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.

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

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

Torre & Guzzo, 1202.5559

The redshift position s:

𝒔=𝒙+𝑣 𝑧/ (𝑎𝐻) �̂�

Reid et al. 2012

RSD modeling I

The redshift position s: 𝒔=𝒙+𝑣 𝑧/ (𝑎𝐻) �̂�

From mass conservation: (1+𝛿𝑠 (𝒔 ) )𝑑3 𝑠=(1+𝛿(𝒙 ))𝑑3 𝑥

The redshift space power spectrum:

Dark matter and LCDM cosmology

Velocity decomposition

Background from Wang et al. 2012

𝑽 (𝒙)rotational component

𝑽 𝑩=𝑽 (𝒌 )−𝑽 𝑬

irrotational component

𝑽 𝑬=[𝑽 (𝒌 ) ∙ �̂�]�̂�𝜃 (𝒌 )=𝑖𝒌∙𝑽 𝑬 (𝒌)/𝑎𝐻

correlated with

𝜃𝛿(𝑘)=𝛿 (𝑘 )𝑊 (𝑘)

uncorrelated with

𝜃𝑆 (𝑘 )=𝜃 (𝑘 )−𝜃𝛿

Velocity power spectrum

Definition:

𝑽 𝛿

𝑽 𝑆

Simulation: 1200 Mpc/h & 100 Mpc/h, 1024^3Nearest Particle method

𝑽 𝐵

Velocity correlation function

Definition:

O(1 Mpc/h) O(10 Mpc/h)

𝑽 𝛿 𝑽 𝑆 𝑽 𝐵

2.Determined by W(k)!

A new RSD formulae 1.Underestimation of by

3. Physical FOG:CL, dispersion, NG

Window function I

𝜃= 𝑓 𝛿

underestimation

~𝑊 (𝑘 )=𝑃𝛿𝜃

𝑓 𝑃𝛿𝛿= 1

1+𝛼 𝑓 𝛽 Δ𝛿𝛿2 (𝑘)

𝛼=0.48 , 𝛽=0.5125% 𝑎𝑡 𝑘≳ 0.7h/𝑀𝑝𝑐

Window function II

Do fitting using region Δ 𝛿𝛿2 =𝑘3 Δ𝛿𝛿

2 /2𝜋

3D velocity reconstruction

1. The 1st Method:

2. The 2nd Method:

By tuning such that is isotropic at large scales, we could obtain the correct and hence the correct field.

k-SZ effect

Application example: k-SZ tomography (Ho et al. 0903.2845, Shao et al. 1004.1301)

Velocity field Momentum field

CMBMissing baryons

Conclusions and discussions

• Conclusions:– a velocity decomposition method a new RSD model lower systematic error.

– a simple fitting formula for – 2 new methods for 3D velocity reconstruction in light of

RSD information.• Future work:– More simulation calculations to impove RSD model and test

its accuracy, halo, galaxy....– Velocity reconstruction methods need more theoretical and

numerical considerations.