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Mass-density relationship in molecular cloud clumps

We study the mass-density relationship n ~ m^x in molecular cloud condensations (clumps), considering various equipartition relations between their gravitational, kinetic, internal and magnetic energies. Clumps are described statistically, with a density distribution that reflects a lognormal probability density function (pdf) in turbulent cold interstellar medium. The clump mass-density exponent $x$ derived at different scales $L$ varies in most of the cases within the range $-2.5\lesssim x \lesssim-0.2$, with a pronounced scale dependence and in consistency with observations. When derived from the global size-mass relationship m ~ l^{γ_{glob}} for set of clumps, generated at all scales, the clump mass-density exponent has typical values $-3.0\lesssim x(γ_{glob}) \lesssim -0.3$ that depend on the forms of energy, included in the equipartition relations and on the velocity scaling law whereas the description of clump geometry is important when magnetic energy is taken into account.