Dark Matter Halo Environment for Primordial Star Formation

We study the statistical properties (such as shape and spin) of high-z halos 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 $<s> = 0.3 \pm 0.1$, and for more than 90% of halos the triaxiality parameter is $T \lesssim 0.4$, showing a clear preference for oblateness over prolateness. Larger halos in the simulation tend to be both more spherical and prolate: we find $s \propto M_h^{\alpha_s}$ and $T \propto M_h^{\alpha_T}$, with $\alpha_s \approx 0.128$ 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 $<\lambda> =0.0184$, 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 (2008) and mapping our halo spin distribution into a PopIII 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 centered at $\approx 65 M_\odot$ (MT1) or $\approx 140 M_\odot$ (MT2). At later times, model MT1 evolves into a bimodal distribution with a second prominent peak located at $35-40 M_\odot$ 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.