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We analyse the virial balance of clumps and cores in a set of three
-dimensional, driven, isothermal, magnetohydrodynamical simulations of
molecular clouds. We apply a clump finding algorithm based on a density
threshold and a friend-of-friend approach to identify clumps and cores
in the simulation box. For each clump, we calculate all the terms that
enter the virial equation in its Eulerian form (EVT). These terms include
the thermal, kinetic and magnetic volume and surface energies (E_th,
E_k, E_m, Tau_th, Tau_k, Tau_m, respectively), the gravitational term (W),
the second time derivative of the moment of Inertia and the first
time derivative of the flux of moment of Inertia through the clump boundary.
We also calculate, for each clump and core, other stability indicators commonly
used in observational and theoretical work such as the Jeans number (J_c),
the mass-to magnetic flux ratio (normalized to the critical value for collapse
, mu_c) , and the gravitational parameter (alpha_c).
We show that :a) Clumps and core are dynamical, out-of-equilibrium
structures, b) Surface energy terms are as important as volume terms in the
overall energy balance, c) Not all clumps that have infall-like motions are
gravitationally bound, d) The near equality of the temporal terms in the EVT
enables the usage of the other terms as a stability indicator (gravity versus
other energies), and e) We establish the relationships between the classical
parameters J_c, mu_c, and alpha_c which are used to compare the ratios of
gravitational to thermal, magnetic and kinetic energies in clumps to their
counterparts in the EVT (e.g., J_c is compared to |W|/|E_th - Tau_th|). Thus,
we propose a method to test the clump stability based on observations of their
combined dynamical, thermal and magnetic properties.
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