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We present idealized numerical simulations of prestellar gravitational collapse of a moderate initial filamentary perturbation with an additional central ellipsoidal enhancement (a core) considering a uniform, and a stratified background, the latter representing flattened clouds. Both simulations maintain the filamentary structure during the collapse, developing a hierarchical accretion flow from the cloud to the plane; from there to the filament, and from the filament to the core. The flow changes direction smoothly at every step of the hierarchy, with no density divergence nor a shock developing at the filament's axis during the studied prestellar evolution. The flow drives accretion onto the central core and drains material from the filament, slowing down the growth of the latter. As a consequence, the ratio of the central density of the core to the filament density increases in time, diverging at the time of singularity formation in the core. The stratified simulation produces the best match for observed Plummer-like radial column density profiles of filaments, while the uniform simulation does not produce a flat central density profile. This result supports recent suggestions that MCs may be preferentially flattened structures. We examine the possibility that the filamentary flow might approach a quasi-stationary regime in which the radial accretion onto the filament is balanced by the longitudinal accretion onto the core. A simple argument suggests that such a stationary state may be an attractor for the system. Our simulations, do not attain this stationary stage, but appear to be approaching it during the prestellar stage.

We present a numerical study of the balance between the gravitational (Eg), kinetic (Ek), and magnetic (Em) energies of structures within a hub-filament system in a simulation of the formation and global hierarchical collapse (GHC) of a giant molecular cloud. For structures defined by various density thresholds, and at different evolutionary stages, we investigate the scaling of the virial parameter, α, with mass M, and of the Larson ratio, ${\cal {L}}_v\equiv \sigma _v/R^{1/2}$, with column density Σ, where σv is the 1D velocity dispersion, and R is an effective radius. We also investigate these scalings for the corresponding magnetic parameters αm and ${\cal {L}}_{\rm {m}}$. Finally, we compare our numerical results with an observational sample of massive clumps. We find that: 1) αm and ${\cal {L}}_{\rm {m}}$ follow similar α-M and ${\cal {L}}$-Σ scalings as their kinetic counterparts, although the ratio Em/Ek decreases as |Eg| increases. 2) The largest objects, defined by the lowest thresholds, tend to appear gravitationally bound (and magnetically supercritical), while their internal substructures tend to appear unbound (and subcritical). This suggests that the latter are being compressed by the infall of their parent structures, and supports earlier suggestions that the measured mass-to-magnetic flux ratio μ decreases inwards in a centrally-peaked cloud under ideal MHD. 3) The scatter in the α-M and ${\cal {L}}$-Σ plots is reduced when Ek and Em are plotted directly against Eg, suggesting that the scatter is due to an ambiguity between mass and size. 4) The clumps in our GHC simulation follow the same trends as the observational sample of massive clumps in the ${\cal {L}}$-Σ and α-M diagrams. We conclude that the main controlling parameter of the energy budget in the structures is Eg, with the kinetic and magnetic energies being derived from it.

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