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Chapter 8 Radiation Hydrodynamics. 8.1 Radiation Transport. Integrated form. (1) Plane geometry. (2) Spherical Geometry. Emissivity and Opacity. Coupling term with electron fluid. Angular moment equation. Radiation energy density Radiation heat flux Radiation pressure. - PowerPoint PPT Presentation
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Chapter 8
Radiation Hydrodynamics
1
),,(),(),(),,(),,(1
rtrtrtrtrttc
III
III
xtc1
IIII
rrtc)1(1 2
SII
dd
dxd
8.1 Radiation Transport
/S
2
)(
)()(
)(),()(
0 )(),0()(
d
xdx
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
Rr
r drrb 22
)(
1
Rr
rrb
r drrb
drrb 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
1 dcIE
4dIF
FPF tc 2
1
dc
IP :1
Angular moment equation
Radiation energy densityRadiation heat fluxRadiation pressure
5
kik
i xPP
)( dc ikki
IP 1
),()(),( 0 xxx II
4
4 ),( dx 21
1 d
0
4 IEc
1
12 dc EF
6
Radiation pressure tensor (1)
PEPE
PP
P
300030000
21
000000
P
1
1
2
21 dEP
EFE cxt
4
FPFcxtc
2
1
7
Radiation pressure tensor (2)
Equation to Radiation Energy Density (Plane Geometry)
EFE crrrt
4)(1 2
2
FEPPFcrrtc
31
2
EP f
1
1
2
21 df
131f
)1(21
8
Equation to Radiation Energy Density (Plane Geometry)
9
Example of Angular Distribution in case of plane gold foil
EEFE cuxdt
d
4)()(
FFPF
)()(cuc
xdtd
c
EEFE currrdt
d
4)]([1)( 22
FEPFPF
r
ccur
rrc
rdtd
c3)(1)()( 2
2
10
Equation of Radiation in Fluid Frame
Plane Geometry
Spherical Geometry
0)(
u
xt
rmmu
xu
tSP
)()( 2
re
m uux
ut
SP
)]
2([)
2(
22
0)()( 22
R
R
uxc
ut
PPF
0])2
([)2
(2
2
RR uu
xu
tFPE
11
8.2 Radiation Hydrodynamics
Total Energy and Momentum Conservation Relations
0
1 dc
rm FS
0
)4( dcre ES
)1(~~ 22 cuo
uu
RR
PE
)(~ 2
2
2 cuo
uc
R
F
cos)(1 x
EF3c
EP31
EF
xc
3
12
The coupling term with matter
EEE cxx
clxt
4)
3(
1
l
118
3
3
kThec
h
B
4
0
4)( TBEEc
RP
R
13
Multi-group Diffusion Approximation
RPP
RRP
RRP c
xcl
xtEEE
4
3
duuld
T
dT
ll RR )(
0
0
0
GB
B
duud
dPP )(
0
0
0
GB
B
2
4
4 )1(415
u
u
R eeu
G
115 3
4 uP e
u
G
14
Near LTE Approximation (Gray Approximation)
Rosseland mean-free-path
Planck opacity
RP
RR
xcl
EF
3
1j
j
id
EE GG NiNj 1,0
iiiii
i cx
cltt
EEE
4)
3(
1
1
j
j
j
ji
dT
dT
ll
B
B
1
1
j
j
j
ji
d
d
B
B
15
Multi-group gray diffusion approximation
ii
i
xcl
EF
3 ii cfs
EF
gni
i
ii c SE
RRF
1
i
i
ii
xl
EE
R
1
31
coscoth1)(
RRR
16
Eddington coefficient (How to model angular distribution)
Ex
cR
4
RcERF )(
)1(coth1)(R
RR
R
211
211
02625.05953.012694.001932.0
31
RRRR
f
211 2
32131
RR
f
131
310
1
1
R
R
17
Variable Edington Factor
18
8.3 Computer Simulation of Gold Foil
19
Spectrum from Gold Foil irradiated by Lasers (Experiment VS Simulation)
20
X-ray Conversion Rate ( Experiment VS Simulation)
21
CRE model is essential for Gold PlasmaCRE: Collisional Radiative Equilibrium
22
X-ray confinement with a variety of gold cavities
23
Radiation Temperature from Gold Cavity
24
8.4 Radiation Hydrodynamics in the Universe
Planetary Nebulae (HST)
25
26
Radiation Hydrodynamics Model of Planetary Nebulae
27
Eagle Nebulaby HST
28
29
30
31
Super-Massive BH of C of G(Image by HST)400 ly88,000 ly
Photo-ionization by X-rays from BH
Accretion Disk and Black Hole
32
33
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>
34
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)
35
Eta-Carina
36
37
Photo-ionized plasma in binary system
38
39
40
Ionization Parameter x
41
8.5 Photo-ionized Plasma Experiment
42
43
44
Experimental setup
• Everything shown is completely destroyed during the experiment!
45
Spectral characterization
300 11.5 m tungsten wires20 MA current100 ns rise time8 ns FWHM peak120 TW peak powerx 25 erg cm/s at the peak165 eV near-BB radiationSynchrotron high energy tail
46
47
48
Cloudy models
49
Super-Massive BH of C of G(Image by HST)400 ly88,000 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.
50
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 plasmaAstrophysical 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 laserPhys. Plasmas 15, 073108 (2008)
Japan-China Joint Research by JSPS and NSFC (2005-2007)
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, 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. 53
54
Photo-ionization of X-ray Binary System (VELA X-1)
S. Watanabe et al., ApJ 651; 421, 200655
He-like Silicon Line Emissions from VELA X-1
N. R. Schultz et al., ApJ 564; L21, 200256
X-ray from Companion Compact Star (Image)
57
X-ray from Companion Star of Cyg X-3
58F. Paerels, et al., Astrophys. J. 533, L135 (2000).Photo-ionization by X-rays from BH candidate (Chandra)
Experiment has been done
59
Spectrum from Imploded CH Core Plasma
60
Experimental Data
61
Experimental Spectrum
62
63
1S
1S3S
3P1P
wz
1/43/4
Courtesy by Prof. Kuni Masai
Az=10-6Aw
Case (1) in AstrophysicsEn
ergy
64
1S
1S3S
3P
wz
1/43/4
Courtesy by Prof. Kuni Masai
Case (2) in Astrophysics
1P
Ener
gy
65
K
Satellite Lines from Be-like Si
Ener
gy
L
Photon from Radiation Source
Photo-ionized electron
Satellite Line
66
Details of Theoretical Spectrum
67
Chandra X-ray Data from VELA
X-1
N. R. Schultz et al., ApJ 564; L21, 2002
68
0.0120.0080.0040.000In
tens
ity (a
.u.)
1.881.861.841.821.80Photon energy (keV)4.00
2.00
0.00Cou
nt/s
/keV
1.881.861.841.821.80Energy (keV)
実験室
ブラックホール
68
Black HoleUniverse
Experiment
Joint Exp. Japan-China-Korea
This is accepted for publication in the Nature-Physics (2009)
69
Poem by Edward Teller:
A fact without a theoryis like a ship without a rail,is like a boat without a rudder,is like a kite without a tail.
A fact without a theoryis 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)
70
Example of Atomic Process Rates
71