Probing reionization with the cross power spectrum of 21 cm and near-infrared radiation backgrounds

The cross-correlation between the 21 cm emission from the high-redshift intergalactic medium and the near-infrared (NIR) background light from the high-redshift galaxies promises to be a powerful probe of cosmic reionization. In this paper, we investigate the cross power spectrum during the epoch of reionization. We employ an improved halo approach to derive the distribution of the density field and consider two stellar populations in the star formation model: metal-free stars and metal-poor stars. The reionization history is further generated to be consistent with the electron-scattering optical depth from cosmic microwave background measurements. Then the intensity of NIR background is estimated by collecting emission from stars in the first-light galaxies. On large scales, we find the 21 cm and NIR radiation backgrounds are positively correlated during the very early stages of reionization. However, these two radiation backgrounds quickly become anti-correlated as reionization proceeds. The maximum absolute value of the cross power spectrum is $|\Delta^2_{\rm{21,NIR}}|\sim10^{-4}$ mK nW $\rm{m}^{-2}$ $\rm{sr}^{-1}$ reached at $\ell\sim1000$, when the mean fraction of ionized hydrogen is $\bar{x}_{i}\sim0.9$. We find that SKA can measure the 21 cm-NIR cross power spectrum in conjunction with mild extensions to the existing CIBER survey, provided that the integration time independently adds up to 1000 and 1 hours for 21 cm and NIR observations, and that the sky coverage fraction of CIBER survey is extended from $4\times10^{-4}$ to 0.1. Measuring the cross-correlation signal as a function of redshift provides valuable information on reionization and helps confirm the origin of the "missing" NIR background.