Primordial gas cooling behind shock waves in merging halos

We investigate thermal regime of the baryons behind shock waves arising in the process of virialization of dark matter halos. We find a fraction of the shocked gas cooled by radiation of HD molecules down to the temperature of the cosmic microwave background (CMB): this fraction increases sharply from about $f_{\rm c}\sim 10^{-3}$ for dark halos of $M=5\times 10^7\msun$ to $\sim 0.1$ for halos with $M=10^8\msun$ at $z=10$. We show, however, that further increase of the mass does not lead to a significant growth of $f_{\rm c}$ -- the assymptotic value for $M\gg 10^8\msun$ is of 0.2. We estimate star formation rate associated with such shock waves, and show that it can be a small but not negligible fraction of the star formation connected with cooling by HI and H$_2$. We argue that extremely metal-poor low-mass stars in the Milky Way may have been formed from primordial gas behind such shocks.