1 / 31

Reionization of Universe:

3D Radiative Transfer Simulations

T. Nakamoto (Univ. of Tsukuba)

1. Why Reionization ?

2. TsuCube Project

3. Toward a New Code

2 / 31

1. Why Reionization ?

-Radiation Feedback ---- Effects for Following Generation- Photoionization- Photodissociation- Photo Heating

-Observation ---- Probe for First Generation

- Emissions- Absorptions

1. Why Reionization ?

3 / 31

3D Reionization Calculations

・ Photon Conservation Method (+ Tree Method) Abel et al. 1999, Abel & Wandelt 2001, Razoumov et al. 2002

・ Direct Incident Radiation　　 Ciardi et al. 2001, Susa & Umemura

・ Local Optical Depth Approx. Gnedin 2000

・ Optically Thin Variable Eddington Tensor Formalism Gnedin & Abel 2001

・ Full 3D Radiative Transfer Nakamoto, Umemura, & Susa 2001

w/ HD +Stellar source

w/o HD +QSO source

4 / 31(Abel & Wandelt 2002)Adaptive Ray Tracing

5 / 31

Razoumov et al. 2002

6 / 31

Ciardi et al. 2001

Monte Carlo

HD+ RT (post processing)

7 / 313D RHD: Cosmic Reionization (Gnedin 2000)

Tngas

XHI

z = 9

Cosmological HD ~1010-12 Msun

RT (Local Optical Depth Approx.)

Star Formation

H, He

H2 form/dest

8 / 31Optically Thin Variable Eddington Tensor (Gnedin & Abel 2001)

LOD OTVET

XHI

9 / 31N3 ＝ 1283 in (8Mpc) 3, Nangle = 1282

Radiative Transfer

Ionization Equilibrium

Isotropic background UV: I21 =0.1Zel’dovich approximation: z = 15An Example:Evolution ofIonization State

Nakamoto, Umemura, & Susa 20011. Why Reionization ?

Neutral Fraction:

€

XHI =nHI

nH

10 / 31

Z=9

Z=5Z=7

Z=15

I21=0.1

Reionization History of an Inhomogeneous Universe

1. Why Reionization ?

11 / 31

Shadowing Effect

Inhomogeneous Homogeneous

12 / 31

3D Reionization Calculations

・ Photon Conservation Method (+ Tree Method) Abel et al. 1999, Abel & Wandelt 2001, Razoumov et al. 2002

・ Direct Incident Radiation　　 Ciardi et al. 2001, Susa & Umemura

・ Local Optical Depth Approx. Gnedin 2000

・ Optically Thin Variable Eddington Tensor Formalism Gnedin & Abel 2001

・ Full 3D Radiative Transfer Nakamoto, Umemura, & Susa 2001

w/ HD +Stellar source

w/o HD +QSO source

13 / 31

2. TsuCube Project Comparisons of 3D RT codes

Common Test Problem(s)

Groups/Codes:

* CRASH (Ferrara, Ciardi, Maselli)* CORAL (Iliev)* OVTET (Gnedin, Abel)* Cen* Razoumov* Tsukuba (Nakamoto, Umemura, Hiroi)

14 / 31

• • I-front propagation (Time Dependence)• UV intensity @ each grid point• computation speed

Test Problem 1:

€

nH =10−3cm−3

€

˙ N γ =1048s−1 at 13.6 eV

€

L = 6.6 kpc

€

Nc =128

€

T =104 K

€

χe =10−3 (collisional)

€

L = 6.6 kpc

€

Nc =128

Input

Output

€

nH − R plot

€

nH =10−3cm−3

€

T =104 K

€

χe =10−3 (collisional)

€

˙ N γ =1048s−1 at 13.6 eV

no dynamics

15 / 31

åıåπÇ©ÇÁÇÃãóó£1283Å~1282

Radia

tion E

nerg

y D

ensi

ty

Distance

Tsukuba's Current Code: Short Characteristics Method

max: 1283 x 1282

Not good for a point source(Better for diffuse radiation)

16 / 31

Improvement of Our Code: ART (Accurate RT)

• Time Dependence

• Accuracy

• (Speed)

3. Toward a New Code

17 / 31Time Dependece

€

dnHI

dt=−nHI

σIhν

dΩdν∫∫ +nenpα

€

1c∂I∂t

+n⋅∇I =−nHIσI +η

€

dnHI

dt=−

−∇⋅F + 4πηhν

dν∫ +nenpα

Current Status: 1D: OK 2D: now struggling 3D: next step

18 / 31

Nx Ny Nz N NNν

Cost

〜

Ray = Group of Segments

Suitable for large simulation, though its accuracy is limited.

Short Characteristics Method (Kunasz&Auer 1988)

Good - # of Operation = Small- Simple

Bad - Numerical Diffusion

Accuracy & Speed

19 / 31

Numerical Diffusion

Long Char. Short Char.

20 / 31

ART (Accurate/Accelerated Ray Tracing) Method

Nx NyNz N NNνCost 〜

This has good points of both the Long Char. & the Short Char.

Radiation - On a radiation meshQuantities on Hydro Mesh -

Interpolated from valueson the radiation mesh.

Good - # of Operation = Small- Small Numerical Diff.

Bad - Complicated

21 / 31

ART

Accuracy of ART ~ Long Char.

Quite smallnumerical diffusion

22 / 31

Computational Time

If…Space 　　 ＝ N2

Angle ＝ 1Frequency ＝ 1

Long Char. ～ N3

Short Char. ～ N2

ART ～ N2

Theoretical Predictedtiming (2D-Plane case)

1 0- 4

1 0- 3

1 0- 2

1 0- 1

1 00

1 01

1 01

1 02

N3

N2

Measured Time (WS)

Tim

e [s

ec]

Space Grid Size = N

Long Char.

ART

Short Char.

23 / 31

r

Ene

rgy

Den

sity

SC (2D: 322 x 1024)

24 / 31

€

E (x,y)×C ×r

SC (2D: 322 x 1024)

25 / 31

2D N×N mesh

Y

N

N X

Nangle

O

26 / 31

r

Ene

rgy

Den

sity

ART (2D: 322 x 1024)

27 / 31

32 x 256

Source (emitting toward One quadrant)VacuumGrids: Space = 32x32, Angle = 256 (= 64 x 4)

28 / 31

€

E (x,y)×C ×r

ART (2D: 322 x 1024)

29 / 31

€

E (x,y)×C ×r

ART (2D: 322 x 64)

30 / 31

€

E (x,y)×C ×r

SC (2D: 322 x 64)

31 / 31

4. Summary

* Reionization Simulations

* TsuCube Project: Comparison of 3D RT Codes

* Developement of a New Code3DTime DependeceAccuracySpeed