Redshift Space Distortion of the 21cm Background from the Epoch of Reionization I: Methodology Re-examined

The peculiar velocity of the intergalactic gas responsible for the cosmic 21cm background from the epoch of reionization and beyond introduces an anisotropy in the three-dimensional power spectrum of brightness temperature fluctuations. Measurement of this anisotropy by future 21cm surveys is a promising tool for separating cosmology from 21cm astrophysics. However, previous attempts to model the signal have often neglected peculiar velocity or only approximated it crudely. This paper presents a detailed treatment of the effects of peculiar velocity on the 21cm signal. (1) We show that properly accounting for finite optical depth eliminates the unphysical divergence of 21cm brightness temperature in the IGM overdense regions found in previous work that employed the usual optically-thin approximation. (2) We show that previous attempts to circumvent this divergence by capping the velocity gradient result in significant errors in the power spectrum on all scales. (3) We further show that the observed power spectrum in redshift-space remains finite even in the optically-thin approximation if one properly accounts for the redshift-space distortion. However, results that take full account of finite optical depth show that this approximation is only accurate in the limit of high spin temperature. (4) We also show that the linear theory for redshift-space distortion results in a ~30% error in the power spectrum at the observationally relevant wavenumber range, at the 50% ionized epoch. (5) We describe and test two numerical schemes to calculate the 21cm signal from reionization simulations which accurately incorporate peculiar velocity in the optically-thin approximation. One is particle-based, the other grid-based, and while the former is most accurate, we demonstrate that the latter is computationally more efficient and can achieve sufficient accuracy. [Abridged