Dark matter halo environment for primordial star formation

We study the statistical properties (such as shape and spin) of high-z haloes likely hosting the first (PopIII) stars with cosmological simulations including detailed gas physics. In the redshift range considered (11 < z < 16) the average sphericity is < s > = 0.3 +/- 0.1, and for more than 90 per cent of haloes the triaxiality parameter is T less than or similar to 0.4, showing a clear preference for oblateness over prolateness. Larger haloes in the simulation tend to be both more spherical and prolate: we find s proportional to M-h(alpha s) and T proportional to M-h(alpha T), with alpha(s) approximate to 0.128 and alpha(T) = 0.276 at z = 11. The spin distributions of dark matter and gas are considerably different at z = 16, with the baryons rotating slower than the dark matter. At lower redshift, instead, the spin distributions of dark matter and gas track each other almost perfectly, as a consequence of a longer time interval available for momentum redistribution between the two components. The spin of both the gas and dark matter follows a lognormal distribution, with a mean value at z = 16 of = 0.0184, virtually independent of halo mass. This is in good agreement with previous studies. Using the results of two feedback models (MT1 and MT2) by McKee & Tan and mapping our halo spin distribution into a PopIII initial mass function (IMF), we find that at high z, the IMF closely tracks the spin lognormal distribution. Depending on the feedback model, though, the distribution can be centred at approximate to 65 M-circle dot (MT1) or approximate to 140 M-circle dot (MT2). At later times, model MT1 evolves into a bimodal distribution with a second prominent peak located at 35-40 M-circle dot as a result of the non-linear relation between rotation and halo mass. We conclude that the dark matter halo properties might be a key factor shaping the IMF of the first stars.