Distribution of thermodynamic variables inside extra-solar protoplanets formed via disk instability

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

“…It can be observed from Fig. 6 that the protoplanet with mass 10 M J is rarer than the protoplanet with masses 5 M J and 7 M J and the protoplanet with mass 0.3 M J (Saturn) can be found to be denser than the protoplanets with masses 1 M J and 3 M J , which strongly support the findings of Senthilkumar and Paul (2012), Paul and Bhattacharjee (2013) and Paul et al (2013). From the figures (Figs.…”

“…Again, it can be observed from Fig. 4 that the central pressure of a protoplanet depends on its mass and such a pressure increases with increasing mass of the protoplanets except the protoplanet with mass 10 M J , which can be found to be in excellent accordance with the corresponding finding in Senthilkumar and Paul (2012), Paul and Bhattacharjee (2013), . The pressure distributions obtained in the study with n = 1 and 1.5 can be found to compare well with the results presented in Senthilkumar and Paul (2012) and .…”

“…There is variation of parameters due to variation in density along with gravitational stratification, as is expected for initially formed protoplanets by disk instability. However, the configuration for density distribution obtained in this study for the polytropic protoplanets with considered masses for the two indices n = 1 and n = 1.5 compares fairly well with the ones obtained in the investigations of Senthilkumar and Paul (2012), Paul and Bhattacharjee (2013) and . But it is pertinent to pin point out here that our obtained density distribution significantly differs with the ones presented in the investigation of Helled and Schubert (2008).…”

“…Boss (1998Boss ( , 2002Boss ( , 2007, in his studies, assumed initial protoplanets to be radiative equilibrium, while Helled and Bodenheimer (2011) found the protoplanets to be fully convective with thin radiative outer zones, which is consistent with Bodenheimer et al (1980). 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.…”

“…Again due to the similar region mentioned above, they have not been included. However, our presented temperature profiles that come out through calculations for all the considered values of the polytropic index n inside all the polytropes can be found to compare well with the ones presented in Helled and Schubert (2008), Senthilkumar and Paul (2012), Paul and Bhattacharjee (2013) and . Our calculated pressure profiles only for the protoplanetary masses 1 M J and 5 M J for different values of the polytropic index n are presented in Fig.…”