The impact of anisotropy from finite light traveltime on detecting ionized bubbles in redshifted 21-cm maps

Abstract

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 traveltime (FLTT) across the bubble. In both models, the bubble has a period of rapid growth beyond which its radius either saturates or grows slowly. We find that the FLTT, whose effect is particularly pronounced for large bubbles, causes the bubble’s image to continue to grow well after its actual growth is over. There are two distinct FLTT distortions in the bubble’s image: (i) its apparent centre is shifted along the line of sight (LOS) towards the observer from the quasar and (ii) it 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 centre of the anisotropic image. The mismatch between the spherical filter and the anisotropic image causes a degradation in the signal-to-noise ratio relative to that of a spherical bubble. The degradation is in the range 10–20 per cent during the period of rapid growth when the image appears elongated and is less than 10 per cent in the later stages when the image appears compressed. We conclude that a spherical filter is adequate for bubble detection. The FLTT distortions do not affect the lower limits for bubble detection with 1000 h of GMRT observations. The smallest spherical filter for which a detection is possible has comoving radii 24 and 33 Mpc for 3σ and 5σ detections, respectively, assuming a neutral fraction 0.6 at z∼ 8.