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. 
David Syphers, Scott F. Anderson, Wei Zheng, Britton Smith, Matthew   Pieri, Gerard A. Kriss, Avery Meiksin, Donald P. Schne...
astro-ph.CO