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Journal of Physical Studies 25(1), Article 1903 [4 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.1903 ACOUSTIC WAVES IN A TURBULENT GIANT MOLECULAR CLOUD TAKING INTO ACCOUNT THE CORRELATIONS OF GRAVITATIONAL FIELD
A. A. Stupka1
1Oles Honchar Dnipro National University,
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A hydrodynamic model for the description of small acoustic oscillations in a turbulent giant molecular cloud is constructed by averaging the Euler equation over Reynolds, taking into account the turbulence of a self-consistent gravitational field that has zero first moment and nonzero second moment in equilibrium. It is shown that, in addition to the Reynolds turbulent stress tensor, the momentum flow tensor includes the second correlation moment of the gravitational field strength, both potential and vortex, for which the time equation is obtained from the Einstein equations in non-relativistic approximation. After linearization, this equation is $ \partial_t \left\langle {g_i g_k } \right\rangle = \left( {\partial _k v_i + \partial _i v_k - 2\partial _l v_l δ _{ik} } \right)\left\langle {g^2 } \right\rangle_0 /6 ,$ where $\partial_t$ ant $\partial_i$ are the time and spatial derivatives, $v_i$ is the mass velocity component, $\left\langle {g^2 } \right\rangle_0$ is the square of a self-consistent gravitational field strength equilibrium value. Two transverse and longitudinal branches of acoustic oscillations in a homogeneous isotropic cloud are obtained. Zeroing of the transverse oscillations velocity gives a limiting condition for the stability of the giant molecular cloud $\left\langle {v^2 } \right\rangle_0 - \left\langle {g^2 } \right\rangle _0 /(8π Gρ _0) \geq 0,$ where $\left\langle {v^2 } \right\rangle_0$ is the mean square turbulent velocity, $G$ is the gravitational constant, $ρ_0$ is the equilibrium density value. Thus, the doubled energy density of the turbulent motion must be greater than the gravitational field energy density. It is shown that the thermal motion does not affect the stability of the system. For the spherical shape of the cloud, the radius of the giant molecular cloud is obtained, which is consistent with observational data.
Key words: giant molecular cloud, Reynolds turbulent stress tensor, second correlation moment of gravitational field strength, branches of acoustic oscillations, stability condition.
