deletions | additions       diff --git a/Filament selection and analysis.tex b/Filament selection and analysis.tex  index aadb89b..5f31309 100644  --- a/Filament selection and analysis.tex  +++ b/Filament selection and analysis.tex 
...
\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 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} \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 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.  DESCRIBE VELOCITY STRUCTURE 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. Filament B contains $\sim 30$ \msun 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}  We now turn to the third dimension of the filaments. 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; filament D in particular is predominantly a 1D structure. 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. It is worth noting that there is nothing in the line-of-sight velocity information that obviously distinguishes filament A from C or D. With the exception of the outlying material at $L\sim 1.5$ to $2.25$, and $v_{los}\sim-1.5$ to $-2$ km s$^{-1}$ (which is the clump at $D\sim 2$ to $3$ pc in figure \ref{filaments3D}), the rest of the material appears to consist of distinct ribbons intertwining in position--velocity space, with some large scale gradients and a mildly supersonic dispersion.