-1cm
\label{sec:methods} Using the well-tested \(N\)-body smoothed particle hydrodynamics (SPH) code GADGET-2 \citep{Springel2005}, we perform our simulations using the same chemistry network and sink particle method as described in \citet{Hummeletal2015}; the relevant details are summarized below. In addition to using the same initial conditions as in \citet{Hummeletal2015} to allow for a comparison of the impact of X-rays versus cosmic rays on the primordial gas, we perform a second suite of simulations using new initial conditions. The minihalo in these simulations collapses at a lower redshift; this allows us to ensure our results are not being influenced by the CMB temperature floor.
\label{setup} The first set of simulations (henceforth referred to as Halo 1) use the same initial conditions as \citet{Hummeletal2015} and \citet{StacyGreifBromm2010}, and are initialised at \(z=100\) in a 140 comoving kpc box with periodic boundary conditions. To accelerate structure formation within the simulation box an artificially enhanced normalisation of the power spectrum, \(\sigma_8 = 1.4\), was used, but the simulations are otherwise initialised in accordance with a \(\Lambda\)CDM model of hierarchical structure formation. For a discussion of the validity of this choice, see \citet{StacyGreifBromm2010}. High resolution in these simulations is achieved using a standard hierarchical zoom-in technique, with nested levels of refinement at 40, 30, and 20 kpc (comoving). Using this technique, the highest resolution SPH particles have a mass \(m_{\rm SPH} = 0.015{\,{\rm M}_{\odot}}\), yielding a minimum mass resolution \(M_{\rm res} \simeq 1.5 N_{\rm neigh} m_{\rm SPH} \lesssim 1{\,{\rm M}_{\odot}}\) for the simulation. Here \(N_{\rm neigh} = 32\) is the number of particles used in the SPH smoothing kernel \citep{BateBurkert1997}.
The initial conditions for the second set of simulations (henceforth referred to as Halo 2) are derived from the simulations described in \citet{StacyBromm2013}. These simulations were initialised at \(z=100\) in a 1.4 comoving Mpc box in accordance with the same \(\Lambda\)CDM structure formation model as Halo 1, but with \(\sigma_8 = 0.9\) rather than the artificially enhanced \(\sigma_8 = 1.4\) used in Halo 1. The use of ‘marker sinks’ for regions reaching densities beyond \(n=10^3\,{\rm cm}^{-3}\) rather than following the gas to higher densities allows for the efficient identification of the first 10 minihaloes to form within the box; we select the final minihalo to form—i.e., Minihalo 10 from \citet{StacyBromm2013}—for further study. After identifying the location of the final minihalo, the cosmological box is re-initialised at \(z=100\) using a standard zoom-in technique with two nested levels of refinement used to improve resolution surrounding the selected minihalo. Each ‘parent’ particle within the most refined region is split into 64 ‘child’ particles, with a minimum mass of \(m_{\rm gas}=1.85{\,{\rm M}_{\odot}}\) and \(m_{\rm \small DM}=12{\,{\rm M}_{\odot}}\). These refined simulations are then run until the gas approaches the typical onset of runaway collapse at \(n=10^4{\,{\rm cm}^{-3}}\).