The micro-structure of the intergalactic medium - I. The 21 cm signature from dynamical minihaloes

A unified description is provided for the 21 cm signatures arising from minihaloes against a bright background radio source and against the cosmic microwave background (CMB), within the context of a dynamical collapsing cosmological spherical halo. The effects of gas cooling via radiative atomic and molecular processes and of star formation on setting the maximum mass of the minihaloes giving rise to a 21 cm signal are included. Models are computed both with and without molecular hydrogen formation, allowing for its possible suppression by an ambient ultraviolet radiation field. The spectral signatures and equivalent width distributions are computed for a ?cold dark matter cosmology. The detectability of minihaloes in absorption against bright background radio sources is discussed in the context of future measurements by a Square Kilometre Array (SKA) and the LOw Frequency ARray (LOFAR). The brightness temperature differential relative to the CMB is also computed. Several generic scenarios are considered. For the cosmological parameter constraints from the Wilkinson Microwave Anisotropy Probe (WMAP), in the absence of any form of galactic feedback, the number of systems per unit redshift in absorption against a bright radio source at 8 < z < 10 is dN/dz similar or equal to 10 for observed equivalent widths exceeding 0.1 kHz. For larger equivalent widths, somewhat fewer systems are predicted at increasing redshifts. The estimated numbers are independent of the presence of star formation in the haloes following molecular hydrogen formation except for rare, high equivalent width systems, which become fewer. LOFAR could plausibly detect a minihalo signal against a 30 mJy source in a 1200 h integration. SKA could detect the signal against a weaker 6 mJy source in as little as 24 h. Adding cosmological constraints from the Atacama Cosmology Telescope (ACT) suppresses the predicted number of all the absorbers by as much as an order of magnitude. In the presence of a background of ambient Ly alpha photons of sufficient intensity to couple the gas spin temperature to the kinetic temperature, as may be produced by the first star-forming objects, the number of weak absorption systems is substantially boosted, by more than two orders of magnitude, rendering the signal readily detectable. Weak absorption features arising from the cold infalling regions around the minihaloes may appear as mock emission lines relative to the suppressed continuum level. A moderate amount of heating of the intergalactic medium (IGM), however, would greatly reduce the overall number of absorption systems. By contrast, the absorption signal of minihaloes against the CMB is distinguishable from the diffuse IGM signature only for a limited scenario of essentially no feedback and moderate redshifts, z < 19. The strength of the signal is dominated by the more massive minihaloes, and so is sensitive to a cut-off in the upper minihalo mass range imposed by any star formation and its consequences. Once the first star-forming systems provide feedback in the form of Lya photons, the diffuse IGM signal will quickly dominate the signal from minihaloes because of the small total fraction of IGM mass in the minihalo cores.