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Keywords:

  • methods: data analysis;
  • cosmology: theory;
  • diffuse radiation

ABSTRACT

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 inline image, inline image and τQ, where inline image and τQ are, respectively, the ionizing photon emission rate and age of the quasar, and inline image 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 inline image is known from the observed infrared spectrum, and C = 30 from theoretical considerations, which gives us the two free parameters inline image and τQ for bubble detection. Considering 1000'h of observation, we find that there is a reasonably large region of parameter space bounded within inline image and (0.2, 7.0) where a 3σ detection is possible if inline image. The available region increases if inline image is larger, whereas we need inline image and inline image if inline image. Considering parameter estimation, we find that in many cases it will be possible to quite accurately constrain τQ and place a lower limit on inline image 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 inline image. We find that the estimated inline image 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 inline image are expected to be within the statistical uncertainties.