New Evidence for Extended HeII Reionization at z>3.5 from HeII Lyman
  Alpha and Beta Transmission Spikes
  We present new high-resolution (R~14,000) spectra of the two brightest
HeII-transparent quasars in the far-UV (FUV) at z>3.5, HE2QSJ2311-1417 (z=3.70)
and HE2QSJ1630+0435 (z=3.81), obtained with the Cosmic Origins Spectrograph
(COS) on the Hubble Space Telescope (HST). In the predominantly saturated HeII
absorption spectra, both sightlines show several isolated resolved (full width
at half maximum FWHM>50 km/s) transmission spikes in HeII Ly$\alpha$ and HeII
Ly$\beta$. The incidence of such spikes decreases with increasing redshift, but
both sightlines show significant spikes at z>3.5, signaling the presence of
fully ionized regions in the z>3.5 intergalactic medium (IGM). We employ an
automated algorithm to compare the number of detected HeII transmission spikes
to predictions from mock spectra created from the outputs of a cubic (100/h
cMpc)^3 optically thin Nyx hydrodynamical simulation, assuming a range of UV
background photoionization rates $\Gamma_\mathrm{HeII}$. From the incidence of
Ly$\alpha$ and Ly$\beta$ transmission spikes we infer similar photoionization
rates of $\Gamma_\mathrm{HeII}=2.0^{+0.6}_{-0.5}\times 10^{-15}$s$^{-1}$ at
3.51<z<3.66 and $\Gamma_\mathrm{HeII}=0.9\pm0.3 \times 10^{-15}$s$^{-1}$ at
3.460<z<3.685, respectively. Because the transmission spikes indicate fully
ionized regions at z>3.5 along both lines of sight, our observations provide
further evidence that HeII reionization had substantially progressed at these
redshifts.
