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 hours 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 4
standard deviations and extract the EoR parameters as $z_r =
7.72^{+0.37}_{-0.18}$ and $\Delta z = 0.53^{+0.12}_{-0.23}$ in 600 hours,
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.
