Statistical analysis of the relative orientations between filaments and magnetic fields using <i>Herschel</i> and <i>Planck</i> data in star-forming regions

Context . Filamentary structures are ubiquitous in the interstellar medium (ISM). This is particularly true in molecular clouds, with most clumps and cores forming inside the densest regions of filaments. Observations and simulations both suggest that magnetic fields play a key role in the formation and evolution of filaments and in the process of star formation, yet their exact role is still poorly understood. In this context, the study of the relative orientations between filaments and magnetic fields has become a go-to method to obtain new insight. Aims . We aim to statistically examine the relative orientations between filaments and magnetic fields in various star-forming regions with different physical properties and Galactic environments. Methods . We used a dedicated method, FilDReaMS , that relies on a template that has the shape of a rectangular bar with a variable width to detect and extract filaments at multiple scales. We applied FilDReaMS to the 116 fields of the Herschel “Galactic Cold Cores” (GCC) key project (18″–36″ resolution), which measured dust emission in diverse star-forming regions. We then compared the filament orientations to the orientation of the plane-of-sky (PoS) magnetic field ( B PoS ), inferred from Planck observations of the dust polarized thermal emission (7′ resolution) using histograms of relative orientations (HROs). Additionally, we used a catalog of dense cold cores detected in the GCC fields to study the relative orientations of filaments hosting cores. Results . We present the results of our statistical analysis of these relative orientations as functions of filament effective width, H 2 column density ( N H 2 ), evolutionary stage, and Galactic environment. We find that low- N H 2 filaments tend to be roughly parallel to B PoS at all scales, while narrow high- N H 2 filaments do not have any preferred orientations and wide high- N H 2 filaments tend to be roughly perpendicular. This change in preferred orientations occurs at transition column density ( N H 2 ) t values typically in the range [0.8, 8] × 10 21 cm −2 , a range that is consistent with results of previous Planck studies. We also analyzed the HROs for filaments with embedded cores and find them to be consistent with HROs for high- N H 2 filaments, although the trend is less pronounced. However, several fields do not follow the general trends, with a variety of behaviors that can be due to factors such as projection effects, confusion along the line of sight (LoS), magnetic field tangling, or different magnetic field strengths. Our analysis of projection effects shows that, statistically, preferred orientations in the PoS are indicative of true preferred orientations in 3D. Our results suggest that higher polarization fractions, p , entail weaker projection effects, consistent with the presumed link between p and the magnetic field inclination to the LoS. Conclusions . Our results confirm the existence of a coupling between magnetic fields at cloud scales and filaments at smaller scales while also highlighting the complexity of the ISM. They also call for further statistical analyses studying magnetic fields and other physical processes at smaller scales to better understand the variety of behaviors seen in the HROs.