Dark matter merging induced turbulence as an efficient engine for gas cooling

We have performed a cosmological numerical simulation of primordial baryonic gas collapsing onto a $3\times10^7$M$_{\odot}$ dark matter (DM) halo. We show that the large scale baryonic accretion process and the merger of few $\sim10^6$ M$_{\odot}$ DM halos, triggered by the gravitational potential of the biggest halo, is enough to create super sonic ($\mathcal{M}>10$) shocks and develop a turbulent environment. In this scenario the post shocked regions are able to produced both H$_2$ and HD molecules very efficiently reaching maximum abundances of $n_\mathrm{H_2}\sim10^{-2}n_\mathrm{H}$ and $n_\mathrm{HD}\sim \mathrm{few}\times10^{-6}n_\mathrm{H}$, enough to cool the gas below 100K in some regions. The kinetic energy spectrum of the turbulent primordial gas is close to a Burgers spectrum, $\hat{E}_k\propto k^{-2}$, which could favor the formation of low mass primordial stars. The solenoidal to total kinetic energy ratio is $0.65\la R_k\la0.7$ for a wide range of wave numbers; this value is close to $R_k\approx 2/3$ natural equipartition energy value of a random turbulent flow. In this way turbulence and molecular cooling seem to work together in order to produce potential star formation regions of cold and dense gas in primordial environments. We conclude that both the mergers and the collapse process onto the main DM halo provide enough energy to develop super sonic turbulence which favor the molecular coolants formation: this mechanism, which could be universal and the main route toward formation of the first galaxies, is able to create potential star forming regions at high redshift.