Does radiative feedback by the first stars promote or prevent second generation star formation?

We study the effect of starlight from the first stars on the ability of other minihaloes in their neighbourhood to form additional stars. The first stars in the Lambda cold dark matter (Lambda CDM) universe are believed to have formed in minihaloes of total mass similar to 10(5-6) M(circle dot) at redshifts z greater than or similar to 20, when molecular hydrogen (H(2)) formed and cooled the dense gas at their centres, leading to gravitational collapse. Simulations suggest that the Population III (Pop III) stars thus formed were massive (similar to 100 M(circle dot)) and luminous enough in ionizing radiation to cause an ionization front (I-front) to sweep outward, through their host minihalo and beyond, into the intergalactic medium. Our previous work suggested that this I-front was trapped when it encountered other, nearby minihaloes, and that it failed to penetrate the dense gas at their centres within the lifetime of the Pop III stars (less than or similar to 3 Myr). The question of what the dynamical consequences were for these target minihaloes, of their exposure to the ionizing and dissociating starlight from the Pop III star requires further study, however. Towards this end, we have performed a series of detailed, one-dimensional (1D), radiation-hydrodynamical simulations to answer the question of whether star formation in these surrounding minihaloes was triggered or suppressed by radiation from the first stars. We have varied the distance to the source (and, hence, the flux) and the mass and evolutionary stage of the target haloes to quantify this effect. We find (1) trapping of the I-front and its transformation from R-type to D-type, preceded by a shock front; (2) photoevaporation of the ionized gas (i.e. all gas originally located outside the trapping radius); (3) formation of an H(2) precursor shell which leads the I-front, stimulated by partial photoionization; and (4) the shock-induced formation of H(2) in the minihalo neutral core when the shock speeds up and partially ionizes the gas. The fate of the neutral core is mostly determined by the response of the core to this shock front, which leads to molecular cooling and collapse that, when compared to the same halo without external radiation, is (a) expedited, or (b) delayed, or (c) unaltered, or (d) reversed or prevented, depending upon the flux (i.e. distance to the source) and the halo mass and evolutionary stage. When collapse is expedited, star formation in neighbouring minihaloes or in merging subhaloes within the host minihalo sometimes occurs within the lifetime of the first star. Roughly speaking, most haloes that were destined to cool, collapse and form stars in the absence of external radiation are found to do so even when exposed to the first Pop III star in their neighbourhood, while those that would not have done so are still not able to. A widely held view that the first Pop III stars must exert either positive or negative feedback on the formation of the stars in neighbouring minihaloes should, therefore, be revisited.