Triggered Population III star formation: the effect of H2 self-shielding

The multiplicity of metal-free (Population III) stars may influence their feedback efficiency within host dark matter halos, affecting subsequent metal enrichment and the transition to galaxy formation. Radiative from massive can trigger nearby star formation in dense self-shielded clouds. In model radiation self-shielding, H$_2$ column density must be accurately computed. this study, we compare two local approximations based on gradient Jeans length with a direct integration along rays. After primary forms, find that no secondary form for both approaches. approximate method reduces computation time by factor 2. approximation overestimates 10, leading five numerically enhanced self-shielded, star-forming clumps. We conclude is sufficiently accurate larger volume simulations, although one still caution cannot fully reproduce result integration.