https://doi.org/10.1140/epjp/s13360-024-05361-2
Regular Article
On the radius spectrum of solid grains settling in polytropic protoplanets
1
Department of Mathematics, University of Rajshahi, 6205, Rajshahi, Bangladesh
2
Department of Mathematics, Mawlana Bhashani Science and Technology University, 1902, Tangail, Bangladesh
Received:
19
April
2024
Accepted:
11
June
2024
Published online:
10
July
2024
The radius spectrum of solid grains settling is investigated through the process of coagulation inside some protoplanets with a mass range 0.3–10 Jupiter masses formed by disk instability assuming that the polytropic law governs their density distribution. With this law, the initial configurations of thermodynamic and other variables inside the polytropic protoplanets are estimated. The growth of the grains inside the polytropic protoplanets, having different initial sizes 
, is investigated by the process of cold welding with the attained distribution of necessary variables. The density distributions given by the polytropic indices 
and 
appear to be closer to reality. The results came out through our investigation indicate that the growth of the grains depends on the initial states of the polytropic protoplanets (PPs) as well as on their masses, and all the grains with the assumed initial sizes get nearly similar distributions in the core region of the corresponding PPs with respective masses.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
