2023MNRAS.523.3376C

We present a numerical study of the balance between the gravitational (E_g), kinetic (E_k), and magnetic (E_m) 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, ${\cal {L}}_{\rm v}\equiv \sigma _{\rm v}/R^{1/2}$, with column density Σ, where σ_v is the 1D velocity dispersion, and R is an effective radius. We also investigate these scalings for the corresponding magnetic parameters α_m and ${\cal {L}}_{\rm {m}}$. Finally, we compare our numerical results with an observational sample of massive clumps. We find that: 1) α_m and ${\cal {L}}_{\rm {m}}$ follow similar α-M and ${\cal {L}}$-Σ scalings as their kinetic counterparts, although the ratio E_m/E_k decreases as |E_g| 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 E_k and E_m are plotted directly against E_g, 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 E_g, with the kinetic and magnetic energies being derived from it.