deletions | additions       diff --git a/Filament selection and analysis.tex b/Filament selection and analysis.tex  index b4d713f..fc1e0f1 100644  --- a/Filament selection and analysis.tex  +++ b/Filament selection and analysis.tex 
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\section{Filament selection and analysis}  After 1.23 Myr and 2.09 Myr of self gravitating evolution, we selected by eye filamentary features in one projection of the cloud, shown in figure \ref{finderimage}. These images were constructed by calculating the surface density of gas in the range $10^3 < n/{\rm cm}^{-3} < 10^{4.5}$. This is roughly the density range traced by C$^{18}$O observations; we then converted the surface density to integrated line intensities. This conversion, using equation 2 of \citet{2001ApJ...551..687M}, is only meant to give a low-order approximation to an observation. This approximate `observation' of our data yields an idea of what this simulation might look like in the motivating observations of \citet{2013A&A...554A..55H}. At 1.23 Myr we chose one feature which, observationally speaking, would probably be deemed an obvious filament (filament D1), two that might be considered a ridge of star formation activity consisting of distinct dense sites linked by more tenuous emission (filaments B and C1), and one region that has entered a collapse phase (filament A). We stress that this is not intended to be a comprehensive study of all the filaments in this projection, but rather an exploratory look at a few of the more prominent features. At this point 34 M$_{\sun}$ of gas is in sinks in filament A, yielding an a global  integrated star sink  formation efficiency of $\sim 0.6\%$. At 2.09 Myr we selected three filamentary features. Two are evolved versions of the features at 1.23 Myr (filaments C2 and D2), while filament E formed in the intervening time. At this point there are more sinks scattered through the box, including at least one in each of the filaments. The total sink mass is 92 M$_{\sun}$, i.e. an a global  integrated star sink  formation efficiency $\sim1.6\%$\footnote{We note in passing that this efficiency is a factor of 1.8 lower than the most equivalent simulation of \citet{2012ApJ...761..156F}, within the expected scatter resulting from different turbulent seeds, box sizes, and densities.}. We chose to analyse these early times, before the gas has begun converting to sinks in earnest, to approximate the evolutionary state of Hacar et al.'s observations. \subsection{Line-of-sight velocity structure}  The rectangles surrounding the selected filaments define a coordinate system with axes aligned along the long axis or length $L$ of the filament, and the width $W$. The depth $D$ is the same axis that the surface density is projected along. We stepped along the $L$ and $W$ coordinates with a stepsize equal to the simulation's base resolution, and calculated at each point the density-weighted line-of-sight velocity integrated along the $D$ axis, using the same density range used to calculate the surface density. We binned these spectra into histograms with bin width 0.05 km s$^{-1}$. 
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E & 36.0 & 79.1 & 1.21 & 0.015 & 1.7 & 0.40 \\  \hline  \end{tabular}  \caption{The masses and dimensions of the filaments as defined by the boxes in figure \ref{finderimage}. $M_{C^{18}O}$ is the moderate density mass contributing to that image; M_{gas} is the total gass mass; $M_{\star}$ is the mass in sinks; $sfe$ is the instantaneous global  sink formation efficiency, efficiency in each filament,  $M_{\star} / (M_{\star} + M_{gas})$.} \end{table}