deletions | additions       diff --git a/Filament selection and analysis.tex b/Filament selection and analysis.tex  index 1e8145d..fda6cd7 100644  --- a/Filament selection and analysis.tex  +++ b/Filament selection and analysis.tex 
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After 1.25 Myr of self gravitating evolution, we selected by eye four filamentary features in one projection of the cloud, shown in figure \ref{finderimage}. This image was 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}. We chose one feature which, observationally speaking, would probably be deemed an obvious filament (filament D), two that might be considered a ridge of star formation activity consisting of distinct dense sites linked by more tenuous emission (filaments A and C), and one region that has entered a collapse phase (filament B). 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.  \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 simulations 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$^{-1}$. In figure \ref{finderimage} we show this data above the blowups of each filament. We summed the histograms along the $W$ dimension, yielding the total velocity distribution along slices perpendicular to the filament's long axis. The general character of the distributions is qualitatively similar to the observations of \citet{2013A&A...554A..55H}; a tangle of individual features with subsonic widths, combined into ropelike features with mildly supersonic dispersions. Note that we plot the raw density weighted velocity structure, rather than the centroids of line fits that like  Hacar et al present. This accounts for the low intensity background in the velocity plots. Nonetheless, arcs of higher intensity signal are clearly seen in our data. There are a few features in individual filaments worth mentioning. Filaments C and D show large scale gradients of approximately 0.5 km s$^{-1}$ pc${^-1}$ on top of which the $\sim 0.5$ km s$^{-1}$ dispersion if overlayed. is overlaid.  Filament B contains $\sim 30$ M$_{\sun}$ of sink masses clustered at around $L = 0.75$. The inflow of material onto this protocluster is clearly visible in the velocity plot, while farther away from the clustering the intertwining filaments in position--velocity space again show up. Filament A contains outlying material at a velocity of about -1.5 km s$^{-1}$, quite distinct from the rest of the signal at mean velocities around 0 to -0.5 km s$^{-1}$, a hint that some material in the ridge is only associated with the rest in projection. To further explore the coherence of the filaments, we turn to the 3D spatial extent of the selected regions. \subsection{The filaments' third spatial dimension}  In figure \ref{filaments3D} we show the $L$--$D$ projections along the $L$--$W$ projections from figure \ref{finderimage}. Filaments B, C, and D are revealed as spatially coherent entities along the projected axis, with most of the material contained in a single connected distribution. Filament D, in particular, is predominantly a 1D structure. Filament B, as the first site of sink particle formation in the simulated volume, is unsurprisingly compact in all three dimensions. Filament A, in contrast, consists of distinct dense clumps, no closer to each other than about 2 pc, that are joined only in projection by more tenuous emission.