Segregation of heavy elements in an initial protoplanet

Solving protoplanetary structure equations using Adomian decomposition method

“…It is relevant to note here that the mass range covers the majority of the detected exoplanets [13]. The protoplanets, during their initial phase, contract quasi-statically [17,30,42]. In this phase, following the mentioned three groups of investigators, we also assume that such a protoplanet is in a steady state in which the Clausius-Clapeyron equation of state holds well, and the source of energy is only the gravitational contraction of gases.…”

“…Such a GI can lead to dense and self-gravitating clumps, which might collapse and contract to form gas giant protoplanets [6,7]. The process of planetary formation through the GI has also been discussed by various other authors [8,9,10,11,12,13,14,15,16,17]. Although some questions arise as to whether stable protoplanets could be formed or not by the GI, the mechanism is believed to be a promising route to the rapid formation of gas giants [5,18,19,20,21,22,23].…”

“…Although some questions arise as to whether stable protoplanets could be formed or not by the GI, the mechanism is believed to be a promising route to the rapid formation of gas giants [5,18,19,20,21,22,23]. However, the primordial structures of the protoplanets, the precursor to planet formation, formed via GI are still unknown, and diverse numerical models report different primordial structures [5,13,15,16,17,24,25,26,27]. For example, simulations due to Boss [28] foresee less dense and colder objects than those of Mayer et al [9,19] and the simulations carried out by the mentioned investigators reported denser and warmer initial profiles over the ones used in the simulations due to DeCampli and Cameron [29] and Bodenheimer et al [30], whereas Paul et al [5,17] found denser protoplanets than that of Helled and Schubert [13], but having similar central temperature profiles.…”

“…Then some mechanisms are needed for the planetary core formation [27]. The obvious mechanism for sedimentation is that the dust grains present in the protoplanets, being heavier than the gas, will grow up through hit-and-stick or other mechanisms and will settle down towards the centre of the protoplanet under its gravitational field [14,15,16,17,27,32]. Therefore, the primordial internal structure of a protoplanet can be an important part of planetary evolution.…”

An effective method in investigating structures of polytropic protoplanets formed via gravitational instability

“…In their investigations, Paul et al [36] , [37] considered such a protoplanet to be convective fully, which is consistent with that found in [38] . On the other hand, Paul and Bhattacharjee [39] and Paul et al [4] , [40] , [41] performed their numerical experiments considering the conductive-radiative heat transport. Paul et al [42] , [43] also used a polytropic equation of state, where they concluded that the polytropic protoplanets (PPs) with polytropic index as well as , the distributions of thermodynamic and other variables are nearer to reality.…”