  It has been shown by Shchekinov & Vasiliev2006 (SV06) that HD molecules can
be an important cooling agent in high redshift z >10 haloes if they undergo
mergers under specific conditions so suitable shocks are created. Here we build
upon Prieto et al. (2012) who studied in detail the merger-generated shocks,
and show that the conditions for HD cooling can be studied by combining these
results with a suite of dark-matter only simulations. We have performed a
number of dark matter only simulations from cosmological initial conditions
inside boxes with sizes from 1 to 4 Mpc. We look for haloes with at least two
progenitors of which at least one has mass M > M_cr (z), where M_cr (z) is the
SV06 critical mass for HD over-cooling. We find that the fraction of
over-cooled haloes with mass between M_cr (z) and 10^{0.2} M_cr (z), roughly
below the atomic cooling limit, can be as high as ~ 0.6 at z ~ 10 depending on
the merger mass ratio. This fraction decreases at higher redshift reaching a
value ~0.2 at z ~ 15. For higher masses, i.e. above 10^{0.2} M_cr (z) up to
10^{0.6} M_cr (z), above the atomic cooling limit, this fraction rises to
values ~ 0.8 until z ~ 12.5. As a consequence, a non negligible fraction of
high redshift z > 10 mini-haloes can drop their gas temperature to the Cosmic
Microwave Background temperature limit allowing the formation of low mass stars
in primordial environments.
