Fisher matrix forecasts on the astrophysics of galaxies during the epoch of reionization from the 21-cm power spectra

The hyperfine 21-cm transition of neutral hydrogen from the early Universe (z > 5) is a sensitive probe of the formation and evolution of the first luminous sources. Using the Fisher matrix formalism we explore the complex and degenerate high-dimensional parameter space associated with the high-z sources of this era and forecast quantitative constraints from a future 21-cm power spectrum (21-cm PS) detection. This is achieved using, a coupled semi-analytic galaxy formation model and reionization simulation, applied to an N-body halo merger tree with a statistically complete population of all atomically cooled galaxies out to z ∼20. Our mock observation assumes a 21-cm detection spanning z [5, 24] from a 1000 h mock observation with the forthcoming Square Kilometre Array, and is calibrated with respect to ultraviolet luminosity functions (UV LFs) at z [5, 10], the optical depth of CMB photons to Thompson scattering from Planck, and various constraints on the IGM neutral fraction at z > 5. In this work, we focus on the X-ray luminosity, ionizing UV photon escape fraction, star formation, and supernova feedback of the first galaxies. We demonstrate that it is possible to recover five of the eight parameters describing these properties with better than 50 per cent precision using just the 21-cm PS. By combining with UV LFs, we are able to improve our forecast, with five of the eight parameters constrained to better than 10 per cent (and all below 50 per cent).