New probe of magnetic fields in the pre-reionization epoch. II. Detectability

In the first paper of this series, we proposed a novel method to probe large-scale intergalactic magnetic fields during the cosmic Dark Ages, using 21-cm tomography. This method relies on the effect of spin alignment of hydrogen atoms in a cosmological setting, and on the effect of magnetic precession of the atoms on the statistics of the 21-cm brightness-temperature fluctuations. In this paper, we forecast the sensitivity of future tomographic surveys to detecting magnetic fields using this method. For this purpose, we develop a minimum-variance estimator formalism to capture the characteristic anisotropy signal using the two-point statistics of the brightness-temperature fluctuations. We find that, depending on the reionization history, and subject to the control of systematics from foreground subtraction, an array of dipole antennas in a compact-grid configuration with a collecting area slightly exceeding one square kilometer can achieve a 1 sigma detection of similar to 10(-21) Gauss comoving (scaled to present-day value) within three years of observation. Using this method, tomographic 21-cm surveys could thus probe ten orders of magnitude below current cosmic microwave background constraints on primordial magnetic fields, and provide exquisite sensitivity to large-scale magnetic fields in situ at high redshift.