Quantifying density-ionization correlations with the 21-cm power spectrum

The epoch of reionization (EoR) - when neutral hydrogen in the intergalactic medium was systematically ionized - is a period in our Universe's history that is currently poorly understood. However, a key prediction of most models is a correlation between the density and ionization field during the EoR. This has consequences for the 21-cm power spectrum. Here, we propose a parametrization for the density-ionization correlation and study the dependence of the 21-cm power spectrum on this parametrization. We use this formalism to forecast the ability of current and future observations to constrain these correlations. We find that upper limits on the dimensionless power spectrum at redshifts 7.5 < z < 8.5 using k bins between $0.1 \lt k \lt 0.75\, \textrm {Mpc}^{-1}$ with error bars at the level of ${\sim\! }20\, \textrm {mK}^2$ about our fiducial model would rule out uncorrelated reionization at $99{{\ \rm per\ cent}}$ credibility. Beyond upper limits, we find that at its full sensitivity, the Hydrogen Epoch of Reionization Array (HERA) will be able to place strong constraints on the sign and magnitude of density-ionization correlations.