Transcript 低温ガスを考える必要がある

Three-dimensional Global MHD
simulations of the Magnetic Loop
Structures in our Galactic Center
Galactic Center Workshop 2009,10,19 Shanghai
MACHIDA Mami (Nagoya Univ.)
collaborator
MATSUMOTO R.(Chiba Univ.), NOZAWA S.(Ibaraki
Univ.), TAKAHASHI K. (JAMSTEC), TORII K., KUDO N.,
and FUKUI Y. (Nagoya Univ.)
Galactic Center Workshop 2009
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Magnetic loop structure in the Galactic center
Length(pc) Mass (Msun)
220 pc
300 pc
loop1
500
loop2
300
1.7
5
×10
※Distance from earth:8500pc
※Estimated mass: lower limit
(We assume LTE to 13CO)
The kinematic energy of lower limit is estimated to be 1051erg.
This energy is too large to be explained by a single supernova explosion.
-> We considered this structure is formed by the magnetic floatation.
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Magnetic flotation of Parker instability
Loop structures observed in the solar corona are produced by the buoyant
rise of magnetic loops from below the photosphere.
⇒ Parker (1966) proposed that magnetic loops can be created in galactic
gas disks by an MHD instability driven by buoyancy.
However, it was hard to observe such galactic magnetic loops.
Magnetic loop in solar corona
(TRACE：191Å)
MHD activities of galactic disks
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
2D MHD simulations Projected on the sky
White curve: magnetic
field lines
Fukui et al. (2006)
Color : horizontal velocity
sliced in the vertical plane.
Numerical
simulations
reproduced
structures similar to
the observed loops.
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
The effect of galactic rotation
Ω
Chou et al. 1997
Coriolis force
Due to the Coriolis force, the magnetic tension
becomes larger that in no rotating layer.
Due to the magnetorotational instability, the
disk becomes turbulent.
Matsumoto, Tajima (1995)
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Purpose of this talk
• We study the evolution of galactic gas disk
inside 1kpc from the Galactic center.
• We try to reproduce of the loop structures by
global simulation.
Machida + (2009)
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Basic equations
Ideal MHD equations
Mass conservati on Eq. of Motion Induction
eq. Energy eq.

t
    v   0
v
1
1
  B   B   
 v v   p 
t

4 
B
t
   v  B 
 
     v   p  v  0
t
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Galactic gravitational potential
Miyamoto & Nagai(1975)
Galactic gravitational potential created by disk + bulge star mass
  , z  
GM

