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Energetic feedback processes during the formation of galaxy clusters may haveheated and ionized a large fraction of the intergalactic gas in proto-clusterregions. When such a highly ionized hot ``super-bubble'' falls along thesightline to a background quasar, it would be seen as a large void, with littleor no absorption, in the Lyman alpha forest. We examine the spectra of 137quasars in the Sloan Digital Sky Survey, to search for such voids, and find noclear evidence of their existence. The size distribution of voids in the range5-70 Angstrom (corresponding to physical sizes of approximately 3-35 comovingMpc/h) is consistent with the standard model for the Lyman alpha forest withoutadditional hot bubbles. We adapt a physical model for HII bubble growth duringcosmological reionization (Furlanetto, Zaldarriaga and Hernquist 2004), todescribe the expected size-distribution of hot super-bubbles at redshift aroundz = 3. This model incorporates the conjoining of bubbles around individualneighboring galaxies. Using the non-detection of voids, we find that models inwhich the volume filling factor of hot bubbles exceeds approximately 20 percentat z=3 can be ruled out, primarily because they overproduce the number of large(40-50 Angstrom) voids. We conclude that any pre-heating mechanism thatexplains galaxy cluster observations must avoid heating the low-density gas inthe proto-cluster regions, either by operating relatively recently (z<3) or bydepositing entropy in the high-density regions.

Constraints on the Abundance of Highly Ionized Proto-Cluster Regions from the Absence of Large Voids in the Lyman Alpha Forest