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 a global integrated 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. a global integrated sink formation efficiency \(\sim1.6\%\)¹. 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. The masses and dimensions of the sinks are summarized in table \ref{filtable}.

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 0.025 km s\(^{-1}\).

In figures \ref{filvels1} and \ref{filvels2} 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 character of the velocity distributions are qualitatively similar to the observations of \citet{2013A&A...554A..55H}; overlapping individual features with subsonic widths, combined into features with mildly supersonic dispersions. Note that we plot the raw density weighted velocity structure, rather than the centroids of line fits 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 C1 and D1 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 is overlaid. The small scale feature’s velocity gradients are larger than the large scales, consistent with the observations. Filament A’s sink particles are clustered around \(L = 0.75\) pc; the inflow of material onto this small protocluster is clearly visible in the velocity plot, while farther away from the clustering the intertwining filaments in position–velocity space again show up. This same signal appears in filament D2, with about 6 M\(_{\sun}\) of sinks at \(L=0.6\) pc. Filament B 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 at 1.23 Myr.

The filaments’ third spatial dimension

In figure \ref{filaments3D} we show the \(L\)–\(D\) projections along with the \(L\)–\(W\) projections from the left panel of figure \ref{finderimage}. Filaments A, C1, and D1 are revealed as spatially coherent entities along the projected axis, with most of the material contained in a single connected distribution. Filament D1, in particular, is predominantly a 1D structure. Filament A, as the first site of sink particle formation in the simulated volume, is unsurprisingly compact in all three dimensions. Filament B, 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 B from C1 or D1. With the exception of the outlying material at \(L\sim 1.5\) to \(2.25\) pc, and \(v_{los}\sim-1.5\) to \(-2\) km s\(^{-1}\) (which is the clump at \(D\sim 2.5\) to \(3.5\) 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.

\label{filtable}