Constraints on the abundance of highly ionized protocluster regions from the absence of large voids in the Lyα forest

Energetic feedback processes during the formation of galaxy clusters may have heated and ionized the majority of the intergalactic gas in protocluster regions. When such a highly ionized superbubble falls along the sight line to a background quasar, it would be seen as a large void with little or no absorption in the Ly alpha forest. We examine the spectra of 137 quasars in the Sloan Digital Sky Survey to search for such voids and find no clear evidence of their existence. The size distribution of voids in the range 5 angstrom less than or similar to Delta lambda less than or similar to 70 angstrom (corresponding to physical sizes of 3 h(-1) P L less than or similar to 35 h(-1) comoving Mpc) is consistent with the standard model for the Ly alpha forest without additional ionized bubbles. We adapt a physical model for H II bubble growth during cosmological reionization to describe the expected size distribution of ionized superbubbles at z similar to 3. This model incorporates the conjoining of bubbles around individual neighboring galaxies. Using the nondetection of voids, we find that models in which the volume filling factor of ionized bubbles exceeds similar to 20% at z similar to 3 can be ruled out, primarily because they overproduce the number of large (40-50 angstrom) voids. We conclude that any preheating mechanism that explains galaxy cluster observations must avoid heating the low-density gas in the protocluster regions, either by operating relatively recently (z less than or similar to 3) or by increasing entropy primarily in high-density regions.