The radius spectrum of solid grains settling in gaseous giant protoplanets

On the implementation of novel RKARMS(4,4) algorithm to study the structures of initial extrasolar giant protoplanets

“…As in Paul et al [1,12], the model of the present study undertakes a spherical giant gaseous protoplanet having a solar composition with mass ranging from 0.3 to 10 M J (1M J ¼ 1.8986Â10 30 gm). The reasoning abaft such a consideration of the range of mass is that it covers the majority of the detected mass-range of the giant extrasolar planets as well as the giant planets of our solar system [10].…”

“…The assumptions can be found to be supported by DeCampli and Cameron [9] and Bodenheimer et al [26]. Now, if the energy is assumed to be transferred by the process of convection, the structure of such an object can be specified by means of the following system of equations as under [1]:…”

“…(4) together with the help of the above transformations, Eqs. (1), (2), and (3) can, respectively, be brought to the following forms [1,12]:…”

“…The discovery of extrasolar planets has intensified interest in them, and a large volume of research works on the physical conditions prevailing inside such planets has been conducted both outside and inside our own solar system [2,3]. There are two feasible end mechanisms in the literature for explaining the evolution process of such planets, namely (i) core accretion and (ii) disk instability [1]. In the first scenario, the formation of gas giant planets or simply gas giants starts with core formation followed by gas accretion [4,5], whereas in the disk instability scenario, the segregation occurs prior to the core formation.…”

Solving protoplanetary structure equations using Adomian decomposition method

“…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.…”