Context. Understanding the role of fragmentation is one of the most important current questions of star formation. To better understand the process of star and cluster formation, we need to study in detail the physical structure and properties of the parental molecular cloud. The Spokes cluster, or NGC 2264 D, is a rich protostellar cluster where previous N2H+(1-0) observations of its dense cores presented linewidths consistent with supersonic turbulence. However, the fragmentation of the most massive of these cores appears to have a scale length consistent with that of the thermal Jeans length, suggesting that turbulence was not dominant. Aims. These two results probe different density regimes. Our aim is to determine if there is subsonic or less-turbulent gas (than previously reported) in the Spokes cluster at higher densities. Methods. We present APEX N2H+(3-2) and N2D+(3-2) observations of the NGC2264-D region to measure the linewidths and the deuteration fraction of the higher density gas. The critical densities of the selected transitions are more than an order of magnitude higher than that of N2H+(1-0). Results. We find that the N2H+(3-2) and N2D+(3-2) emission present significantly narrower linewidths than the emission from N2H+(1-0) for most cores. In two of the spectra, the nonthermal component is close (within 1-sigma) to the sound speed. In addition, we find that the three spatially segregated cores, for which no protostar had been confirmed show the highest levels of deuteration. Conclusions. These results show that the higher density gas, probed with N2H+ and N2D+(3-2), reveals more quiescent gas in the Spokes cluster than previously reported. More high-angular resolution interferometric observations using high-density tracers are needed to truly assess the kinematics and substructure within NGC2264-D. (Abridged)
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