The optimal redshift for detecting ionized bubbles in H i 21-cm maps

The detection of individual ionized bubbles in H i 21-cm maps is one of the most promising, direct probes of the epoch of reionization (EoR). At least 1000 h of observation would be required for such a detection with either the currently functioning Giant Metrewave Radio Telescope (GMRT) or the upcoming Murchison Widefield Array (MWA). Considering the large investment for telescope time, it is essential to identify the ‘optimal redshift’ where the prospects of a detection are most favourable. We find that the optimal redshift is determined by a combination of instrument dependent factors and the evolution of the neutral fraction x_H i. We find that the redshift range 8.1 ± 1.1 and 9.8 ± 1 are optimum for detecting ionized bubbles with the GMRT and MWA, respectively. The prospects of a detection, we find, are more favourable in a scenario with late reionization with x_H i≈ 0.5 at z≈ 7.5 as compared to an early reionization model where x_H i≈ 0.5 at z≈ 10. In the late reionization scenario, for both instruments a 3σ detection is possible for bubbles of comoving radius R_b≥ 30 Mpc with 1000 h of observation. Future observations will either lead to the detection of ionized bubbles, or in the event of non-detection, lead to constraints on the product x_H iR^γ_b for the observational volume, where γ= 1.5 and 2 for GMRT and MWA, respectively.