Stella Offner edited section_Methods_subsection_Numerical_Simulations__.tex  over 8 years ago

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In this paper, we analyze the magneto-hydrodynamic simulations performed by \citet{Offner15} of a small group of wind-launching stars, which are embedded in a turbulent molecular cloud. We refer the reader to that paper for full numerical details. Table \ref{simprop} summarizes the simulation properties for the specific evolutionary times we analyze here. In brief, the calculations are performed using the {\sc orion} adaptive mesh refinement code \citep[e.g.,]{li12}. They include supersonic turbulence, magnetic fields, and five star particles endowed with a prescription for launching isotropic stellar winds. The domain size for all runs is 5 pc and the molecular gas is initially 10 K with a velocity dispersion of $2.0$\kms. The turbulent realization, magnetic field strength and wind properties vary between runs as stated in Table \ref{simprop}.  \begin{deluxetable*}{lccccccc}  \tablecolumns{8}  \tablecaption{Model Properties\tablenotemark{a} \label{simprop}}  \tablehead{ \colhead{Model } &   \colhead{B($\mu G$)} &  \colhead{ $\beta$} &  \colhead{$t_{\rm evol}$(Myr)} &  \colhead{$\dot M_{\rm tot}(10^{-6 }\msun {\rm yr}^{-1})$\tablenotemark{b}} &  \colhead{ $v_{\rm max}$ ($\kms$)} &  \colhead{ $d_{x}$ (AU)} &  \colhead{Driving }}  \startdata  W1\_T1\_t1 & 13.5 & 0.1 & 0.1 & 41.7 & 200 & 10$^3$ &N \\ %2a  W1\_T2 & 13.5 & 0.1 & 0.2 & 41.7 & 200 & 10$^3$ &N \\ %2b  W2\_T2 & 13.5 & 0.1 & 0.2 & 4.5 & 200 & 10$^3$ &Y \\ %3a  W2\_T3\tablenotemark{c} &5.6 & 0.6 & 0.1 & 4.5 & 200 & 10$^3$ &Y \\ %3b  W2\_T4\tablenotemark{c} &30.1 & 0.02 & 0.1 & 4.5 & 200 & 10$^3$ &N \\ %3c  \enddata  \tablenotetext{a}{[Ryan modify to reflect the outputs you analyzed] Model name, initial mean magnetic field, ratio of thermal to magnetic pressure, the evolutionary time, the total stellar mass-loss rate, the maximum wind velocity, minimum grid resolution, and whether external driving is continued simultaneously with winds or whether winds alone inject energy. All models have $L=5$pc, $M=3762 \msun$, $T_i=10$K and $N_*=5$. } %rho=2.04d-21  \tablenotetext{b}{The estimated mass-loss rate from all stellar winds in Perseus is $9.49 \times 10^{-6}\msun$yr$^{-1}$ (Arce et al.~2011). }  \tablenotetext{c}{Same wind model as W2\_T2 but a different initial magnetic field. }  \tablenotetext{d}{Same initial turbulence as run W2\_T2, but containing only a single isolated star with the given mass-loss rate.}  \end{deluxetable*}  \subsection{CO Emission Modeling}  As in \citet{Offner15}, we post-process each output with the radiative transfer code {\sc radmc-3d}\footnote{http://www.ita.uni-heidelberg.de/~dullemond/software/radmc-3d/} in order to compute the $^{12}$CO (1-0) emission. We solve the equations of radiative statistical equilibrium using the Large Velocity Gradient (LVG) approach \citep{shetty11}. We perform the radiative transfer using the densities, temperatures, and velocities of the simulations flattened to a uniform $256^3$ grid. We convert to CO number density by defining $n_{\rm H_2} = \rho/(2.8 m_p)$ and adopting a CO abundance of [$^{12}$CO/H$_2$] =$10^{-4}$ \citep{frerking82}. Gas above 800 K or with $n_{\rm H_2} < 10$ cm$^{-3}$ is set to a CO abundance of zero. This effectively means that gas inside the wind bubbles is CO-dark. The CO abundance in regions with densities $n_{\rm H_2} > 2 \times 10^4$ cm$^{-3}$ is also set to zero, since CO freezes-out onto dust grains at higher densities \citep{tafalla04a}. In the radiative transfer calculation, we include sub-grid turbulent line broadening by setting a constant micro-turbulence of 0.25$\kms$. The data cubes have a velocity range of $\pm 10\kms$ and a spectral resolution of $\Delta v = 0.156~ \kms$.