We study the signatures of reionization and ionizing properties of the early galaxies in the cross-correlations between the 21cm emission from the spin-flip transition of neutral hydrogen (HI) and the underlying galaxy population, in particular a sub-population of galaxies visible as Lyman Alpha Emitters (LAEs). With both observables simultaneously derived from a $zsimeq6.6$ hydrodynamical simulation (GADGET-2) snapshot post-processed with a radiative transfer code (pCRASH) and a dust model, we perform a parameter study and aim to constrain both the average intergalactic medium (IGM) ionization state ($1-langle chi_{HI} rangle$) and the reionization topology (outside-in versus inside-out). We find that in our model LAEs occupy the densest and most-ionized regions resulting in a very strong anti-correlation between the LAEs and the 21cm emission. A 1000h SKA-LOW1 - Subaru Hyper Suprime Cam experiment can provide constraints on $langle chi_{HI} rangle$, allowing us to distinguish between IGM ionization levels of 50%, 25%, 10% and fully ionized at scales $r<10$ comoving Mpc (assuming foreground avoidance for SKA). Our results support the inside-out reionization scenario where the densest knots (under-dense voids) are ionized first (last) for $langle chi_{HI} rangle >= 0.1$. Further, 1000h SKA-LOW1 observations should be able to confirm the inside-out scenario by detecting a lower 21cm brightness temperature (by about 2-10 mK) in the densest regions ($> 2$ arcminute scales) hosting LAEs compared to lower-density regions devoid of them.
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