Chapter 8 Radiation Hydrodynamics 1. 8.1 Radiation Transport 2.

Chapter 8

Radiation Hydrodynamics

1

),,(),(),(),,(),,(1

rtrtrtrtrttc

III

III

xtc

1

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

1d

cIE

4dIF

FPF tc 2

1

dc

IP :1

Angular moment equation

Radiation energy densityRadiation heat fluxRadiation pressure

5

kik

i xPP

)( dc ikki

IP1

),()(),( 0 xxx II

4

4 ),( dx2

1

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 crrrt

4)(1 2

2

F

EPPF

crrtc

31

2

EP f

1

1

2

2

1 df

1

31f)1(2

1

8

Equation to Radiation Energy Density (Plane Geometry)

9

Example of Angular Distribution in case of plane gold foil

EEFE

cuxdt

d

4)()(

FFP

F

)()(c

uc

xdt

d

c

EEFE

currrdt

d

4)]([1

)( 22

F

EPFP

F

r

cc

ur

rrc

rdt

d

c

3)(

1)()( 2

2

10

Equation of Radiation in Fluid Frame

Plane Geometry

Spherical Geometry

0)(

uxt

rmmu

xu

tSP

)()( 2

re

m uu

xu

tS

P

)]2

([)2

(2

2

0)()( 22

R

R

uxc

ut

PPF

0])2

([)2

(2

2

RR u

ux

ut

FP

E

11

8.2 Radiation Hydrodynamics

Total Energy and Momentum Conservation Relations

0

1 dc

rm FS

0

)4( dcre 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

12

The coupling term with matter

EEE cxx

cl

xt

4)3

(

1

l

1

183

3

kThec

h

B

4

0

4)( TBEE

cRP

R

13

Multi-group Diffusion Approximation

RPP

RRP

RRP c

x

cl

xtEEE

43

duuld

T

dT

ll RR )(

0

0

0

GB

B

duud

dPP )(

0

0

0

GB

B

2

4

4 )1(4

15u

u

R e

eu

G

1

15 3

4

uP e

u

G

14

Near LTE Approximation (Gray Approximation)

Rosseland mean-free-path

Planck opacity

RP

RR

x

clEF

3

1j

j

id

EE GG NiNj 1,0

iiii

i

i cx

cl

tt

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

i

i

i

x

cl

EF

3

ii cfs EF

gni

i

i

i c SER

RF

1

i

i

ii

xl

EE

R

1

3

1

coscoth

1)(

RRR

16

Eddington coefficient (How to model angular distribution)

Ex

cR

4

RcERF )(

)1

(coth1

)(R

RR

R

211

211

02625.05953.01

2694.001932.0

3

1

RR

RRf

211 2

3

2

13

1

RR

f

13

13

10

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 mm tungsten wires20 MA current100 ns rise time8 ns FWHM peak120 TW peak power =x 25 erg cm/s at the peak

165 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

0.012

0.008

0.004

0.000Inte

nsi

ty (

a.u

.)

1.881.861.841.821.80

Photon energy (keV)4.00

2.00

0.00Co

un

t/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