Chapter 8
Radiation Hydrodynamics
1
8.1 Radiation Transport
1 

c t




I (t , r ,  )     I (t , r ,  )   (t , r )   (t , r ) I (t , r ,  )
1 
c t
1 
c t
I
I
d
d






x

r

I




 I

(1   ) 
2
I


I I S
r


d 
I





 I


dx
S



  /

2
Integrated form
(1) Plane geometry

I (x)  e
 e
  ( x )
   ( x )

( I (0, ) 

( I ( d , ) 

x

d
e

S ( x) d  )
 

S ( x ) d   )
0
e
x
 
(2) Spherical Geometry


r
I



I (r , b)  e


 I
 

1


x

 dx
0

[I (R, b) 



e

R
1 b
2
r
r
2


 dx
x

S d  ]

 (r )

d

0
   r
  
1
dr  2 b

 (r )
1 b
2
R
r
2
dr  r
 (r )
1 b
2
r
2
dr
3
Emissivity and Opacity




 , Te 







 

ff
ff
 



fb
bf

 
 



 , Te 
bb

bb
Coupling term with electron fluid

S r    d  d 

 
 I

4
Angular moment equation

t
E


 F
E


1
c
F


 4 






 c E

I d
4
Radiation energy density
Radiation heat flux
Radiation pressure
I  d
4
1 
c
2
t
F

 P


  F
P



1
c

  :  I d
5
Radiation pressure tensor (1)


( P ) i 
x k

P ki 
P ki

1


c

k
 i I d

I ( x ,  )  I 0 ( x ) ( , x )
 
4
E

( , x )



d   4
4
c

I0
1

 d  2
1
F


c
2
E


1

 d
1
6
Radiation pressure tensor (2)
 P

P   0
 0

0 
0
 1
0   0
2

P 
0
0
P
0
P



0

E   3 P 
0
0
E   3 P
0
1

E


1
1
2

  d
2
Equation to Radiation Energy Density (Plane Geometry)

E

t
1 
c
2
t

F


x

F

x

P
 4 

 



 c E


c
F

7
Equation to Radiation Energy Density (Plane Geometry)

t
E
2

1 
r
1 
c

t
F

r
2


P

f
2
P
r

f
3P


E


 c E

 
r


 f E

1
2


 ( r F )  4 

1
1


F

c


  d
1 3
 
 1
2
 1
   2 (   1)
8
Example of Angular Distribution in case of plane gold foil
9
Equation of Radiation in Fluid Frame
Plane Geometry
d

(
dt
 d

E
)

(
F
c dt

x

)

(F

x


 u E )  4 
(cP


u



 c E

F )   F


c
Spherical Geometry

d
(
E

dt
 d
c dt
(

F
)
r


1 
)

r
2
r
2
[r (F

(cP ) 


 u E )]  4 
1 
r
2
r
(r
2
u
c


F )c

 c E
3P


 E


  F
r
10

8.2 Radiation Hydrodynamics

t

t

t
 
(  
x

( u ) 


( u )  0
(  u  Pm )  S m
2
x
u )
2
2

x
r
[  u ( 
Pm


u
2
)]  S e
r
2
Total Energy and Momentum Conservation Relations

t

t
( u 
(  
F
c

2
R
2
)

x
u  E )
2
R
( u  P  P )  0
2

x
[  u ( 
R
P


u
2
)F
R
] 0
2
11
The coupling term with matter
S
S
E
F


2

1

c
r
e
R
u


r
m
~




 F d
0



(c E


 4  ) d 
0
P
R
u
2
~ o(
1 u
 c
F
)
R
c u
2
~ o(
u
2
c
2
)

 1   ( x ) cos 
c
3

 E

P


1
3
E

F

 

c
3

x
E

12
Multi-group Diffusion Approximation

t
E



x

(
l c 
3 x
l
B



E

8 h 

 cx E


3
3
 E (
R
P

1

c
R

E )  4
1
e


0
h  kT

1
B )
4 
T
4
c
13
Near LTE Approximation (Gray Approximation)

t
EP 
R
 lRc 
E P  4 
R
x 3 x
R
 c P E P
R
Rosseland mean-free-path
lR 


l
0




0

B d
T


B d
T



0

l G R ( u ) du
Planck opacity
P 




 B d
0


0
GR 

B d



0
4
15
4
u e
4
(1  e
u
u
)

