  Interferometry of the cosmic 21-cm signal is set to revolutionize our
understanding of the Epoch of Reionization (EoR), eventually providing 3D maps
of the early Universe. Initial detections however will be low signal-to-noise,
limited by systematics. To confirm a putative 21-cm detection, and check the
accuracy of 21-cm data analysis pipelines, it would be very useful to
cross-correlate against a genuine cosmological signal. The most promising
cosmological signals are wide-field maps of Lyman alpha emitting galaxies
(LAEs), expected from the Subaru Hyper-Suprime Cam (HSC) Ultra-Deep field. Here
we present estimates of the correlation between LAE maps at z~7 and the 21-cm
signal observed by both the Low Frequency Array (LOFAR) and the planned Square
Kilometer Array Phase 1 (SKA1). We adopt a systematic approach, varying both:
(i) the prescription of assigning LAEs to host halos; and (ii) the large-scale
structure of neutral and ionized regions (i.e. EoR morphology). We find that
the LAE-21cm cross-correlation is insensitive to (i), thus making it a robust
probe of the EoR. A 1000h observation with LOFAR would be sufficient to
discriminate at >1 standard deviation a fully ionized Universe from one with a
mean neutral fraction of xHI~0.50, using the LAE-21cm cross-correlation
function on scales of R~3-10 Mpc. Unlike LOFAR, whose detection of the LAE-21cm
cross-correlation is limited by noise, SKA1 is mostly limited by ignorance of
the EoR morphology. However, the planned 100h wide-field SKA1-Low survey will
be sufficient to discriminate an ionized Universe from one with xHI~0.25, even
with maximally pessimistic assumptions.
