Gravity, Magnetic Field, and Turbulence: Relative Importance and Impact on Fragmentation in the Infrared Dark Cloud G34.43+00.24

(Abbreviated) We investigate the interplay between magnetic (B) field, gravity, and turbulence in the fragmentation process of cores within the filamentary infrared dark cloud G34.43+00.24. We observe the magnetic field (B) morphology across G34.43 and compare with the kinematics obtained from N2H+ across the filament. We derive local velocity gradients from N2H+, tracing motion in the plane of sky, and compare with the observed local B field orientations in the plane of sky. Besides a large-scale east-west velocity gradient, we find a close alignment between local B field orientations and local velocity gradients toward the MM1/MM2 ridge. This local correlation in alignment suggests that gas motions are influenced by the magnetic field morphology or vice versa. Additionally, this alignment seems to be getting even closer with increasing integrated emission in N2H+, possibly indicating that a growing gravitational pull is more and more aligning B field and gas motion. We analyze and quantify B field, gravity, turbulence, and their relative importance toward the MM1, MM2 and MM3 regions with various techniques over two scales, a larger clump area at 2 pc scale and the smaller core area at 0.6 pc scale. While gravitational energy, B field, and turbulent pressure all grow systematically from large to small scale, the ratios among the three constituents develop clearly differently over scale. We propose that this varying relative importance between B field, gravity, and turbulence over scale drives and explains the different fragmentation types seen at sub-pc scale (no fragmentation in MM1; aligned fragmentation in MM2; clustered fragmentation in MM3). We discuss uncertainties, subtleties, and the robustness of our conclusion, and we stress the need of a multi-scale joint analysis to understand the dynamics in these systems.