A variety of observations now indicate that intergalactic helium was fully ionized by z \sim 3 .
The most recent measurements of the high-redshift quasar luminosity function imply that these sources had produced at least \sim 2.5 ionizing photons per helium atom by that time , consistent with a picture in which the known quasar population drives He ii reionization .
Here we describe the distribution of ionized and neutral helium gas during this era .
Because the sources were rare and bright ( with the photon budget dominated by quasars with luminosities L \gtrsim L _ { \star } ) , random fluctuations in the quasar population determined the morphology of ionized gas when the global ionized fraction \bar { x } _ { i } was small , with the typical radius R _ { c } of a He iii bubble \sim 15 – 20 comoving Mpc .
Only when \bar { x } _ { i } \gtrsim 0.5 did the large-scale clustering of the quasars drive the characteristic size of ionized regions above this value .
Still later , when \bar { x } _ { i } \gtrsim 0.75 , most ionizing photons were consumed by dense , recombining systems before they reached the edge of their source ’ s ionized surroundings , halting the bubble growth when R _ { c } \sim 35 – 40 \mbox { Mpc } .
These phases are qualitatively similar to those in hydrogen reionization , but the rarity of the sources makes the early stochastic phase much more important .
Moreover , the well-known characteristics of the z = 3 intergalactic medium allow a much more robust description of the late phase in which recombinations dominate .