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In this study we investigate the formation and properties of prestellar andprotostellar cores using hydrodynamic, self-gravitating Adaptive MeshRefinement simulations, comparing the cases where turbulence is continuallydriven and where it is allowed to decay. We model observations of these coresin the C$^{18}$O$(2\to 1)$, NH$_3(1,1)$, and N$_2$H$^+(1\to 0)$ lines, and fromthe simulated observations we measure the linewidths of individual cores, thelinewidths of the surrounding gas, and the motions of the cores relative to oneanother. Some of these distributions are significantly different in the drivenand decaying runs, making them potential diagnostics for determining whetherthe turbulence in observed star-forming clouds is driven or decaying. Comparingour simulations with observed cores in the Perseus and $\rho$ Ophiuchus cloudsshows reasonably good agreement between the observed and simulated core-to-corevelocity dispersions for both the driven and decaying cases. However, we findthat the linewidths through protostellar cores in both simulations are toolarge compared to the observations. The disagreement is noticably worse for thedecaying simulation, in which cores show highly supersonic infall signatures intheir centers that decrease toward their edges, a pattern not seen in theobserved regions. This result gives some support to the use of driventurbulence for modeling regions of star formation, but reaching a firmconclusion on the relative merits of driven or decaying turbulence will requiremore complete data on a larger sample of clouds as well as simulations thatinclude magnetic fields, outflows, and thermal feedback from the protostars.

The Kinematics of Molecular Cloud Cores in the Presence of Driven and Decaying Turbulence: Comparisons with Observations