Distinctive rings in the 21 cm signal of the epoch of reionization

Context. It is predicted that sources emitting UV radiation in the Lyman band during the epoch of reionization show a series of discontinuities in their Ly alpha flux radial profile as a consequence of the thickness of the Lyman-series lines in the primeval intergalactic medium. Through unsaturated Wouthuysen-Field coupling, these spherical discontinuities are also present in the 21 cm emission of the neutral IGM. Aims. We study the effects that these discontinuities have on the differential brightness temperature of the 21 cm signal of neutral hydrogen in a realistic setting that includes all other sources of fluctuations. We focus on the early phases of the epoch of reionization, and we address the question of the detectability by the planned Square Kilometre Array (SKA). Such a detection would be of great interest because these structures could provide an unambiguous diagnostic tool for the cosmological origin of the signal that remains after the foreground cleaning procedure. These structures could also be used as a new type of standard rulers. Methods. We determine the differential brightness temperature of the 21 cm signal in the presence of inhomogeneous Wouthuysen-Field effect using simulations that include (hydro) dynamics as well as ionizing and Lyman lines 3D radiative transfer with the code LICORICE. We include radiative transfer for the higher-order Lyman-series lines and consider also the effect of backreaction from recoils and spin diffusivity on the Ly alpha resonance. Results. We find that the Lyman horizons are difficult to indentify using the power spectrum of the 21 cm signal but are clearly visible in the maps and radial profiles around the first sources of our simulations, if only for a limited time interval, typically Delta z approximate to 2 at z similar to 13. Stacking the profiles of the different sources of the simulation at a given redshift results in extending this interval to Delta z approximate to 4. When we take into account the implementation and design planned for the SKA (collecting area, sensitivity, resolution), we find that detection will be a challenging task. It may be possible with a 10 km diameter for the core, but will be difficult with the currently favored design of a 5 km core.