 G P ( u ) du
GP 
15

4
u
3
e 1
u
14
2
Multi-group gray diffusion approximation
F


j 1


E d  E
E
t
i

 
lR c 
3 x
i
R
EP
j  0 N G ,
i  1 N G
j

l
R

j 1
i
l
j


j 1
j




t

(
l ic 
3 x
E
i
)  4
i


B d
T


B d
T
 c

i


j 1
i
E

i

 B d
j


j 1

B d
j
15
Eddington coefficient (How to model angular distribution)

F
F
i
i

R
 
R
l ic 
3 x
i
1 R
i

1
3
 ( ) 
E
i
l
cE
i
i

F fs i  c E
i
 S gn

1
E
i
i
x
E
i
1
R coth R  R cos 
16
Variable Edington Factor
R  

c
4 

x
E

 (R) 
F
1
(coth R 
R
f


1
f
  ( R )  RcE
1

)
R
0 . 01932 R 1  0 . 2694 R 1
2

3



1  0 . 5953 R 1  0 . 02625 R 1
2
1
0  R1 
3

1
2
 R1 
3
2
R
2
1
1
3
1
3
 R1  1
17
8.3 Computer Simulation of Gold Foil
18
Spectrum from Gold Foil irradiated by Lasers
(Experiment VS Simulation)
19
X-ray Conversion Rate ( Experiment VS Simulation)
20
CRE model is essential for Gold Plasma
CRE: Collisional Radiative Equilibrium
21
X-ray confinement with a variety of gold cavities
22
Radiation Temperature from Gold Cavity
23
8.4 Radiation Hydrodynamics in the Universe
Planetary Nebulae (HST)
24
25
Radiation Hydrodynamics Model of Planetary Nebulae
26
Eagle Nebula
by HST
27
28
29
30
Accretion Disk and Black Hole
Photo-ionization by X-rays
from BH
Super-Massive
BH of C of G
(Image by HST)
400 ly
88,000 ly
31
32
多くの銀河の中心には、質量
が太陽の一千万倍を超える巨
大ブラックホールがあると考
えられていますが、確実な証
拠はこれまでつかむことがで
きませんでした。
このたびVLBI観測によって中
心天体のまわりの小さな領域
で高速に回転するガスや星の
すがたがとらえられました。
この回転が太陽系の惑星のよ
うなケプラー運動なら、中心
天体の質量は簡単に算出でき
ます。NGC4258(M106) という
銀河系の中心近くのガス回転
運動の様子をVLBI観測等に
よって調べたところ、半径
0.13 パーセクより小さい領
域に太陽の3600万倍の質量が
存在することがわかりました。
平均密度はこれまでブラック
ホールの候補と考えられてき
た天体の40倍と大きく、
NGC4258の中心にブラック
ホールが存在する有力な証拠
と考えられています。
＜三好 真＞
33
Figure 1: NRAO Very Large Array image of the radio galaxy 3C 403 at a wavelength of 3.6
cm. The intensity range of the colors (in Jansky, Jy, units) is indicated at the right hand side.
The red arrow points at the galaxy's nucleus. The spectrum shown in the upper left hand
inset was taken with the Effelsberg 100m telescope. The y-axis is flux density in Jy, while the
x-axis gives the recession velocity (in km/s), i.e. the speed which with 3C 403 and the Milky
Way are moving apart. The green arrow points at the systemic radial velocity of the whole
galaxy.
34
Image: National Radio Astronomy Observatory/Rick Perley (NRAO/AUI/NSF)
Eta-Carina
35
36
Photo-ionized plasma in binary system
37
38
39
Ionization Parameter x
40
8.5 Photo-ionized Plasma Experiment
41
42
43
Experimental setup
• Everything shown is completely destroyed
during the experiment!
44
Spectral characterization
• 300 11.5 m tungsten
wires
• 20 MA current
• 100 ns rise time
• 8 ns FWHM peak
• 120 TW peak power
• x  25 erg cm/s at the peak
• 165 eV near-BB radiation
• Synchrotron high energy
tail
45
46
47
Cloudy models
48
8.6 Photo-ionization in X-ray Binary System
Photo-ionization by X-rays
from BH
Super-Massive
BH of C of G
(Image by HST)
400 ly
88,000 ly
49
Japan-China Joint Research funded by
JSPS and NSFC (2005-2007) still on going.
PI(project): H. Takabe (Japan) and J. Zhang(China)
PI(experiment): H. Nishimura (Japan) and Y. Li (China)
