Constraining the epoch of reionization with the variance statistic: simulations of the LOFAR case

Several experiments are underway to detect the cosmic-redshifted 21-cm signal from neutral hydrogen from the Epoch of Reionization (EoR). Due to their very low signal-to-noise ratio, these observations aim for a statistical detection of the signal by measuring its power spectrum. We investigate the extraction of the variance of the signal as a first step towards detecting and constraining the global history of the EoR. Signal variance is the integral of the signal's power spectrum, and it is expected to be measured with a high significance. We demonstrate this through results from a simulation and parameter estimation pipeline developed for the Low-Frequency Array (LOFAR)-EoR experiment. We show that LOFAR should be able to detect the EoR in 600 h of integration using the variance statistic. Additionally, the redshift (z(r)) and duration (Delta z) of reionization can be constrained assuming a parametrization. We use an EoR simulation of z(r) = 7.68 and Delta(z) = 0.43 to test the pipeline. We are able to detect the simulated signal with a significance of four standard deviations and extract the EoR parameters as z(r) = 7.72(-0.18)(+0.37) and Delta z = 0.53(-0.23)(+0.12) in 600 h, assuming that systematic errors can be adequately controlled. We further show that the significance of detection and constraints on EoR parameters can be improved by measuring the cross-variance of the signal by cross-correlating consecutive redshift bins.