Fossil HII regions: self-limiting star formation at high redshift

Recent results from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite suggest that the intergalactic medium (IGM) was significantly reionized at redshifts as high as z similar to 17. At this early epoch, the first ionizing sources probably appeared in the shallow potential wells of mini-haloes with virial temperatures T-vir < 10(4) K. Once such an ionizing source turns off, its surrounding H II region Compton cools and recombines. None the less, we show that the 'fossil' H II regions left behind remain at high adiabats, prohibiting gas accretion and cooling in subsequent generations of mini-haloes. This greatly amplifies feedback effects explored in previous studies, and early star formation is self-limiting. We quantify this effect to show that star formation in mini-haloes cannot account for the bulk of the electron scattering opacity measured by WMAP, which must be due to more massive objects. We argue that gas entropy, rather than IGM metallicity, regulates the evolution of the global ionizing emissivity and impedes full reionization until lower redshifts. We discuss several important consequences of this early entropy floor for reionization. It reduces gas clumping, curtailing the required photon budget for reionization. An entropy floor also prevents H-2 formation and cooling, due to reduced gas densities: it greatly enhances feedback from ultraviolet photodissociation of H-2. An early X-ray background would also furnish an entropy floor to the entire IGM; thus, X-rays impede rather than enhance H-2 formation. Future 21-cm observations may probe the topology of fossil H II regions.