2
1
 z  b
2
2
1

1/ 2

GM



2
Subscription 1: Bulge component
Subscription 2: Disk component
a
1.Bulge
2.Disk
0
b

2
 a 2  z  b
2

 
2
2 1/ 2
2
1/ 2
Nishikori et al. (2006)
M
7.258 2.05
0.495 0.520 25.47
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Initial Model
Equilibrium gas disk threaded by toroidal magnetic fields （Okada et al. 1989）
・Angular momentum L∝r0.496
・Sound velocity
cs0= 0.14 v0 0.05v0
・Specific heat ratio
・Plasmaβ
γ=5/3、1.05
β=1, 10 ,100
◇ We simulated warm component of the inter stellar gas (T～104K) because the
size of the magnetic loops is determined by the scale height of this warm
component.
◇ We ignore self-gravity of gas and radiative cooling.
Units
Length
Velocity
Mass
Temperature
r0 = 1kpc
v0 = 207 km/s
M0 = 1010Msolar
T0 = 5×106 K
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Magnetic Loops on the Galactic Corona
left） Blue surface： volume rendered image of the gas density
Curves： Floating magnetic loops. Color depicts vertical velocity from minus to
plus: blue – white –red.
right） Enlarged figure of the left panel. Curves are same on the left panel.
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Schematic picture showing the formation of
magnetic loops
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Summary 1
• NANTEN observations discovered molecular loops in
the Galactic center region.
• Global 3D MHD simulations of galactic center gas
disks showed that magnetic loops with length 1kpc
and height several hundred pc can be created.
• About 400 magnetic loops are formed in the corona.
• Gas temperature became about 105 K by the
adiabatic heating.
Galactic gases have multiple component, such as cool molecule
(10K), warm HI (1000K), and hot plasma (106K).
We have to consider the cooling and heating effect.
Before including the molecular cooling, we try to calculate an
iso-thermal (～104K) model .
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Density and magnetic structure of isothermal model
• About 20 magnetic loop are formed in the corona.
•The size of loop is about 1kpc length, 60pc height.
•Smaller loops are emerging below the large loop.
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Conclusion
• Magnetic loops with length 1kpc and height several
hundred pc can be created by the global 3D MHD
simulations.
• About 400 magnetic loops are formed in the corona.
• Gas temperature became about 105 K by the
adiabatic heating.
• In the iso-thermal model, about 20 magnetic loops
are formed.
• Loop size in isothermal model becomes smaller than
in the adiabatic model.
HIガスの鉛直方向分布
21cm線の観測により、鉛直方向1kpc
以上までHIガスが一様に広がっている
事がわかった。(Oosterloo et al 2007)
↓
暖かいHIガスに対応する
10000Kの等温ガス円盤を仮定し
た数値実験を行い、その振る舞
いを調べる
ガス円盤上のループ構造
•大きなループ構造の下に多数
の浮上途中の構造が形成され
ている。
•全長1.5kpc程度の大きな浮上
構造の上に小さなループが多
数連なっている。小ループの長
さは約300pcである。これは、お
およそ円盤のスケールハイトの
10倍になっている。
•高さ50pcまでは弓型の膨張を
しているが、50pcを超えると急
激に浮上する箇所が見られ、
立った構造になる。
Galactic Center Workshop
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Critical wavelength for the Parker instability
Buoyancy （ρ’－ρ）ｇ ＞ Magnetic tension B2 /（４πｒ’）
When the buoyancy force created by sliding down the gas along the magnetic field
line exceeds the restoring magnetic tension.
λ ＞ λｃ ＝ ８（１＋１/β） H1/2
Instability grows for long wave length perturbations along the magnetic field lines.
The most unstable wave length is about 10 times of the scale height.
EANAM2006. 11.1
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
General Properties of Magnetized
Disks
The initial weak magnetic fields are
amplified due to the magneto-rotational
instability (MRI).
Due to the MRI, the disk becomes turbulent.
Averaged plasma β is about 10 inside the
disk.
Mass accretes to the central region losing
the angular momentum.
When the magnetic energy comparable to
the gas pressure, magnetic pressure driven
outflows emerge from the central region.
This outflows create a large-scale poloidal
magnetic field in the inner most region.
EANAM2006. 11.1
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Histogram of Magnetic Loops
Gray shade boxes show the
loops whose height exceed
over 200pc.
(a) Maximum loop height
(b) Length between loop footpoints.
(c) Distribution of the
azimuthal angle
(d) Distribution of the radial
direction
About 180 loops picked up on
the upper half of the gaseous
disk.
Some concentrations appear
both in azimuthal range and
radial range.
EANAM2006. 11.1
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Relation of the density to magnetic
loops
left） equatorial density averaged in |z| <0.06. Gray scale indicates the density. Dotted curves show the
magnetic loops projected on to the equatorial plane.
right） equatorial density normalized by the azimuthally averaged density ρ/<ρ>. Symbols denote the
position of the loop tops.
Equatorial density shows the m=1 one-armed distribution.
Loops are formed in the lower density region because the magnetic energy
becomes higher in lower density region.
EANAM2006. 11.1
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Distribution of quantities along the
loop
Sound speed
Vz
Loop foot points becomes high density, high plasma β, and loop top is lower density and
β=1. It means that this loop is formed by the Parker instability.
EANAM2006. 11.1
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Position – Velocity diaglam
This magnetic loop is same as yellow magnetic loop on the density distribution.
Foot points show the larger velocity dispersion than the loop top.
浮上ループの形成（町田ら2009）
• 銀河円盤とバルジを考慮し
た、銀河ガス円盤の磁気流
体数値実験を行った。
• 円盤コロナ中にパーカー不
安定性による磁気ループ構
造が数多く形成される事を示
した。
• ループ形成位置には空間的
に偏りがある事がわかった。
円盤ガスはおおよそ10万度
→ 10度～1万度のガス＋100万度程度のプラズマ
低温ガスを考える必要がある
Isothermal disk model
• Exponential density
distribution
• Isothermal ～ 10000K
→We assume that the heating
of the magnetic dissipation
balance with the cooling.
• Kepler rotation
• Initial magnetic fields has only
azimuthal component and the
magnetic pressure is β=100.
Basic equations
Resistive MHD equations (isothermal)
Mass conservati on Eq. of motion Induction
v
t
equation t
   v   0
 v v  
B
t

1

p 
   v  B    J
1
4 
  B   B   
2
  0.005 ( x  0.1 kpc)
5  10
Miyamoto
-4
( x  0.1kpc)
- Nagai Potential ：   , z  
GM

2

1
 z b
2
2
1

1/ 2

GM



2


2
 a2  z  b
2


2
2 1/ 2
2


1/ 2
Galactic Center Workshop 2009
Introduction: Observations
Introduction: Theory
Models
Numerical Results
Conclusion
Magnetic loop structure in the Galactic center
Length(pc) Mass (Msun)
220 pc
300 pc
loop1
500
loop2
300
1.7
5
×10
※Distance from earth:8500pc
※Estimated mass: lower limit
(We assume LTE to 13CO)
・kinetic energy
～1.5×1051erg
→ 100 × SN energy