A Halo Model Approach to the $\rm{21\, cm}$ and $\rm{Ly}\alpha$
  Cross-correlation
  We present a halo-model-based approach to calculate the cross-correlation
between $\rm{21\,cm}$ HI intensity fluctuations and $\rm{Ly}\alpha$ emitters
(LAE) during the epoch of reionization (EoR). Ionizing radiation around dark
matter halos are modeled as bubbles with the size and growth determined based
on the reionization photon production, among other physical parameters. The
cross-correlation shows a clear negative-to-positive transition, associated
with transition from ionized to neutral hydrogen in the intergalactic medium
during EoR. The cross-correlation is subject to several foreground
contaminants, including foreground radio point sources important for
$\rm{21\,cm}$ experiments and low-$z$ interloper emission lines, such as
$\rm{H}\alpha$, OIII, and OII, for $\rm{Ly}\alpha$ experiments. Our
calculations show that by masking out high fluxes in the $\rm{Ly}\alpha$
measurement, the correlated foreground contamination on the
$\rm{21\,cm}$-$\rm{Ly}\alpha$ cross-correlation can be dramatically reduced. We
forecast the detectability of $\rm{21\,cm}$-$\rm{Ly}\alpha$ cross-correlation
at different redshifts and adopt a Fisher matrix approach to estimate
uncertainties on the key EoR parameters that have not been well constrained by
other observations of reionization. This halo-model-based approach enables us
to explore the EoR parameter space rapidly for different $\rm{21\,cm}$ and
$\rm{Ly}\alpha$ experiments.
