Galactic Cold Cores. VIII. Filament formation and evolution: Filament
  properties in context with evolutionary models
  Filaments are key for star formation models. As part of the study carried out
by the Herschel GCC Programme, here we study the filament properties presented
in GCC.VII in context with theoretical models of filament formation and
evolution. A conservative sample of filaments at a distance D<500pc was
extracted with the Getfilaments algorithm. Their physical structure was
quantified according to two main components: the central (Gaussian) region
(core component), and the power-law like region dominating the filament column
density profile at larger radii (wing component). The properties and behaviour
of these components relative to the total linear mass density of the filament
and its environmental column density were compared with theoretical models
describing the evolution of filaments under gravity-dominated conditions. The
feasibility of a transition to supercritical state by accretion is dependent on
the combined effect of filament intrinsic properties and environmental
conditions. Reasonably self-gravitating (high Mline-core) filaments in dense
environments (av\sim3mag) can become supercritical in timescales of t\sim1Myr
by accreting mass at constant or decreasing width. The trend of increasing
Mline-tot (Mline-core and Mline-wing), and ridge Av with background also
indicates that the precursors of star-forming filaments evolve coevally with
their environment. The simultaneous increase of environment and filament Av
explains the association between dense environments and high Mline-core values,
and argues against filaments remaining in constant single-pressure equilibrium
states. The simultaneous growth of filament and background in locations with
efficient mass assembly, predicted in numerical models of collapsing clouds,
presents a suitable scenario for the fulfillment of the combined filament
mass-environment criterium that is in quantitative agreement with Herschel
observations.
