The infrared detection of a z > 7 quasar has opened up a window to directly probe the intergalactic medium (IGM) during the epoch of reionization. It is anticipated that future observations will yield more quasars extending to higher redshifts. In this paper, we theoretically consider the possibility of detecting the ionized bubble around a z = 8 quasar using targeted redshifted 21-cm observations with the GMRT. The apparent shape and size of the ionized bubble, as seen by a distant observer, depends on the parameters , and τQ, where and τQ are, respectively, the ionizing photon emission rate and age of the quasar, and and C are, respectively, the neutral fraction and clumping factor of the IGM. The 21-cm detection of an ionized bubble, thus, holds the promise of allowing us to probe the quasar and IGM properties at z = 8.
In this work we have analytically calculated the apparent shape and size of a quasar's ionized bubble assuming a uniform IGM and ignoring other ionizing sources besides the quasar, and used this as a template for matched-filter bubble search with the GMRT visibility data. We have assumed that is known from the observed infrared spectrum, and C = 30 from theoretical considerations, which gives us the two free parameters and τQ for bubble detection. Considering 1000'h of observation, we find that there is a reasonably large region of parameter space bounded within and (0.2, 7.0) where a 3σ detection is possible if . The available region increases if is larger, whereas we need and if . Considering parameter estimation, we find that in many cases it will be possible to quite accurately constrain τQ and place a lower limit on with 1000'h of observation, particularly if the bubble is in the early stage of growth and we have a very luminous quasar or a high neutral fraction. Deeper follow-up observations (4000 and 9000'h) can be used to further tighten the constraints on τQ and . We find that the estimated is affected by uncertainty in the assumed value of C. The quasar's age τQ however is robust and is unaffected by the uncertainty in C.
The presence of other ionizing sources and inhomogeneities in the IGM distort the shape and size of the quasar's ionized bubble. This is a potential impediment for bubble detection and parameter estimation. We have used the seminumerical technique to simulate the apparent shape and size of quasar ionized bubbles incorporating these effects. If we consider a 9000'h of observation with the GMRT, we find that the estimated parameters τQ and are expected to be within the statistical uncertainties.