Measuring the Redshift of Reionization with a Modest Array of Low-Frequency Dipoles

The designs of the first generation of cosmological 21-cm observatories are split between single dipole experiments which integrate over a large patch of sky in order to find the global (spectral) signature of reionization, and interferometers with arcminute-scale angular resolution whose goal is to measure the 3D power spectrum of ionized regions during reionization. We examine whether intermediate scale instruments with complete Fourier (uv) coverage are capable of placing new constraints on reionization. We find that even without using a full power spectrum analysis, the global redshift of reionization, z_reion, can in principle be measured from the variance in the 21-cm signal among multiple beams as a function of frequency at a roughly 1 degree angular scale. At this scale, the beam-to-beam variance in the differential brightness temperature peaks when the average neutral fraction was around 50%, providing a convenient flag of z_reion. We choose a low angular resolution of order 1 degree to exploit the physical size of the ionized regions and maximize the signal-to-noise ratio. Thermal noise, foregrounds, and instrumental effects should also be manageable at this angular scale, as long as the uv coverage is complete within the compact core required for low-resolution imaging. For example, we find that z_reion can potentially be detected to within a redshift uncertainty of less than around 1 in around 500 hours of integration on the existing MWA prototype (with only 32x16 dipoles), operating at an angular resolution of around 1 degree and a spectral resolution of 2.4 MHz.