Neutral hydrogen at high redshifts as a probe of structure formation - II. Line profile of a protocluster

The formation of structures at z ≲ 10.0 can be proved using the 21-cm line emission from the neutral hydrogen. Two of us (KS and TP, Paper I) previously computed the expected abundance of protoclusters as a function of the flux density at various redshifts, in the cold dark matter (CDM) and the hot dark matter (HDM) models. As a complement to Paper I, here we work out in detail how the H I line profile from a spherically symmetric protocluster evolves as it decouples from Hubble expansion and collapses. Our paradigm for structure formation is the CDM model where structures form hierarchically. Neutral hydrogen, in the small-scale clumps that form the protocluster, is the source of H I line emission. We find that the peak fluxes of the H I line profile in this model are typically of order 0.5-0.7 mJy, while the widths (FWHM) are of order 0.3-1.8 MHz. The major uncertainty in our calculations is the fraction of mass of the protocluster in the form of neutral hydrogen. If the neutral hydrogen factor ƒ is of the order of the value we have adopted (ƒ = 0.025) in our calculations or greater, then a typical protocluster could indeed be detectable by future facilities, like the Giant Metrewave Radio Telescope (GMRT) which is currently being built in India. If the neutral hydrogen fraction is much less than the value we have adopted, then a more sensitive instrument is needed to detect the H I line emission from a typical protocluster.