Lyman Alpha Emitters and the 21cm Power Spectrum as Probes of
  Density-Ionization Correlation in the Epoch of Reionization
  Due to the large cross section of Ly$\alpha$ photons with hydrogen, Lyman
Alpha Emitters (LAEs) are sensitive to the presence of neutral hydrogen in the
intergalactic medium (IGM) during the Epoch of Reionization (EoR): the period
in the Universe's history where neutral hydrogen in the IGM is ionized. The
correlation of the ionized regions in the IGM with respect to the underlying
intrinsic LAEs has a pronounced effect on the number of observed LAEs and their
apparent clustering. As a result, observations of LAEs during the EoR can be
used as a probe of the EoR morphology. Here we build on previous works where we
parametrize the density-ionisation correlation during the EoR, and study how
the observed number density and angular correlation function (ACF) of LAEs
depends on this parametrization. Using Subaru measurements of the number
density of LAEs and their ACF at z = 6.6, we place constraints on the EoR
morphology. We find that measurements of LAEs at z = 6.6 alone cannot
distinguish between different density-ionization models at $68\%$ credibility.
However, adding information regarding the number density, and ACF, of LAEs at
$z = 6.6$ to 21cm power spectrum measurements using the hydrogen Epoch of
Reionization Array (HERA) at the midpoint of reionization can rule out
uncorrelated and outside-in reionization at $99\%$ credibility.
