Gravitational settling time of solid grains in gaseous protoplanets

Solving protoplanetary structure equations using Adomian decomposition method

“…An initial protoplanet having a cold origin definitely will have a low surface temperature [14,43]. Thus, in the first approximation, the surface temperature can be set to zero [5,15,16]. Further, the protoplanetary atmospheric mass is just an infinitesimal fraction of its total mass [44].…”

“…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.…”

“…In this connection, it is worth noting that the protoplanets can give birth to Earth-mass or more massive cores by grain growth and sedimentation, and be tidally disrupted, potentially providing a 'new' pathway to forming all kinds of planets [31]. The grain growth and sedimentation depend, among others, on the primordial internal structure of a protoplanet where the material is found to be distributed due to gravitational stratification of other parameters [16,27]. Then some mechanisms are needed for the planetary core formation [27].…”

“…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.…”