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We study the instantaneous virial balance of clumps and cores (CCs) in 3Dsimulations of driven, MHD, isothermal molecular clouds (MCs). The modelsrepresent a range of magnetic field strengths in MCs from subcritical tonon-magnetic regimes. We identify CCs at different density thresholds, and foreach object, we calculate all the terms that enter the Eulerian form of thevirial theorem (EVT). A CC is considered gravitationally bound when thegravitational term in the EVT is larger than the amount for the system to bevirialized, which is more stringent than the condition that it be large enoughto make the total volume energy negative. We also calculate, quantitiescommonly used in the observations to indicate the state of gravitationalboundedness of CCs such as the Jeans number J_c, the mass-to magnetic fluxratio mu_c, and the virial parameter alpha_vir. Our results show that: a) CCsare dynamical out-of-equilibrium structures. b) The surface energies are of thesame order than their volume counterparts c) CCs are either in the process ofbeing compressed or dispersed by the velocity field. Yet, not all CCs that havea compressive net kinetic energy are gravitationally bound. d) There is no1-to-1 correspondence between the state of gravitational boundedness of a CC asdescribed by the virial analysis or as implied by the classical indicators. Ingeneral, in the virial analysis, we observe that only the inner regions of theobjects are gravitationally bound, whereas J_c, alpha_vir, and mu_c estimatestend to show that they are more gravitationally bound at the lowest thresholdlevels and more magnetically supercritical. g) We observe, in the non-magneticsimulation, the existence of a bound core with structural and dynamicalproperties that resemble those of the Bok globule Barnard 68 (B68).Comment: Accepted to ApJ. Discussion substantially enlarged, a few corrections  and additional figures. Main conclusions unchange

The Virial Balance of Clumps and Cores in Molecular Clouds