chapter 8 radiation hydrodynamicsips.sjtu.edu.cn/upload/takabe_ppt_2009/radhydro.pdf · e q f q sk...

Chapter 8

Radiation Hydrodynamics

1

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

rtrtrtrtrt

tc

III

III

xtc

1

IIII

rrtc

)1(1 2

SIId

ddxd

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)

25

Radiation Hydrodynamics Model of Planetary Nebulae

26

Eagle Nebula

by HST

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

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

36

Photo-ionized plasma in binary system

39

Ionization Parameter x

40

8.5 Photo-ionized Plasma Experiment

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

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

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

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