Probing reionization with LOFAR using 21-cm redshift space distortions

One of the most promising ways to study the epoch of reionization (EoR) is through radio observations of the redshifted 21-cm line emission from neutral hydrogen. These observations are complicated by the fact that the mapping of redshifts to line-of-sight positions is distorted by the peculiar velocities of the gas. Such distortions can be a source of error if they are not properly understood, but they also encode information about cosmology and astrophysics. We study the effects of redshift space distortions on the power spectrum of 21-cm radiation from the EoR using large scale $N$-body and radiative transfer simulations. We quantify the anisotropy introduced in the 21-cm power spectrum by redshift space distortions and show how it evolves as reionization progresses and how it relates to the underlying physics. We go on to study the effects of redshift space distortions on LOFAR observations, taking instrument noise and foreground subtraction into account. We find that LOFAR should be able to directly observe the power spectrum anisotropy due to redshift space distortions at spatial scales around $k \sim 0.1$ Mpc$^{-1}$ after $\gtrsim$ 1000 hours of integration time. At larger scales, sample errors become a limiting factor, while at smaller scales detector noise and foregrounds make the extraction of the signal problematic. Finally, we show how the astrophysical information contained in the evolution of the anisotropy of the 21-cm power spectrum can be extracted from LOFAR observations, and how it can be used to distinguish between different reionization scenarios.