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tokens: resolution surrounding the selected minihalo. Each ‘parent’ particle within the most refined region is split into 64 ‘child’ particles, with a minimum mass of m gas = 1.85 M ⊙ and . These refined simulations are then run until the gas approaches the typical onset of runaway collapse at n = 10 4 cm −3 . 3.1.1 Halo 2 cut-out and refinement Once the simulation reaches 10 4 cm −3 all particles beyond 10 comoving kpc from the centre of the collapsing minihalo are removed to conserve computational resources. To achieve a maximum resolution comparable to Halo 1, all particles within the 10 comoving kpc volume are split into two child particles placed randomly within the smoothing kernel of the parent particle. This particle-splitting is repeated twice more; all particles within 8 comoving kpc are replaced by eight child particles; within 6 comoving kpc, each of these child particles is split into an additional 8 for a total of 128 child particles in the most refined region. At each step, the mass of the parent particle is evenly divided among the child particles and the smoothing length is set to , where h is the smoothing length of the parent and N new is the number of child particles created. All particles inherit the same entropy, velocity, and chemical abundances as their parent, ensuring conservation of mass, internal energy, and momentum. While our cut-out technique leads to a rarefaction wave propagating inward from the suddenly introduced vacuum boundary condition, the average sound speed at the edge of the most refined region is ∼1 km s −1 . As a result the wave only travels ∼0.5 pc over the remaining 400 000 yr of the simulation, a negligible fraction of the ∼350 pc physical box size. 3.2 Chemistry and thermodynamics We employ the chemistry network described in detail by Greif et al. ( 2009 ), which follows the abundance evolution of H, H + , H − , H 2 , , He, He + , He ++ , D, D + , HD and e − . All relevant cooling mechanisms are accounted for, including H and He collisional excitation and ionization, recombination, bremsstrahlung and inverse Compton scattering. In order to properly model the chemical evolution at high densities, H 2 cooling induced by collisions with H and He atoms and other H 2 molecules is also included. Three-body reactions involving H 2 become important above n ≳ 10 8 cm −3 ; we employ the intermediate rate from Palla, Salpeter Stahler ( 1983 ), but see Turk et al. ( 2011 ) for a discussion of the uncertainty of these rates. In addition, the efficiency of H 2 cooling is reduced above ∼10 9 cm −3 as the ro-vibrational lines of H 2 become optically thick above this density. To account for this we employ the Sobolev approximation together with an escape probability formalism (see Yoshida et al. 2006 ; Greif et al. 2011b for details). 3.3 Cosmic ray ionization and heating Each time a CR proton ionizes a hydrogen atom, an electron with average energy 〈 E 〉 = 35 eV is produced (Spitzer Tomasko 1968 ). Including the