Constraining reionization using 21-cm observations in combination with CMB and Lyα forest data

In this paper, we explore the constraints on the reionization history that are provided by current observations of the Ly alpha forest and the cosmic microwave background. Rather than using a particular semi-analytic model, we take the novel approach of parametrizing the ionizing sources with arbitrary functions and perform likelihood analyses to constrain possible reionization histories. We find model-independent conclusions that reionization is likely to be mostly complete by z = 8 and that the intergalactic medium was 50 per cent ionized at z = 9-10. Upcoming low-frequency observations of the redshifted 21-cm line of neutral hydrogen are expected to place significantly better constraints on the hydrogen neutral fraction at 6 less than or similar to z less than or similar to 12. We use our constraints on the reionization history to predict the likely amplitude of the 21-cm power spectrum and show that observations with the highest signal-to-noise ratio will most likely be made at frequencies corresponding to z = 9-10. This result provides an important guide to the upcoming 21-cm observations. Finally, we assess the impact that measurement of the neutral fraction will have on our knowledge of reionization and the early source population. Our results show that a single measurement of the neutral fraction mid-way through the reionization era will significantly enhance our knowledge of the entire reionization history.