Recent Herschel observations of nearby molecular clouds have shown that filamentary structures are ubiquitous and that most prestellar cores form in dense filaments. Probing the detailed density and velocity structure of molecular filaments is therefore crucial for improving our observational understanding of the star formation process. We aim to characterize both the density and the velocity field of a typical molecular filament in the process of fragmenting into cores. We mapped a portion of the NGC 2024 region in the Orion B molecular cloud with the Nobeyama 45m telescope, in the ^12^CO (J=1-0), ^13^CO (J=1-0), C^18^O (J=1-0), and H^13^CO+ (J=1-0) lines, and the southwestern part of NGC 2024, corresponding to the NGC 2024S filament, with the NOEMA interferometer in H^13^CO+ (J=1-0). The maps of ^13^CO, C^18^O, and H^13^CO+ emission trace at least part of the filamentary structure seen in the 800-resolution ArTeMiS+Herschel data. The median radial column density profile of the NGC 2024S filament as derived from ArTeMiS+Herschel dust emission data is well fitted by a Plummer profile with a half-power diameter D^Plummer^HP=0.081+/-0.014pc, which is similar to the findings of previous studies of nearby molecular filaments with Herschel. On the other hand, the half-power diameters of NGC 2024S as measured from the Nobeyama ^13^CO and C^18^O data are broader, while the half-power diameter derived from the H^13^CO+ data is narrower, than the filament diameter measured with Herschel. These results suggest that the ^13^CO and C^18^O data trace only the (low-density) outer part of the Herschel filament and the H^13^CO+ data only the (dense) inner part. We identified four cores in the portion of the Herschel map covered by NOEMA and found that each Herschel core corresponds to a single core detected in the combined NOEMA+45m H^13^CO+ data cube. The Nobeyama H^13^CO+ centroid velocity map reveals velocity gradients along both the major and the minor axis of the NGC 2024S filament, as well as velocity oscillations with a period ~0.2pc along the major axis. Comparison between the centroid velocity and the column density distribution shows a tentative {lambda}/4 phase shift in H^13^CO+ or C^18^O. This {lambda}/4 shift is not simultaneously observed for all cores in any single tracer but is tentatively seen for each core in either H^13^CO+ or C^18^O. The difference between the H^13^CO+ and C^18^O velocity patterns may arise from differences in the range of densities probed by H^13^CO+ and C^18^O. We produced a toy model taking into account the three velocity-field components: a transverse velocity gradient, a longitudinal velocity gradient, and a longitudinal oscillation mode caused by fragmentation. Examination of synthetic data shows that the longitudinal oscillation component produces an oscillation pattern in the velocity structure function of the model. Since the velocity structure function of the Nobeyama H^13^CO+ centroid velocity data does show an oscillation pattern, we suggest that our observations are partly tracing core-forming motions and fragmentation of the NGC 2024S filament into cores. We also found that the mean core mass in NGC 2024S corresponds to the effective Bonnor-Ebert mass in the filament. This is consistent with a scenario in which higher-mass cores form in higher line-mass filaments. We revealed that (1) the widths of filaments vary among tracers, (2) filaments a re breaking into cores, and (3) cores with higher mass form in filaments with a higher line-mass.
Cone search capability for table J/A+A/672/A133/list (List of fits datacubes)
