The Evolution of the He II-ionizing Background at Redshifts 2.3 < z < 3.8 Inferred from a Statistical Sample of 24 HST/COS HeII Lyα Absorption Spectra

We present measurements of the large-scale (approximate to 40 comoving Mpc) effective optical depth of He II Ly alpha absorption, tau(eff), at 2.54 < z < 3.86 toward 16 He II-transparent quasars observed with the Cosmic Origins Spectrograph on the Hubble Space Telescope, to characterize the ionization state of helium in the intergalactic medium (IGM). We provide the first statistical sample of tau(eff) measurements in six signal-to-noise ratio greater than or similar to 3 He II sightlines at z > 3.5, and study the redshift evolution and sightline-to-sightline variance of tau(eff) in 24 He II sightlines. We confirm an increase of the median tau(eff) from similar or equal to 2 at z = 2.7 to tau(eff) greater than or similar to 5 at z > 3, and a scatter in tau(eff) that increases with redshift. The z > 3.5 He II absorption is predominantly saturated, but isolated narrow (Delta v < 650 kms(-1)) transmission spikes indicate patches of reionized helium. We compare our measurements to predictions for a range of UV background models applied to outputs of a large-volume (146 comoving Mpc)(3) hydrodynamical simulation by forward-modeling our sample's quality and size. At z > 2.74, the variance in teff significantly exceeds expectations for a spatially uniform UV background, but is consistent with a fluctuating radiation field sourced by variations in the quasar number density and the mean free path in the post-reionization IGM. We develop a method to infer the approximate median He II photoionization rate Gamma(He) (II) of a fluctuating UV background from the median tau(eff), finding a factor similar or equal to 5 decrease in Gamma(He) (II) between z similar or equal to 2.6 and z similar or equal to 3.1. At z similar or equal to 3.1, Gamma(He II) = [9.1(-1.2)(+1.1) (stat) (+2.4)(-3.4) (sys)] x 10(-16) s(-1) corresponds to a median He II fraction of similar or equal to 2.5%, indicating that our data probe the tail end of He II reionization.