Helium diffusion during formation of the first galaxies

We investigate the possible impact of diffusion on the abundance of helium and other primordial elements during formation of the first structures in the early Universe. We consider the primary collapse of a perturbation and subsequent accretion of matter onto the virialized halo, restricting our consideration to halos with masses considerably above the Jeans limit. We find that diffusion in the cold and nearly neutral primordial gas at the end of the Dark Ages could raise the abundance of primordial elements relative to hydrogen in the first virialized halos: helium enrichment could reach $\delta Y_p/Y_p \sim 10^{-4}$ in the first star-forming minihalos of $\sim 10^5-10^6 M_{\odot}$. A moderate (to ~ 100 K) preheating of the primordial gas at the beginning of cosmic reionization could increase this effect to $\delta Y_p/Y_p \sim 3\times 10^{-4}$ for $\sim 10^6 M_{\odot}$ halos. Even stronger abundance enhancements, $\delta Y_p/Y_p$ ~ a few $10^{-3}$, may arise at much later, post-reionization epochs, z ~ 2, in protogroups of galaxies ($\sim 10^{13} M_{\odot}$) as a result of accretion of warm-hot intergalactic medium with T ~ 10^6 K. The diffusion-induced abundance changes discussed here are small but comparable to the already achieved ~ 0.1 % precision of cosmological predictions of the primordial He abundance. If direct helium abundance measurements (in particular, in low-metallicity HII regions in dwarf galaxies) achieve the same level of precision in the future, their comparison with the BBN predictions may require consideration of the effects discussed here.