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

The detection of individual ionized bubbles in HI 21-cm maps is one of the most promising, direct probes of the epoch of reionization(EoR). Atleast 1000 hrs of observation would be required for such a detection with either the currently functioning GMRT or the upcoming MWA. Considering the large investment of 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_HI. 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_HI \approx 0.5 at z \approx 7.5 as compared to an early reionization model where x_HI \approx 0.5 at z \approx 10. In the late reionization scenario, for both instruments a 3 \sigma detection is possible for bubbles of comoving radius R_b>= 30 Mpc with 1000 hrs 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_HI R_b^\gamma for the observational volume, where \gamma=1.5 and 2 for GMRT and MWA respectively.