Overcooled haloes at z ≥ 10: a route to form low-mass first stars

It has been shown by Shchekinov and Vasiliev (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. 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 overcooling. We find that the fraction of overcooled 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 similar to 0.6 at z approximate to 10 depending on the merger mass ratio. This fraction decreases at higher redshift reaching a value similar to 0.2 at z approximate to 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 greater than or similar to 0.8 until z approximate to 12.5. As a consequence, a non-negligible fraction of high redshift z greater than or similar to 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.