Dust grain growth and settling in initial gaseous giant protoplanets

Abstract

Dust grain growth and settling time inside initial gaseous giant protoplanets in the mass range 0.3 to 5 Jovian masses, formed by gravitational instability, have been investigated. We have determined the distribution of thermodynamic and physical variables inside the protoplanets solving the structure equations assuming their gas blobs to be fully convective and with this distribution we have calculated growth and settling time of grains with different initial sizes (10 −2 cm ≤ r 0 ≤ 1 cm). The results of our calculations are found to be in good agreement with those obtained by different approaches.

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

“…Eq. (5) also validates that at the surface of the protoplanets, i.e., at r ¼ R, MðrÞ ¼ M. Further, initially formed protoplanets having fairly cold centre must have reasonably low surface temperature [12]. Hence, the surface temperature, in the first approximation, can be set to zero.…”

“…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].…”

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

“…Thus, we need approximate boundary conditions and that can be attained through Frobenius method. As in Paul et al [12], the following approximate surface boundary conditions are adopted:…”

“…It is noticeable that planetary evolutions are highly dependent on the initial configurations of the protoplanets. Unfortunately, so far, there does not exist a single model with its definite initial structure and various models in this regard report different initial profiles [9,10,11,12]. It is of interest to note here that an analytic solution of the system of equations used in configuring structure of such a protoplanet is not possible [12] without any drastic assumptions.…”