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 / 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 ・ 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 Monte Carlo HD + RT (post processing)

7 / 31 3D RHD: Cosmic Reionization (Gnedin 2000) T n gas X HI z = 9 Cosmological HD ~ M sun RT (Local Optical Depth Approx.) Star Formation H, He H 2 form/dest

8 / 31 Optically Thin Variable Eddington Tensor (Gnedin & Abel 2001) LOD OTVET X HI

9 / 31 N 3 ＝ in (8Mpc) 3, N angle = Radiative Transfer Ionization Equilibrium Isotropic background UV: I 21 =0.1 Zel’dovich approximation: z = 15 An Example: Evolution of Ionization State Nakamoto, Umemura, & Susa Why Reionization ? Neutral Fraction:

10 / 31 Z=9 Z=5 Z=7 Z=15 I 21 =0.1 Reionization History of an Inhomogeneous Universe 1. Why Reionization ?

11 / 31 Shadowing Effect InhomogeneousHomogeneous

12 / 31 3D Reionization Calculations ・ Photon Conservation Method (+ Tree Method) Abel et al. 1999, Abel & Wandelt 2001, Razoumov et al ・ 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 / 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 each grid point computation speed Test Problem 1: Input Output no dynamics

15 / 31 Radiation Energy Density Distance Tsukuba's Current Code: Short Characteristics Method max: x 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 / 31 Time Dependece Current Status: 1D: OK 2D: now struggling 3D: next step

18 / 31 N x N y N z N  N  N 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 N x N y N z N  N  N Cost 〜 This has good points of both the Long Char. & the Short Char. Radiation - On a radiation mesh Quantities on Hydro Mesh - Interpolated from values on the radiation mesh. Good- # of Operation = Small - Small Numerical Diff. Bad- Complicated

21 / 31 ART Accuracy of ART ~ Long Char. Quite small numerical diffusion

22 / 31 Computational Time If… Space ＝ N 2 Angle ＝ 1 Frequency ＝ 1 Long Char. ～ N 3 Short Char. ～ N 2 ART ～ N 2 Theoretical Predicted timing (2D-Plane case) N 3 N 2 Measured Time (WS) Time [sec] Space Grid Size = N Long Char. ART Short Char.

23 / 31 r Energy Density SC (2D: 32 2 x 1024)

24 / 31 SC (2D: 32 2 x 1024)

25 / 31 2D N×N mesh Y N N X N angle O

26 / 31 r Energy Density ART (2D: 32 2 x 1024)

27 / x 256 Source (emitting toward One quadrant) Vacuum Grids: Space = 32x32, Angle = 256 (= 64 x 4)

28 / 31 ART (2D: 32 2 x 1024)

29 / 31 ART (2D: 32 2 x 64)

30 / 31 SC (2D: 32 2 x 64)

31 / Summary * Reionization Simulations * TsuCube Project: Comparison of 3D RT Codes * Developement of a New Code 3D Time Dependece Accuracy Speed