The role of magnetic field and stellar feedback in the evolution of filamentary structures in collapsing star-forming clouds

Context: Filaments are common features in molecular clouds and they play a key role in star formation (SF). Studying their life cycle is essential to fully understand the SF process. Aims: We aim to characterise the impact of magnetic field ($B$) and stellar feedback on the evolution of filamentary structures in star-forming clouds. Methods: We performed two numerical simulations of a collapsing $10^4\,$M$_\odot$ cloud with different mass-to-flux ratios ($\mu=2$ and $\mu=8$), including early stellar feedback (jets and HII regions). Using DisPerSE, we extracted the three-dimensional filamentary network and analysed its properties as it evolves throughout the SF event. Results: We observed that the filamentary network in the simulations follow two distinct evolutionary pathways. In the strongly magnetised case, the cloud maintains a sparser filamentary network, and the arising filaments are predominantly perpendicular to $B$ lines. With a weak field, the cloud develops a single central hub, with converging filaments favouring a parallel alignment relative to $B$. Furthermore, while always accreting, filaments exhibit faster flows towards the hub relative to the surrounding gas. In the weakly magnetised run, the central hub dominates the dynamics, and filaments exhibit faster flows as they approach the central hub. Finally, once the expanding HII region impacts the filaments, they align to $B$ independently of the initial configuration. Conclusions: Magnetic fields play a critical role in shaping the structure and dynamics of molecular clouds. Stronger magnetic fields slow the cloud's evolution and inhibit the formation of central hubs, promoting a broader filamentary network instead. However, ionising feedback dominates the late-stage evolution, overriding the initial differences and dictating the final filament configuration.