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We show that gaseous \HI disks of primordial composition irradiated by anexternal radiation field can develop a multiphase medium with temperaturesbetween 10^2 and 10^4 K due to the formation of molecular hydrogen. For a given\HI column density there is a critical value of the radiation field below whichonly the cold \HI phase can exist. Due to a time decreasing quasar background,the gas starts cooling slowly after recombination until the lowest stabletemperature in the warm phase is reached at a critical redshift $z=z_{cr}$.Below this redshift the formation of molecular hydrogen promotes a rapidtransition towards the cold \HI phase. We find that disks of protogalaxies with$10^{20}\simlt N_{HI}\simlt 10^{21} cm^{-2}$ are gravitationally stable at$T\sim 10^4$ K and can start their star formation history only at $z \simltz_{cr}\sim 2$, after the gas in the central portion of the disk has cooled totemperatures $T\simlt 300$ K. Such a delayed starbust phase in galaxies of lowgas surface density and low dynamical mass can disrupt the disks and cause themto fade away. These objects could contribute significantly to the faint bluegalaxy population.Comment: 16 pages (LaTeX), 2 Figures to be published in Astrophysical Journal  Letter

Star Formation in Disk Galaxies Driven by Primordial H[TINF]2[/TINF]