The rich complexity of 21-cm fluctuations produced by the first stars

We explore the complete history of the 21-cm signal in the redshift range z = 7-40. This redshift range includes various epochs of cosmic evolution related to primordial star formation, and should be accessible to existing or planned low-frequency radio telescopes. We use semi-numerical computational methods to explore the fluctuation signal over wavenumbers between 0.03 and 1 Mpc$^{-1}$, accounting for the inhomogeneous backgrounds of Ly-$\alpha$, X-ray, Lyman-Werner and ionizing radiation. We focus on the recently noted expectation of heating dominated by a hard X-ray spectrum from high-mass X-ray binaries. We study the resulting delayed cosmic heating and suppression of gas temperature fluctuations, allowing for large variations in the minimum halo mass that contributes to star formation. We show that the wavenumbers at which the heating peak is detected in observations should tell us about the characteristic mean free path and spectrum of the emitted photons, thus giving key clues as to the character of the sources that heated the primordial Universe. We also consider the line-of-sight anisotropy, which allows additional information to be extracted from the 21-cm signal. For example, the heating transition at which the cosmic gas is heated to the temperature of the cosmic microwave background should be clearly marked by an especially isotropic power spectrum. More generally, an additional cross-power component $P_X$ directly probes which sources dominate 21-cm fluctuations. In particular, during cosmic reionization (and after the just-mentioned heating transition), $P_X$ is negative on scales dominated by ionization fluctuations and positive on those dominated by temperature fluctuations.