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On the Issue of the Gravitational Instability of the Solar Protoplanetary Disk

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Abstract

The gravitational instability of a homogeneous isotropic infinite gravitating gaseous medium is investigated in order to study the physical processes that take place during the formation of the solar planetary system. The analytical and numerical solutions of the motion equations of such a medium are considered in two approximations: cold gas and gas at a finite temperature. The real solutions describing the behavior of both wave density disturbances of a homogeneous medium and single disturbances are obtained. Waves of gravitational instability whose amplitude grows exponentially and whose highs and lows, as well as their nodal points, retain their positions in space follow the basic laws of Jean’s model. The authors interpret this wave of instability as an analogue of protoplanetary rings, which can be formed in protoplanetary disks. According to the numerical calculation results, the reaction of a homogeneous gravitating medium to the single initial perturbation of its density is significantly different from the laws of Jean’s model. The instability localized in single initial perturbations extends to the region λ < λJ, although in this case the growth of the perturbation density is considerably less than for λ > λJ. It is discovered that the gravitational instabilities in the region λ > λJ suppress sound. It is shown that, without taking into account the rotation of the Sun’s protoplanetary disk medium, its critical density in the event of a large-scale gravitational instability is about four orders of magnitude smaller than the critical density in accordance with the theory of planet formation by the accumulation of solids and particles.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia

    G. V. Dolgoleva, M. S. Legkostupov & L. A. Pliner

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  1. G. V. Dolgoleva
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  2. M. S. Legkostupov
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  3. L. A. Pliner
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Correspondence to G. V. Dolgoleva.

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Original Russian Text © G.V. Dolgoleva, M.S. Legkostupov, L.A. Pliner, 2018, published in Matematicheskoe Modelirovanie, 2018, Vol. 30, No. 2, pp. 130–148.

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Dolgoleva, G.V., Legkostupov, M.S. & Pliner, L.A. On the Issue of the Gravitational Instability of the Solar Protoplanetary Disk. Math Models Comput Simul 10, 616–628 (2018). https://doi.org/10.1134/S2070048218050058

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  • DOI: https://doi.org/10.1134/S2070048218050058

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