If you are a member of an institution with an active account, you may be able to access content in one of the following ways: Get help with access Institutional accessĪccess to content on Oxford Academic is often provided through institutional subscriptions and purchases. However, we obtain that gas near the core is not virialized and its state is marginally bound since the energy of the fluid element vanishes. At scales near the core, one cannot neglect the second derivative of the moment of inertia of the gas, which prevents derivation of an analytic equation for the density profile. the solution is unstable or at best marginally bound.
In Case 3, the energy of the fluid element is positive or zero, i.e. In Cases 1 and 2, the energy of the fluid element can be negative or zero thus the solution is dynamically stable and shall be long lived. For trans- or subsonic flows, we obtain a balance between the gravitational and thermal energy (Case 1) or between the gravitational, turbulent, and thermal energies (Case 2) while for supersonic flows, the possible balance is between the gravitational and turbulent energy (Case 3). This solution corresponds to three possible configurations for the energy balance. The result confirms the solution ϱ(ℓ) = ℓ −2 found in the previous papers. Making use of the Eulerian virial theorem at an arbitrary scale, far from the cloud core, we derive an equation for the density profile and solve it in approximate way. In this work, we apply virial analysis to the model of self-gravitating turbulent cloud ensembles introduced by Donkov & Stefanov in two previous papers, clarifying some aspects of turbulence and extending the model to account not only for supersonic flows but for trans- and subsonic ones as well.
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