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Numerical Simulations
for Reionization of the Universe
Nakamoto, T. (Univ. of Tsukuba)
Hiroi, K.
Umemura, M.
1. Why Reionization by 3-D RT ?
2. TsuCube Project
3. Tsukuba's New Code
1. Why Reionization ?
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-Radiation Feedback
---- Effects for Following Generation
- Photoionization
- Photodissociation
- Photo Heating
-Observation
---- Probe for First Generation
- Emissions
- Absorptions
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3D Reionization Calculations
・Photon Conservation Method (+ Tree Method)
Abel et al. 1999, Abel & Wandelt 2001, Razoumov et al. 2002
・Optically Thin Variable Eddington Tensor Formalism
Gnedin & Abel 2001
w/ HD
・Direct Incident Radiation
Susa & Umemura
・Monte Carlo 3D RT
Ciardi et al. 2001, Maselli, Ferrara, & Ciardi 2003
w/o HD
・Grid Base 3D RT with Short Characteristics
Nakamoto, Umemura, & Susa 2001
An Example:
Evolution of
Ionization State
N3＝1283 in (8Mpc) 3, Nangle =
1282 background
Isotropic
UV: I21z=0.1
Zel’dovich
approximation:
= 15
Radiative Transfer
Ionization Equilibrium
Neutral Fraction:
X HI 
nHI
nH
Nakamoto, Umemura, & Susa 2001
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Shadowing Effect
Inhomogeneous
Homogeneous
N3＝1283 in (8Mpc) 3, Nangle =
1282 background UV: I21 =0.1
Isotropic
Radiative Transfer
Ionization Equilibrium
But...
* Steady Solution (No Time Evolution)
* Only Background Radiation (No Point Source)
* Isothermal (No Temperature Evolution)
Neutral Fraction:
* Only One Incident UV Spectrum (Iν∝ν-1)
X HI 
nHI
nH
Nakamoto, Umemura, & Susa 2001
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We want to update our code!
1. Point Sources in Computational Domain
2. Time Evolution
3. Various Types Incident UV Spectrum
4. Temperature Evolution
We can apply our new code to more problems!
2. TsuCube Project
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Comparison of 3D RT codes
(A. Ferrara, B. Ciardi ...)
Common Test Problems: Test #1, #2, #3
Groups/Codes:
* CRASH (Ferrara, Ciardi, Maselli)
* CORAL (Iliev)
* OTVET (Gnedin, Abel)
* Cen
* Razoumov
* Tsukuba (Nakamoto, Umemura, Hiroi)
Deadline: January 31, 2004
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Test Problem 1:
Input



nH 103 cm3
T  10 4 K
 e 1.2 103 (collisional)

no dynamics

NÝ 1048 s1 at 13.6 eV 
L  6.6 kpc

Output


N c  128
nH 103 cm3
NÝ 1048 s1 at 13.6 eV
L  6.6 kpc
N c  128
T  10 4 K
 e 1.2 103 (collisional)



• Xe-R relation
• I-front propagation (Time Evolution)
• UV intensity @ each grid point
• computation speed
Test Problem 2:
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(128,128,128)
Input
nH  9.3104 cm3
nHe  7 105 cm3


(1,1,1)



Nú  5 1048 s1
@13.6 eV and 60 eV
L  6.6 kpc
N c  128
T 102 K (initial)
 H   He   He  0 (initial)



no dynamics

non-isothermal
(Temperature Change should be followed.)
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Test Problem 3:
nH  9.3104 cm3
Input
nHe  7 105 cm3






nH  9.3101cm3
nHe  7 102 cm3
L  6.6 kpc
N c  128
T 102 K (initial)
 H   He   He  0 (initial)



no dynamics

non-isothermal
(Temperature Change should be followed.)
3. New Code
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Tsukuba's New Code
Radiative Transfer Solver
1. Short Characteristics
with point source(s)
Time Evolution
* 2nd order
implicit scheme
2. ART (Accurate RT)
Ionization State
Incident UV Spectrum
* H, He
* 3 (6)-frequency method
* arbitrary spectrum
Temperature
Evolution
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Radiation Energy Density
Point Source(s) in Computational Domain
Distance
RT: Short Characteristics
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Time Evolution
dn HI
I
 nHI 
dd  ne n p
dt
h
1 I
 n  I  nHII  
c t

2nd order implicit scheme (Crank-Nicholson)

nHI
n 1
 nHI
t
n

1 
 nHI
2 

n

n 1


I
dd  nen p   nHI
h


n I  nHI I n  n
n

n 


I
dd  nen p  
h
 

-6
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J (Mean Intensity)
Time Evolution
log J
-7
TsuCube Test #1
-8
-9
-10
0
Spherically Sym. Solution
by 1-D code
log XHI
-1
-2
-3
-4
100
XHI (Neutral Frac.)
[pc]
R 1000
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4. Summary
* Reionization Simulations
* TsuCube Project: Comparison of 3D RT Codes
* Developement of a New Code
Point Sources
Time Evolution of Ionization State
Various Incident UV Spectra
Temperature Evolution

テスト

Slides

CV - Dominic Ryan

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