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The Dynamical State of The Serpens South Filamentary Infrared Dark Cloud

We present the results of N$_2$H$^+$ ($J=1-0$) observations toward Serpens South, the nearest cluster-forming, infrared dark cloud. The physical quantities are derived by fitting the hyperfine structure of N$_2$H$^+$. The Herschel and 1.1-mm continuum maps show that a pc-scale filament fragments into three clumps with radii of $0.1-0.2$ pc and masses of $40-230M_\odot$. We find that the clumps contain smaller-scale ($\sim 0.04$ pc) structures, i.e., dense cores. We identify 70 cores by applying CLUMPFIND to the N$_2$H$^+$ data cube. In the central cluster-forming clump, the excitation temperature and line-width tend to be large, presumably due to protostellar outflow feedback and stellar radiation. However, for all the clumps, the virial ratios are evaluated to be $0.1-0.3$, indicating that the internal motions play only a minor role in the clump support. The clumps exhibit no free-fall, but low-velocity infall, and thus the clumps should be supported by additional forces. The most promising force is the globally-ordered magnetic field observed toward this region. We propose that the Serpens South filament was close to magnetically-critical and ambipolar diffusion triggered the cluster formation. We find that the northern clump, which shows no active star formation, has a mass and radius comparable to the central cluster-forming clump, and therefore, it is a likely candidate of a {\it pre-protocluster clump}. The initial condition for cluster formation is likely to be a magnetically-supported clump of cold, quiescent gas. This appears to contradict the accretion-driven turbulence scenario, for which the turbulence in the clumps is maintained by the accretion flow.