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Stella Offner edited section_Methods_label_methods_subsection__.tex
over 8 years ago
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As in \citet{Offner_2015}, 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{Tafalla_2004}. 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 $\pm 20\kms$ and a spectral resolution of $\Delta v = 0.156~ \kms$.
[Ryan - explain the next steps in 2-3 sentences] We produce synthetic observations of the nearby Perseus molecular cloud by setting
our the spectral cubes at a distance of 250
pc, (and redefining their domain’s dimensions as angular position). pc. The
emission’s (?) emission units are
scaled converted to temperature (K) using the Rayeigh-Jeans approximation.
Noise is considered in some of the statistics as described below.
\subsection{Statistical Analysis}
We characterize our synthetic spectral cubes by applying statistical analysis techniques established in the literature. Table ??? enumerates our astrostatistical toolkit. %This is a good idea -- we can list the statistics, their functional definitions and literature citation.
We group the statistics into three categories based on their method of analysis: {\it intensity statistics} quantify emission distributions, {\it Fourier statistics} analyze N-dimensional power spectra obtained through spatial integration techniques, and {\it morphology statistics} characterize structure and emission properties. We define the apply the statistics following Koch et al. (2015). They provide a detailed theoretical description of each turbulent statistic, and so we give only brief descriptions here.
%For each simulation data cube, we compute the intensity moment maps and implement the statistical analysis techniques.
To perform the statistical analysis, we use TurbuStat, a Python package developed by Koch et al. (2015).
TurbuStat measures differences between the spectral cubes by computing a pseudo-distance metric as proposed in \citet{yeremi14} and further developed in Koch et al. (2015). We focus our discussion on those statistics deemed by Koch et al. (2015) to be ``good", i.e., those which exhibit a response to changes in underlying physical parameters rather than to statistical fluctuations in the data. (And then other part in sec 4)
[Ryan with input from Eric - a paragraph?]
We characterize our synthetic observations through (trying to use "use" less) statistical This analysis
techniques established in extends the
literature. Table ??? enumerates our astrostatistical toolkit. We classify statistics by their method of analysis: intensity statistics quantify emission distributions, fourier statistics analyze N-dimensional power spectra obtained through spatial integration techniques, and morphology statistics characterize structure and emission properties. Koch et al. (2015) provides a theoretical description study of
each turbulent statistic. (2015). For each data cube, we compute the intensity moment maps, and implement the statistical analysis techniques. We measure differences between synthetic observations with (use 'use' less) pseudo-distance metrics, as proposed in Yeremi et al. (2014) and further developed in Koch et al. (2015). To perform all numerical calculations, we use TurbuStat, a Python package containing detailed algorithms for (turbulent/turbulence) statistics and their respective distance metrics. (WHAT IF..) We will focus our discussion on those statistics deemed K15 by
Koch et al. (2015) to be ``good", i.e., those which exhibit a response to changes in underlying physical parameters rather than to statistical fluctuations in the data. (And then other part in sec 4)
[Here or elsewhere?] examining simulations including feedback from stellar winds.
Unlike the study carried out in
Koch et al.~(2015), K15, our simulation suite does not utilize experimental design to set the
simulation parameter values. As discussed in \citet{Yeremi_2014}, comparisons between outputs in one-factor-at-a-time approaches may give a misleading signal since the statistical effects are not fully calibrated. However,
here we
will focus our discussion on those statistics deemed by
Koch et al. (2015) K15 to be ``good", i.e., those which exhibit a response to changes in underlying physical parameters rather than to statistical fluctuations in the data.