Constraining the epoch of reionization with the variance statistic

The Epoch of Reionization (EoR) is the epoch in which most of the neutral gas in the Universe was re-ionized by the radiation from the first stars and galaxies. Many projects are underway to detect the redshifted 21 cm signal of the neutral hydrogen from the EoR with the low frequency radio telescopes. These experiments aim for a statistical detection of the signal due to its very low signal-to-noise ratio. We study extraction of the sample variance of the signal to constrain the global properties of the EoR. We show that the LOw Frequency ARray (LOFAR) should be able to detect the signal with a significance of 3 standard deviations in 600 hours of integration. Additionally, it should be able to constrain the timing and duration of reionization with uncertainties of 0.4 and 1 redshifts, respectively, with 95 percent confidence. We also show the upper limits on the signal detection obtained from the analysis of 115 hours of the observed data with LOFAR. In the observed redshift range of 7 to 11, our current best upper limits are 25 mK at 1 MHz, 12 arcmin spectral and spatial resolutions, respectively.