Cross-correlations between 21 cm, X-ray and infrared backgrounds

The history of the cosmological reionization is still unclear. Two ionizing sources, stars and QSOs, are believed to play important roles during this epoch. Besides the 21 cm signals, the infrared emission from Pop Ⅲ stars and X-ray photons from QSOs can be powerful probes of the reionization. Here we present a cross-correlation study of the 21 cm, infrared and X-ray backgrounds. The advantage of doing such cross-correlations is that we could highlight the correlated signals and eliminate irrelevant fore-grounds. We develop a shell model to describe the 21 cm signals and find that PopⅢ stars can provide higher 21 cm signals than QSOs. Using the ROSAT data for X-ray and AKARI data for infrared, we predict various cross power spectra analytically and dis-cuss prospects for detecting these cross-correlation signals in future low frequency radio surveys. We find that, although these cross-correlational signals have distinct features, so far, they have been difficult to detect due to the high noise of the soft X-ray and infrared backgrounds given by ROSAT and AKARI.