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 1σ detection of ∼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.