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Chapter 8
Radiation Hydrodynamics
1
),,(),(),(),,(),,(1
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8.1 Radiation Transport
/S
2
)(
)()(
)(),(
)(
0)(),0(
)(
d
xd
x
xx
dee
deex
x
x
SI
SII
x
dx0
1
d
xdx
1
II
r
]),([),(0
debRebr SII
Integrated form
(2) Spherical Geometry
(1) Plane geometry
R
r
rdr
rb 22
)(
1
R
r
rr
b
rdr
rbdr
rb 22
)(
22
)(
112
3
, Te
,Te
ff
fb
bb
ff
bf
bb
Sr d d
I
Emissivity and Opacity
Coupling term with electron fluid
4
EFE ct
4
4
1d
cIE
4dIF
FPF
tc2
1
dc
IP :
1
Angular moment equation
Radiation energy density
Radiation heat flux
Radiation pressure
5
ki
k
ix
PP
)(
dc
ikki
IP
1
),()(),( 0 xxx II
4
4),( dx
21
1
d
0
4IE
c
1
12 d
cEF
6
Radiation pressure tensor (1)
PE
PE
P
P
P
300
030
000
2
1
00
00
00
P
1
1
2
2
1 dEP
EFE cxt
4
FPF
cxtc
2
1
7
Radiation pressure tensor (2)
Equation to Radiation Energy Density (Plane Geometry)
EFE cr
rrt
4)(
1 2
2
F
EPPF
crrtc
312
EP f
1
1
2
2
1 df
1
31f
)1(2
1
8
Equation to Radiation Energy Density (Plane Geometry)
EEFE
cuxdt
d
4)()(
FFP
F
)()(
c
uc
xdt
d
c
EEFE
currrdt
d
4)]([
1)( 2
2
F
EPFP
F
rc
c
ur
rrc
rdt
d
c
3)(
1)()( 2
2
9
Equation of Radiation in Fluid Frame
Plane Geometry
Spherical Geometry
0)(
u
xt
r
mmux
ut
SP
)()( 2
r
em u
ux
ut
SP
)]
2([)
2(
22
0)()( 2
2
RR
uxc
ut
PPF
0])2
([)2
(2
2
RR uu
xu
tF
PE
10
8.2 Radiation Hydrodynamics
Total Energy and Momentum Conservation Relations
0
1 d
c
r
m FS
0
)4( dcr
e ES
)1
(~~22 c
uo
uu
RR
PE)(~
2
2
2 c
uo
uc
R
F
cos)(1 x
EF3
c
EP
3
1
EF
x
c
3
11
The coupling term with matter
EEE cxx
cl
xt
4)
3(
1l
1
183
3
kThec
h
B
4
0
4)( TBEE
c
R
P
R
12
Multi-group Diffusion Approximation
R
PP
RR
PRR
P cx
cl
xtEEE
4
3
duul
dT
dT
l
l RR )(0
0
0
G
B
B
duud
d
PP )(0
0
0
GB
B
2
4
4 )1(4
15u
u
Re
eu
G
1
15 3
4
uPe
u
G
13
Near LTE Approximation (Gray Approximation)
Rosseland mean-free-path
Planck opacity
R
PRR
x
clEF
3
1j
j
id
EEGG NiNj 1,0
iiii
i
i cx
cl
tt
EEE
4)
3(
1
1
j
j
j
ji
dT
dT
l
l
B
B
1
1
j
j
j
ji
d
d
B
B
14
Multi-group gray diffusion approximation
i
i
i
x
cl
EF
3ii cfs
EF
gni
i
i
i c SER
RF
1
i
i
ii
xl
E
ER
1
3
1
coscoth
1)(
RRR
15
Eddington coefficient (How to model angular distribution)
E
x
cR
4 RcERF )(
)1
(coth1
)(R
RR
R
2
11
2
11
02625.05953.01
2694.001932.0
3
1
RR
RRf
2
112
3
2
1
3
1
RR
f
13
1
3
10
1
1
R
R
16
Variable Edington Factor
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
Super-Massive
BH of C of G
(Image by HST)
400 ly
88,000 ly
Photo-ionization by X-rays
from BH
Accretion Disk and Black Hole
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. Image: National Radio Astronomy Observatory/Rick Perley (NRAO/AUI/NSF)
34
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
Super-Massive
BH of C of G
(Image by HST)
400 ly
88,000 ly
Photo-ionization by X-rays
from BH
8.6 Photo-ionization in X-ray Binary System
At Institute of Physics, Beijing, China, Summer 2006
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.
49
Two Type of Experiments have been done with GXII and Shengang II
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)
Japan-China Joint Research by JSPS and NSFC (2005-2007)
50
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.
51
H. Takabe1, S. Fujioka1, N. Yamamoto1, F. L. Wang2, D.
Saltzmann3, Y. T. Li4, Q.L. Dong4, S.J. Wang4, Y. Zhang4, Yong-
Woo Lee5, Yong-Joo Rhee5, Jae Min Han5, M. Tanabe1, T.
Fujiwara1, Y. Nakabayashi1, J. Zhang4, H. Nishimura1,
1Institute of Laser Engineering, Osaka University, 2-6 Yamada-
oka, Suita, Osaka, 565-0871,Japan.2National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100012, China.3Department of Plasma Physics, Soreq Nuclear Research Center,
Yavne, Israel.4Beijing National Laboratory for Condensed Matter Physics,
Institute of Physics, Chinese Academy of Sciences, Beijing
100080, China.5Quantum Optics Center, Korea Atomic Energy Research Institute,
1045 Daedeok Street Yuseonggu, Daejon 305-353, Korea.52
53
Photo-ionization of X-ray Binary System (VELA X-1)
S. Watanabe et al., ApJ 651; 421, 200654
He-like Silicon Line Emissions from VELA X-1
N. R. Schultz et al., ApJ 564; L21, 200255
X-ray from Companion Compact Star (Image)
56
X-ray from Companion Star of Cyg X-3
57F. Paerels, et al., Astrophys. J. 533, L135 (2000).
Photo-ionization by X-rays from
BH candidate (Chandra)
Experiment has been done
58
Spectrum from Imploded CH Core Plasma
59
Experimental Data
60
Experimental Spectrum
61
62
1S
1S3S
3P1P
wz
1/43/4
Courtesy by Prof. Kuni Masai
Az=10-6Aw
Case (1) in AstrophysicsEn
erg
y
63
1S
1S3S
3P
wz
1/43/4
Courtesy by Prof. Kuni Masai
Case (2) in Astrophysics
1P
Ene
rgy
64
K
Satellite Lines from Be-like Si
Ene
rgy
L
Photon from Radiation Source
Photo-ionized electron
Satellite Line
65
Details of Theoretical Spectrum
66
Chandra X-ray Data from VELA X-1
N. R. Schultz et al., ApJ 564; L21, 2002
67
0.012
0.008
0.004
0.000
Inte
nsit
y (
a.u
.)
1.881.861.841.821.80
Photon energy (keV)4.00
2.00
0.00Co
un
t/s/k
eV
1.881.861.841.821.80
Energy (keV)
実験室
ブラックホール
67
Black HoleUniverse
Experiment
Joint Exp. Japan-
China-Korea
This is accepted for publication in the Nature-Physics (2009)
68
Example of Atomic Process Rates
69
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