The Evolution of the HeII-Ionizing Background at Redshifts 2.3<z<3.8 Inferred from a Statistical Sample of 24 HST/COS HeII Ly$α$ Absorption Spectra

Abstract: We present measurements of the large-scale (~40 comoving Mpc) effective optical depth of HeII Ly$\alpha$ absorption, $\tau_{\rm eff}$, at 2.54<z\<3.86 toward 16 HeII-transparent quasars observed with the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST), to characterize the ionization state of helium in the intergalactic medium (IGM). We provide the first statistical sample of $\tau_{\rm eff}$ measurements in six signal-to-noise ratio \>3 HeII sightlines at z>3.5, and study the redshift evolution and sightline-to-sightline variance of $\tau_{\rm eff}$ in 24 HeII sightlines. We confirm an increase of the median $\tau_{\rm eff}$ from ~2 at z=2.7 to >5 at z>3, and a scatter in $\tau_{\rm eff}$ that increases with redshift. The z>3.5 HeII absorption is predominantly saturated, but isolated narrow ($\Delta v<650$ km/s) 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 $\tau_{\rm eff}$ 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 HeII photoionization rate $\Gamma_{\rm HeII}$ of a fluctuating UV background from the median $\tau_{\rm eff}$, finding a factor ~5 decrease in $\Gamma_{\rm HeII}$ between z~2.6 and z~3.1. At z~3.1 a $\Gamma_{\rm HeII}=\left[9.1^{+1.1}{-1.2}\,\mathrm{(stat.)}\,^{+2.4}{-3.4}\,\mathrm{(sys.)}\right]\times10^{-16}\,\mathrm{s}^{-1}$ corresponds to a median HeII fraction of ~2.5%, indicating that our data probe the tail end of HeII reionization.