Staff: S. Fujioka, N. Yamamoto, W. Feilu, D. Salzman etc.
At Institute of Physics, Beijing, China, Summer 2006
50
Two Type of Experiments have been
done with GXII and Shengang II
Japan-China Joint Research by JSPS and NSFC (2005-2007)
1. H. G. Wei et al., Opacity studies of silicon in radiatively
heated plasma
Astrophysical J. Lett. 683, Page 577–583, (2008)
2. Fei-lu Wang et al., Experimental evidence and
theoretical analysis of photo-ionized plasma under x-ray
radiation produced by intense laser
Phys. Plasmas 15, 073108 (2008)
51
We are carrying out the second step.
Radiation Temperature Tr = 0.5 keV
Final Purpose is the Prediction of
Candidate of X-ray Laser Object near
Compact Object in Universe.
52
H. Takabe1, S. Fujioka1, N. Yamamoto1, F. L. Wang2, D.
Saltzmann3, Y. T. Li4, Q.L. Dong4, S.J. Wang4, Y. Zhang4, YongWoo Lee5, Yong-Joo Rhee5, Jae Min Han5, M. Tanabe1, T.
Fujiwara1, Y. Nakabayashi1, J. Zhang4, H. Nishimura1,
1
Institute of Laser Engineering, Osaka University, 2-6 Yamadaoka, Suita, Osaka, 565-0871,Japan.
2
National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100012, China.
3
Department of Plasma Physics, Soreq Nuclear Research Center,
Yavne, Israel.
4
Beijing National Laboratory for Condensed Matter Physics,
Institute of Physics, Chinese Academy of Sciences, Beijing
100080, China.
5
Quantum Optics Center, Korea Atomic Energy Research Institute,
1045 Daedeok Street Yuseonggu, Daejon 305-353, Korea.
53
Photo-ionization of X-ray Binary System (VELA X-1)
54
S. Watanabe et al., ApJ 651; 421, 2006
55
He-like Silicon Line Emissions from VELA X-1
56
N. R. Schultz et al., ApJ 564; L21, 2002
X-ray from Companion Compact Star (Image)
57
X-ray from Companion Star of Cyg X-3
Photo-ionization by X-rays from
BH candidate (Chandra)
F. Paerels, et al., Astrophys. J. 533, L135 (2000).
58
Experiment has been done
59
Spectrum from Imploded CH Core Plasma
60
Experimental
Data
61
Experimental Spectrum
62
63
Case (1) in Astrophysics
1P
Energy
3/4
1/4
z
3P
3S
1S
Az=10-6Aw
w
1S
Courtesy by Prof. Kuni Masai
64
Case (2) in Astrophysics
Energy
1P
3/4
1/4
z
3P
3S
1S
w
1S
65
Courtesy by Prof. Kuni Masai
Satellite Lines from Be-like Si
Photo-ionized
electron
Photon from
Radiation Source
Energy
L
Satellite Line
K
66
Details of Theoretical Spectrum
67
Universe
Black Hole
In te n s ity (a .u .)
This is accepted for publication in the Nature-Physics (2009)
実験室
0.012
0.008
0.004
0.000
C o u n t/s /k e V
1.80
4.00
1.82
1.84
1.86
1.88
1.86
1.88
ブラックホール
Photon energy (keV)
2.00
0.00
1.80
1.82
1.84
Energy (keV)
Experiment
Chandra X-ray
Data from
VELA X-1
N. R. Schultz et al., ApJ 564; L21, 2002
Joint Exp. JapanChina-Korea
68
Poem by Edward Teller:
A fact without a theory
is like a ship without a rail,
is like a boat without a rudder,
is like a kite without a tail.
A fact without a theory
is like an inconclusive act.
But if there’s one thing worse,
in this confusing universe,
it’s a theory without a fact
Edward Teller
(Nuclear Physicist
and Founder of
LLNL)
69
Example of Atomic Process Rates
70
71