Grain Sedimentation Time in a Gaseous Protoplanet

Implementation of polytropic method to study initial structures of gas giant protoplanets

“…The choice of the mass range is because it covers most of the observed mass range of extrasolar giant planets (Helled and Schubert, 2008). Following Paul et al (2011), we assume that the object, during its initial stage, contracts quasi-statically (DeCampli and Cameron, 1979;Bodenheimer et al, 1980), which is in a steady state of quasi-static equilibrium, where the gravitational contraction of the gas is only the source of energy. The structure of the object during its initial stage then can be given by the polytropic equation of state (Paul et al, 2011)…”

“…Paul et al (2012a,b) neglected the thin outer radiative zone and assumed such protoplanets to be fully convective, which can be found to be consistent with (Helled et al, 2005), whereas Paul and Bhattacharjee (2013) and conducted their investigations assuming the protoplanets to be in conductive-radiative equilibrium. In their investigation Paul et al (2011) investigated solid grain settling time inside a polytropic protoplanet determining its structure, where they concluded that the segregation time scale obtained by the polytropic method is quite realistic.…”

Dust grain growth and settling in initial gaseous giant protoplanets

“…It is noted that Paul et al (2011) investigated grain growth and grain sedimentation time inside a giant gaseous protoplanet of mass M = 2 × 10 30 g and radius R = 3 × 10 12 cm assuming the gas blob of the protoplanet to be polytropic taking into account the same set of equations presented in this section.…”

“…Following Podolak (2003), computed thermal evaluation of a gaseous clump formed by the disk instability and examined how silicate grain growth and settling can proceed with time against convective motion, where they neglected two important effects, namely radiative heating by the surrounding medium and the contraction of the gas near the center by the increased pressure due to the core itself. The settling process was also investigated, in details, by several authors (see, e.g., McCrea and Williams, 1965;Williams and Handbury, 1974;Helled and Schubert, 2008;Paul et al, 2011). All the investigations conclude that a solid core inside the protoplanets can form by sedimentation of dust grains in a reasonable short period of time.…”

“…Thus the segregation time obtained by both the investigations may be somewhat different from reality. In their calculations Boss (1998b) assumed the protoplanet to be in radiative equilibrium, whereas Helled and Schubert (2008) and found the gas blob to be fully convective with a thin outer radiative zone, while Paul et al (2011) investigated the problem with a simple polytropic method.…”