Context : The onset of star formation is intimately linked with the presence of massive , unstable filaments .
These structures are therefore key for theoretical models aiming to reproduce the observed characteristics of the star formation process .

Aims : As part of the filament study carried out by the Herschel Galactic Cold Cores Key Programme , here we study the filament properties presented in GCC VII ( Paper I ) in context with theoretical models of filament formation and evolution .

Methods : A conservative sample of filaments at a distance D < 500 pc was extracted with the getfilaments algorithm .
The physical structure of the filaments 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 the predictions from theoretical models describing the evolution of filaments under gravity-dominated conditions .

Results : The feasibility of a transition from a subcritical to supercritical state by accretion is dependent on the combined effect of filament intrinsic properties and environmental conditions .
Reasonably self-gravitating ( high M _ { \mathrm { line,core } } ) filaments in dense environments ( A _ { \mathrm { V } } \approx 3 mag ) can become supercritical in timescales of t \sim 1 Myr by accreting mass at constant or decreasing width .
The trend of increasing M _ { \mathrm { line,tot } } ( M _ { \mathrm { line,core } } and M _ { \mathrm { line,wing } } ) , and ridge A _ { \mathrm { V } } with background also indicates that the precursors of star-forming filaments evolve coevally with their environment .
The simultaneous increase of environment and filament A _ { \mathrm { V } } explains the association between dense environments and high M _ { \mathrm { line,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 .

Conclusions :