Peculiar Velocity Decomposition, Redshift Space Distortion and Velocity Reconstruction in Redshift Surveys - I. The Methodology

摘要

Massive spectroscopic surveys will measure the redshift space distortion(RSD) induced by galaxy peculiar velocity to unprecedented accuracy. We developa new method to improve the RSD modeling and to carry out robust reconstructionof the 3D large scale peculiar velocity through galaxy redshift surveys, inlight of RSD. (1) We propose a mathematically unique and physically motivateddecomposition of peculiar velocity into three eigen-components of differentorigins, different scale dependences and different impacts on RSD. (2) Thisdecomposition has the potential to simplify and improve the RSD modeling. Wederive a new formula for the redshift space power spectrum. Under the velocitydecomposition scheme, all high order Gaussian corrections and non-Gaussiancorrection of order $\delta^3$ can be taken into account without introducingextra model uncertainties. We find that the leading order contribution $\propto(1+f\tilde{W}(k)u^2)^2$ differs from the Kaiser formula by a function$\tilde{W}(k)\leq 1$. We hence identify a significant systematic error causingunderestimation of the structure growth parameter $f$ by as much as $O(10%)$even at relatively large scale $k=0.1h/$Mpc. The velocity decomposition alsoreveals the three origins of the finger of God (FOG) effect. (3) The velocitydecomposition clarifies issues in peculiar velocity reconstruction through 3Dgalaxy distribution. We discuss two possible ways to carry out the velocityreconstruction. Both use the otherwise troublesome RSD in velocityreconstruction as a valuable source of information. Both have the advantage torender the reconstruction of a stochastic 3D field into the reconstruction of adeterministic window function $W^s(k,u)$ of limited degrees offreedom...[abridged]