He II Ly{\beta} Gunn-Peterson Absorption: New HST Observations, and
  Theoretical Expectations
  Observations of He II Ly{\alpha} Gunn-Peterson troughs have proved to be a
valuable probe of the epoch of helium reionization at z~3. Since this optical
depth can become unmeasurably large even for modest He II fractions, various
alternate techniques have been proposed to push to higher redshift, and among
the more promising is looking at higher order Lyman-series troughs. We here
report four new observations of the He II Ly{\beta} trough, including new data
on the only sightline with a prior Ly{\beta} observation. However, the
effective optical depth ratio {\tau}_eff,{\beta}/{\tau}_eff,{\alpha} is not
simply predicted by (f_{\beta} {\lambda}_{\beta})/(f_{\alpha}
{\lambda}_{\alpha})=0.16, and we analyze cosmological simulations to find that
the correct ratio for helium at z~3 is ~0.35. In one case we infer
{\tau}_eff,{\alpha} > 8.8, strong evidence that helium was not fully reionized
at z=3.2--3.5, in agreement with previous measurements suggesting a later
completion of reionization.
