Acoustic waves in a turbulent giant molecular cloud taking into account the correlations of gravitational field

Abstract

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 (cid:28)eld that has zero (cid:28)rst moment and nonzero second moment in equilibrium. It is shown that, in addition to the Reynolds turbulent stress tensor, the momentum (cid:29)ow tensor includes the second correlation moment of the gravitational (cid:28)eld 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 ∂ t (cid:104) g i g k (cid:105) = ( ∂ k v i + ∂ i v k − 2 ∂ l v l δ ik ) (cid:10) g 2 (cid:11) 0 / 6 , where ∂ t ant ∂ i are the time and spatial derivatives, v i is the mass velocity component, (cid:10) g 2 (cid:11) 0 is the square of a self-consistent gravitational (cid:28)eld 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 (cid:10) v 2 (cid:11) 0 − (cid:10) g 2 (cid:11) 0 / (8 πGρ 0 ) ≥ 0 , where (cid:10) v 2 (cid:11) 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 (cid:28)eld energy density. It is shown that the thermal motion does not a(cid:27)ect 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.