tokens: individual column density slices along the filaments (shown in the first three panels of Fig. E.1 ). Although a Plummer may reasonably well describe slice 50 in the north-west filament (and perhaps even the centre-most portion of slice 54 in the north-east filament) the extended emission in the majority of slices renders fitting them with Gaussian or Plummer profiles inappropriate. We have evaluated further the impact of constraining the Gaussian fit parameters on the goodness of the fit itself. While setting the peak position of the Gaussian profiles to lie on the spine (i.e. x = 0) does not improve the produced fits, restricting the fitting to the inner portion of the filaments does result in better Gaussian fits of the central portion of the filament. However, filament properties (width and line mass) derived from such fits are very much dependent on the exact fitting range used. Such properties calculated from Trapezoidal integration of the asymmetrical profiles (as shown in Table 3 and Fig. 14 ) are less affected by such restrictions, and therefore more robust. Characterising filaments is fraught with difficulty, and caution must be observed whilst deriving global properties from their mean profiles (e.g. Panopoulou et al. 2017 ). Fig. E.1 Results of fitting Gaussian (red line) and Plummer (blue dashed line) profiles to individual radial column density slices (orange circles in the first , second and third panels of each row ) and the mean radial column density profile (black circles in the fourth panel of each row) of (a) the north-east filament ( top row ) and (b) the north-west filament ( bottom row ). The grey points in the background of each panel plots all of the radial column density slices simultaneously. Plummer profiles may on occasion well describe the inner regions of the filaments only, whilst Gaussian profiles fail to fit any of the distributions. Gaussian profiles are only found to reasonably fit some of the data once the fitting range is restricted tothe inner portion of the filament. Appendix F Derivation of the analytical expression of the virial ratio Consider a uniform density filament fragmenting at the length scale equal to the separation of a core, λ core . In an idealised scenario, energy is conserved during collapse whilst fragmentation is happening. However, there is a fraction of energy converted from gravitational potential energy ( E g ) into kinetic energy ( E k ) at the time the filament fragmentation starts. This conversion may be expressed in the virial equation as an efficiency ε , where if no energy is converted, ε = 0. If energy conversion does occur, this can be expressed as a fractional increase in E k , expressed as E k = E k ,0 + Δ E k , where E k ,0 is the initial kinetic energy of the fragmenting core before collapse. This fractional increase in kinetic energy can be expressed as , where E g ,0 is the initial gravitational potential energy. Substitution into the standard virial ratio of α vir = 2
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