1. Peculiar velocity decomposition, redshift distortion and velocity reconstruction in redshift surveys Zheng, Yi 郑逸 Shanghai Astronomical Observatory P. Zhang, J. Pan, and Y. Zheng, 1207.2722. Y. Zheng, P. Zhang et al. (2012), in preparation.

2. Outline I. Introduction. (Why RSD interesting?) II. Velocity decomposition. (What do decomposed velocity components look like?) III. RSD modeling and velocity reconstruction. IV. Discussions and conclusions

3. Introduction A. J. S. Hamilton, astro-ph/9708102 Observationally: Euclid, BigBOSS et all: O(1%) 5-10% Theoretically: 1.Nonlinear mapping 2.Nonlinear evolution 3.Bias modelling Theoretically: 1.Nonlinear mapping 2.Nonlinear evolution 3.Bias modelling Torre & Guzzo, 1202.5559 The redshift position s: Reid et al. 2012

4. RSD modeling I The redshift position s: From mass conservation: The redshift space power spectrum: Dark matter and LCDM cosmology

5. Velocity decomposition Background from Wang et al. 2012 rotational component irrotational component

6. Velocity power spectrum Definition: Simulation: 1200 Mpc/h & 100 Mpc/h, 1024^3 Nearest Particle method Simulation: 1200 Mpc/h & 100 Mpc/h, 1024^3 Nearest Particle method

7. Velocity correlation function Definition: O(1 Mpc/h)O(10 Mpc/h)

8. 2.Determin ed by W(k)! A new RSD formulae 3. Physical FOG: CL, dispersion, NG 3. Physical FOG: CL, dispersion, NG

11. 3D velocity reconstruction 1. The 1 st Method: 2. The 2 nd Method: k-SZ effect Application example: k-SZ tomography (Ho et al. 0903.2845, Shao et al. 1004.1301) Velocity field Momentum field CMB Missing baryons

12. Conclusions and discussions