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We use the non-local thermodynamical equilibrium radiative transfer code {\sc radmc-3d}\footnote{http://www.ita.uni-heidelberg.de/~dullemond/software/radmc-3d/} to compute the line emission   in $^{12}$CO(1-0) and $^{13}$CO(1-0). We adopt the Large Velocity Gradient (LVG) approximation \citep{shetty11}, which solves for the rotational level populations by solving the equations for local radiative statistical equilllibrium. {\sc radmc-3d} requires 3D input gas densities, velocities and temperatures, which are produced as outputs by the hydrodynamic simulation. We perform the radiative transfer on a uniform $256^3$ grid, where we interpolate all the AMR data to the second refinement level ($\Delta x =0.001$pc). We include turbulent line broadening on scales at and below the grid resolution by adding a constant microturbulence of 0.05 km s$^{-1}$. For $^{12}$CO we smooth the velocity field by using a doppler parameter of 0.025, such that the velocity field is linearly interpolated between velocity jumps greater that 0.025$c_s$, where $c_s$ is the local sound speed. $^{13}$CO has a doppler parameter of 0.25. %This parameter mainly affects the emission in cells abutting the warm atomic gas; it has negligible impact on the emission of the cooler, denser gas.  To obtain the CO abundances from the total gas density, we assume that molecular Hydrogen dominates in all gas cooler than 1,000 K, where $n_{{\rm H}_2}=\rho/(2.8 m_p)$. We adopt constant CO abundances of [$^{12}$CO/H$_2$]=$8.6 \times 10^{-5}$ and [$^{12}$CO/$^{13}$CO]=62 for gas cooler than 900 K; otherwise the CO abundance is set to zero. Thus, line emission only originates in relatively cold gas in the dense core and gas entrained by the outflow; the warm, low-density ambient material and the hot, outflow gas, which is ionized by construction, do not emit. We adopt the molecular collisional coefficients from \citet{schoier05}.