The hydrodynamics of relict cosmological H II regions and the formation of objects at high redshift

Discrete sources of photoionizing radiation present at the time the intergalactic medium is largely neutral will create expanding H II regions. A source which turns off or dims quickly enough will not be able to maintain the advance of its ionization front indefinitely. The high pressure of the relict H II region will then drive a shock into the cold, neutral ambient medium. We discuss the hydrodynamical evolution of relict cosmological H II regions generated at redshifts z ∼ 5-15. We approximate the resulting flow as the cosmological analog of a laboratory shock tube and present an exact analytical solution for the flow. This solution is suitable as a test problem for cosmological, numerical hydrodynamics codes. A thin shell of shocked material develops around the H II region. The peculiar velocity of the shell is typically 10-20 km s-1. The dense shell may cool and fragment into objects with baryonic masses as high as 106-108 M⊙ and column densities of order 1019 cm-2. These values are independent of the nature of the photoionizing source. They are set only by the density of the IGM, the sound speed of 104 K gas, and the age of the shell. The fragmentation process ceases once the filling factor of the H II regions reaches unity and the IGM is photoionized. The fraction of the IGM which may be affected by the shocks decreases with increasing shell radius. For typical quasar luminosities, 1% of the IGM could be processed. For protogalactic strength sources, the fraction could be as large as 10%. The clouds formed may account for the Lyoc forest seen in the spectra of high-redshift QSOs. For a filling factor of the H II regions near unity, the cloud autocorrelation function will be small if the ionizing sources are randomly distributed. Gravitationally bound fragments may be candidates for compact blue galaxies nearby and for blue-excess galaxies at high redshift.