http://arxiv.org/abs/2203.04005
In the present work we apply virial analysis to the model of self-gravitating turbulent cloud ensembles introduced by Donkov & Stefanov (2018) and extended by Donkov & Stefanov (2019). Using 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. The result confirms the solution $\varrho(\ell)=\ell^{-2}$ found in the previous papers. At scales far from the core, we obtain virial equilibrium between i) gravitational energy and accretion kinetic energy, or ii) between gravitational energy and accretion plus turbulent kinetic energy per unit mass — depending on the adopted scaling relation for the turbulent velocity. Thus the obtained solution for density profile is dynamically stable and shall be observable. 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. However, we obtain the qualitative result that gas near the core is not virialized and its state can be characterized as marginally bound since the total energy of the fluid element is close to zero.
S. Donkov, I. Stefanov, T. Veltchev, et. al.
Wed, 9 Mar 22
64/68
Comments: 9 pages, no figures; submitted to MNRAS
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