Specific Angular momentum distribution
34
Magnetic Torque, Angular Momentum Inflow/Outflow
Rate
Mass
35
Ambipolar Diffusion?

• 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
  important.
• Assuming (on core
  formation), rotation period of centrifugal
  radius

36
Summary

• In dynamically collapsing clouds, the outflow
  emerges just after the core formation (t1000yr).
• In the accretion phase, the centrifugal wind
  mechanism magnetic pressure force work
  efficiently.
• In t7000 yr ( ), the outflow
  reaches 2000 AU. Maximum speed reaches
  

37
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.

38
Parameters

• Angular Rotation Speed
• Magnetic to thermal pressure ratio

39
Nest (Self-Similar) Structure
Run-away Collapse Phase
Along z-axis
40
Run-away Collapse

• Evolution characterized as self-similar

41
Magnetocentrifugal Wind ModelBlandford 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 qlt60deg the particle is
  accelerated. For qgt60deg decelerated.

Effective potential for a particle rotating with
w.
42
Momentum Flux (Observation)

• Low-Mass YSOs (Bontemps et al.1996)

Momentum

l
Luminosity
43
Angular Momentum
Angular Momentum Problem
(1) Mass measured from the center
(2) Angular momentum in
(3) Specific Angular momentum distribution
44
Effective Outflow Speed
a1
a0.1
W1
W5
W1
W5
45
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?

46
Momentum Driving Rate

• Molecular Outflows (Class 01 Objects) show
  Momentum Outflow Rate (Bontemps et
  al.1996)

47
Effect of B-Field Strength
B¹0, W¹0
Accretion Phase

• In small a model, toroidal B-fields become
  dominant against the poloidal ones.
• Poloidal B-fields are winding.
• Small a and slow rotation lead less effective
  acceleration.

48
Angular Momentum Problem
Angular Momentum Problem

• Typical specific angular momentum of T Tauri
  stars
• Angular momentum of typical molecular cores
• Centrifugal Radius

49
Molecular Outflow
Saito, Kawabe, KitamuraSunada 1996
L1551 IRS5
Optical Jets