  We characterize in detail the two ~0.3 pc long filamentary structures found
within the subsonic region of Barnard 5. We use combined GBT and VLA
observations of the molecular lines NH$_3$(1,1) and (2,2) at a resolution of
1800 au, as well as JCMT continuum observations at 850 and 450 $\mu$m at a
resolution of 4400 au and 3000 au, respectively. We find that both filaments
are highly super-critical with a mean mass per unit length, $M/L$, of ~80
M$_\odot$ pc$^{-1}$, after background subtraction, with local increases
reaching values of ~150 M$_\odot$ pc$^{-1}$. This would require a magnetic
field strength of ~500 $\mu$G to be stable against radial collapse.
  We extract equidistant cuts perpendicular to the spine of the filament and
fit a modified Plummer profile as well as a Gaussian to each of the cuts. The
filament widths (deconvolved FWHM) range between 6500-7000 au (~0.03 pc) along
the filaments. This equals ~2.0 times the radius of the flat inner region. We
find an anti-correlation between the central density and this flattening
radius, suggestive of contraction. Further, we also find a strong correlation
between the power-law exponent at large radii and the flattening radius. We
note that the measurements of these three parameters fall in a plane and derive
their empirical relation. Our high-resolution observations provide direct
constraints of the distribution of the dense gas within super-critical
filaments showing pre- and protostellar activity.
