The impact of anisotropy from finite light travel time on detecting
  ionized bubbles in redshifted 21-cm maps
  The detection of ionized bubbles around quasars in redshifted 21-cm maps is
possibly one of the most direct future probes of reionization. We consider two
models for the growth of spherical ionized bubbles to study the apparent shapes
of the bubbles in redshifted 21-cm maps, taking into account the finite light
travel time (FLTT) across the bubble. We find that the FLTT, whose effect is
particularly pronounced for large bubbles, causes the bubble's image to
continue to grow well after it's actual growth is over. There are two distinct
FLTT distortions in the bubble's image: (i) its apparent center is shifted
along the line of sight (LOS) towards the observer from the quasar; (ii) it's
shape is anisotropic along the LOS. The bubble initially appears elongated
along the LOS. This is reversed in the later stages of growth where the bubble
appears compressed. The FLTT distortions are expected to have an impact on
matched filter bubble detection where it is most convenient to use a spherical
template for the filter. We find that the best matched spherical filter gives a
reasonably good estimate of the size and the shift in the center of the
anisotropic image. The mismatch between the spherical filter and the
anisotropic image causes a 10 - 20% degradation in the SNR relative to that of
a spherical bubble. We conclude that a spherical filter is adequate for bubble
detection. The FLTT distortions do not effect the lower limits for bubble
detection with 1000 hr of GMRT observations. The smallest spherical filter for
which a detection is possible has comoving radii 24 Mpc and 33 Mpc for a
3-sigma and 5-sigma detection respectively, assuming a neutral fraction 0.6 at
z \sim 8.
