We simulated a 10 pc periodic cube of a molecular cloud, beginning from fully developed isothermal turbulent initial conditions. We generated the turbulent initial conditions using version 4.2 of the ATHENA code \citep{2005JCoPh.205..509G,2008JCoPh.227.4123G,2008ApJS..178..137S,2009NewA...14..139S}. The turbulent driving was technically similar to that of \citet{2009ApJ...691.1092L}. Briefly, on a \(1024^{3}\) grid with domain length 1 we applied divergence-free velocity perturbations at every timestep to an initially uniform medium. The perturbations had a Gaussian random distribution with a Fourier power spectrum \(\left | d {\bf v}_{k}^{2} \right | \propto k^{-2}\), for wavenumbers \(2 < k/2 \pi < 4\). Similarly to, e.g., \citet{Federrath_2013}, turbulence on smaller length scales was generated self-consistently from the large scale driving. The driving continued until the box reached a saturated state at a Mach number \(\mathcal{M}\) of roughly 8. During this driving stage we did not include gravitational forces.
At this point we scaled the box to a physical size \(S = 10\) pc, mean number density \(n = 100\) cm\(^{-3}\) at mean molecular weight \(\mu=2.33\) (giving a total gas mass \(\sim5700\) M\(_{\sun}\)), and a constant sound speed \(c_s\) = 0.2 km s\(^{-1}\). After turning off the forcing and turning on self gravity, we turned the simulation over to the adaptive mesh refinement (AMR) code RAMSES \citep{2002A&A...385..337T}. The \(1024^{3}\) base grid was maintained along with 4 steps of adaptive refinement (i.e. a maximum effective resolution of \(16384^{3}\)), with each level of refinement triggered when the local Jeans length became shorter than 32 grid cells \citep{http://adsabs.harvard.edu/abs/2011ApJ...731...62F,1997ApJ...489L.179T}.
Regions collapsing beyond this point were replaced by sink particles, using the sink implementation described in \citet{2010MNRAS.409..985D}, which largely follows the implementation of \citet{2004ApJ...611..399K}. The salient points of this implementation are that regions exceeding the Truelove density limit on the finest level of refinement and that are collapsing along all directions are replaced by sink particles. The sinks accrete gas in a momentum conserving fashion from a region 4 cells in radius (\(\sim0.01\) pc) at the local Bondi-Hoyle rate in that region. While the sinks are addressed in this paper, we can approximate the integrated star (rather, sink) formation efficiency as the fraction of the total mass in sinks at some time.
We integrated the box through \(\sim2.1\) Myr of self gravitating evolution. Following \citet{2007ApJ...665..416K}’s definition of the turbulent turnover time in a box , \(T_{turb} = S/(2 c_s \mathcal{M})\), we have \(T_{turb} \sim 3\) Myr. The free-fall time \(T_{ff} = [3\pi / (32 G \rho)]^{1/2}\), at the mean density of the simulation, is also roughly 3 Myr. In this paper we focus on moderately dense gas, with \(10^3 < n/{\rm cm}^{-3} < 10^{4.5}\); at these densities we have \(0.2 \lesssim T_{ff} / \rm{Myr} \lesssim 1.1\). After 1 Myr the global structure of the simulated box is thus still dominated by the initial turbulence, while the denser gas has had time to become organized by self gravity.