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Spatially Extended 21 cm Signal from Strongly Clustered UV and X-Ray Sources in the Early Universe

We present our prediction for the local 21 cm differential brightness temperature ($δT_{b}$) from a set of strongly clustered sources of Population III (Pop III) and II (Pop II) objects in the early Universe, by a numerical simulation of their formation and radiative feedback. These objects are located inside a highly biased environment, which is a rare, high-density peak ("Rarepeak") extending to $\sim7$ comoving Mpc. We study the impact of ultraviolet (UV) and X-ray photons on the intergalactic medium (IGM) and the resulting $δT_{b}$, when Pop III stars are assumed to emit X-ray photons by forming X-ray binaries very efficiently. We parameterize the rest-frame spectral energy distribution (SED) of X-ray photons, which regulates X-ray photon-trapping, IGM-heating, secondary Lyman-alpha pumping and the resulting morphology of $δT_{b}$. A combination of emission ($δT_{b}>0$) and absorption ($δT_{b}<0$) regions appears in varying amplitudes and angular scales. The boost of the signal by the high-density environment ($δ\sim0.64$) and on a relatively large scale combine to make Rarepeak a discernible, spatially-extended ($θ\sim10'$) object for 21 cm observation at $13\lesssim z\lesssim17$, which is found to be detectable as a single object by SKA with integration time of $\sim1000$ hours. Power spectrum analysis by some of the SKA precursors (LOFAR, MWA, PAPER) of such rare peaks is found difficult due to the rarity of these peaks, and the contribution only by these rare peaks to the total power spectrum remains subdominant compared to that by all astrophysical sources.