Helium Reionization Simulations. III. The Helium Lyman-$\alpha$ Forest
  In La Plante et al. (2017), we presented a new suite of hydrodynamic
simulations with the aim of accurately capturing the process of helium II
reionization. In this paper, we discuss the observational signatures present in
the He II Ly$\alpha$ forest. We show that the effective optical depth of the
volume $\tau_\mathrm{eff}$ is not sufficient for capturing the ionization state
of helium II, due to the large variance inherent in sightlines. However, the He
II flux PDF can be used to determine the timing of helium II reionization. The
amplitude of the one-dimensional flux power spectrum can also determine the
ionization state of helium II. We show that even given the currently limited
number of observations ($\sim$50 sightlines), measurements of the flux PDF can
yield information about helium II reionization. Further, measurements using the
one-dimensional power spectrum can provide clear indications of the timing of
reionization, as well as the relative bias of sources of ionizing radiation.
