Geodesic
On the issue of gravitational instability of the Sun protoplanetary disk
Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 130-148

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With the purpose of study of physical processes that take place at formation of the planetary systems of the Sun, gravitational instability of a homogeneous isotropic infinite gravitating gaseous medium was investigated. There were considered the analytical and numerical solutions of the motion equations of such medium in two approximations: "cold" gas and gas at the finite temperature. There were obtained real solutions, describing the behavior of homogeneous medium wave disturbances, and single disturbances. Waves of gravitational instability, the amplitude of which is growing exponentially, and the highs and lows of this wave, as well as its nodal points, retain its position in space, follow the basic laws of Jeans model. The authors interpret this wave of instability as an analogue protoplanetary rings that can be formed in protoplanetary disks. According to the results of numerical calculations homogeneous gravitating medium reaction to the initial single perturbation of its density is significantly different from the laws of Jeans model. Instability localized initial perturbations extends to the region $\lambda\lambda_J$, although in this case the growth of density perturbations is considerably less than when $\lambda>\lambda_J$. It was found that the gravitational instability in the region $\lambda>\lambda_J$ suppress sound. It is shown that without taking into account the rotation of the medium of the Sun protoplanetary disk its critical density in the event of a large-scale gravitational instability to four orders of magnitude is less than the critical density, obtained in the framework of the theory of formation of planets by accumulation of solids and particles.
Keywords: homogeneous isotropic gas medium, gravitational instability, dispersion equation, sound wave, wave of gravitational instability. 
@article{MM_2018_30_2_a8,
     author = {G. V. Dolgoleva and M. S. Legkostupov and L. A. Pliner},
     title = {On the issue of gravitational instability of the {Sun} protoplanetary disk},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {130--148},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_2_a8/}
}
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G. V. Dolgoleva; M. S. Legkostupov; L. A. Pliner. On the issue of gravitational instability of the Sun protoplanetary disk. Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 130-148. http://geodesic.mathdoc.fr/item/MM_2018_30_2_a8/