The structure of gas-accreting protoplanets and the condition of the critical core mass

TL;DR

This paper investigates the internal structure of gas-accreting protoplanets using polytropic models to understand the factors determining the critical core mass that triggers runaway gas accretion, considering different boundary conditions and envelope structures.

Contribution

It introduces a polytropic framework to analyze the critical core mass, revealing how boundary conditions and envelope properties influence the onset of runaway accretion.

Findings

Protoplanets resemble red giant structures with centrally-condensed envelopes.

Critical core mass depends on polytropic index and boundary conditions, occurring at different envelope locations.

The roles of radiative and convective zones are clarified in the context of critical core mass.

Abstract

In the core accretion model for the formation of gas giant planets, runaway gas accretion onto a core is the primary requisite, triggered when the core mass reaches a critical value. The recently revealed wide diversity of the extrasolar giant planets suggests the necessity to further the understanding of the conditions resulting in the critical core mass that initiates runaway accretion. We study the internal structure of protoplanets under hydrostatic and thermal equilibria represented in terms of a polytropic equation of state to investigate what factors determine and affect the critical core mass. We find that the protoplanets, embedded in protoplanetary disks, have the same configuration as red giants, characterized by the envelope of the centrally-condensed type solution. Applying the theory of stellar structure with homology invariants, we demonstrate that there are three types of criteria for the critical core mass depending on the stiffness of polytrope and the nature of outer boundary condition. For the stiff polytropes of index $N \le 3$ with the Bondi radius as the outer boundary, the criterion governing the critical core mass occurs at the surface. For stiff polytropes with the Hill outer boundary and for soft polytropes of $N>3$, this criterion acts at the bottom of gaseous envelope. Further, we elucidate the roles and effects of coexistent radiative and convective zones in the envelope of critical core mass. Based on the results, we discuss the relevance of Bondi and Hill surface conditions and explore the parameter dependences of critical core mass.