  The association of filaments with protostellar objects has made these
structures a priority target in star formation studies. The datasets of the
Herschel Galactic Cold Cores Key Programme allow for a statistical study of
filaments with a wide range of intrinsic and environmental characteristics.
Characterisation of this sample can be used to identify key physical parameters
and quantify the role of environment in the formation of supercritical
filaments. Filaments were extracted from fields at D<500pc with the
getfilaments algorithm and characterised according to their column density
profiles and intrinsic properties. Each profile was fitted with a
beam-convolved Plummer-like function and quantified based on the relative
contributions from the filament 'core', represented by a Gaussian, and 'wing'
component, dominated by the power-law of the Plummer-like function. These
parameters were examined for populations associated with different background
levels. We find that filaments increase their core (Mcore) and wing (Mwing)
contributions while increasing their total linear mass density (Mtot). Both
components appear to be linked to the local environment, with filaments in
higher backgrounds having systematically more massive Mcore and Mwing. This
dependence on the environment supports an accretion-based model for filament
evolution in the local neighbourhood (D<500pc). Structures located in the
highest backgrounds develop the highest central Av, Mcore, and Mwing as Mtot
increases with time, favoured by the local availability of material and the
enhanced gravitational potential. Our results indicate that filaments acquiring
a significantly massive central region with Mcore>Mcrit/2 may become
supercritical and form stars. This translates into a need for filaments to
become at least moderately self-gravitating in order to undergo localised star
formation or become star-forming filaments.
