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We examine aspects of primordial star formation in the presence of amolecular hydrogen-dissociating ultraviolet background. We compare a set of AMRhydrodynamic cosmological simulations using a single cosmological realizationbut with a range of ultraviolet background strengths in the Lyman-Werner band.This allows us to study the effects of Lyman-Werner radiation on suppressing H2cooling at low densities as well as the high-density evolution of thecollapsing core in a self-consistent cosmological framework. We find that theaddition of a photodissociating background results in a delay of the collapseof high density gas at the center of the most massive halo in the simulationand, as a result, an increase in the virial mass of this halo at the onset ofbaryon collapse. We find that, contrary to previous results, Population IIIstar formation is not suppressed for J$_{21} \geq 0.1$, but occurs even withbackgrounds as high as J$_{21} = 1$. We find that H2 cooling leads to collapsedespite the depressed core molecular hydrogen fractions due to the elevated H2cooling rates at $T=2-5 \times 10^3$ K. We observe a relationship between thestrength of the photodissociating background and the rate of accretion onto theevolving protostellar cloud core, with higher LW background fluxes resulting inhigher accretion rates. Finally, we find that the collapsing halo cores in oursimulations do not fragment at densities below $n \sim 10^{10}$ cm$^{-3}$regardless of the strength of the LW background, suggesting that Population IIIstars forming in halos with T$_{vir} \sim 10^4$ K may still form in isolation.

Population III star formation in a Lambda CDM universe, II: Effects of a photodissociating background