Can We Detect the Anisotropic Shapes of Quasar H II Regions during Reionization through the Small-Scale Redshifted 21 cm Power Spectrum?

Light-travel time delays distort the apparent shapes of H II regions surrounding bright quasars during early stages of cosmic reionization. Individual H II regions may remain undetectable in forthcoming redshifted 21 cm experiments. However, the systematic deformation along the line of sight may be detectable statistically, either by stacking tomographic 21 cm images of quasars identified, for example, by the James Webb Space Telescope, or as small-scale anisotropy in the three-dimensional 21 cm power spectrum. Here we consider the detectability of this effect. The anisotropy is largest when H II regions are large and expand rapidly, and we find that if bright quasars contributed to the early stages of reionization, then they can produce significant anisotropy, on scales comparable to the typical sizes of H II regions of the bright quasars (≲30 Mpc). The effect therefore cannot be ignored when analyzing future 21 cm power spectra on small scales. If 10% of the volume of the intergalactic medium at z≃ 10 is ionized by quasars with typical ionizing luminosity of S≳ 5 × 10⁵⁶ s⁻¹, the distortions cause an ≳10 percent enhancement of the 21 cm power spectrum in the radial (redshift) direction, relative to the transverse directions. The level of this anisotropy exceeds that due to redshift-space distortion and has the opposite sign. We show that ongoing experiments such as Murchison Widefield Array (MWA, formerly known as the Mileura Widefield Array) should be able to detect this effect. A detection would reveal the presence of bright quasars and shed light on the ionizing yield and age of the ionizing sources and the distribution and small-scale clumping of neutral intergalactic gas in their vicinity.