Optimal survey parameters: Ly <i>?</i> and H <i>?</i> intensity mapping for synergy with the 21-cm signal during reionization

Intensity mapping of multiple emission lines is emerging as a new branch to astronomy, probe both properties ionizing sources and the medium between, in particular intergalactic medium. For Epoch Reionization (EoR) studies, multi-line experiments analysis methods are still their infancy. Here we explore optimal survey parameters for Ly$\alpha$ (and H$\alpha$) intensity up high redshifts reionization, requirements optimised synergy with 21cm experiments. We investigate line sensitivity, spectral resolution detector pixel size (high signal-to-noise) mission output. Power cross-power spectra fiducial setup derived, mock maps. power spectrum measurements cumulative signal-to-noise O$\left(10^3 \right)$, respective cross-spectra SKA observations O$\left(10\right)$ O$\left(10^2\right)$ possible per redshift bin around midpoint reionization. These tomographic reach sensitivities $>8\times 10^{-18}$erg$\,$s$^{-1}$sr$^{-1}$Hz$^{-1}$, $R>250$ sizes $<2\,$arcsec; all three met by proposed Cosmic Dawn Mapper (CDIM). CDIM similar S/N values H$\alpha$. Already planned NASA SPHEREx will detect during EoR autopower cross 21cm, better than $10^{-18}$erg$\,$s$^{-1}$sr$^{-1}$Hz$^{-1}$ moderate foreground scenario (better $10^{-17}$erg$\,$s$^{-1}$sr$^{-1}$Hz$^{-1}$ an optimistic scenario). advocate IR missions flavor leap IM finish providing cookbook successful EoR.