How initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non viscous SPH simulations

TL;DR

This study uses 2D inviscid SPH simulations to analyze how initial and boundary conditions influence protoplanet migration in turbulent, sub-Keplerian accretion discs, revealing migration timescales vary significantly with planetary mass and disc kinematics.

Contribution

It provides new insights into protoplanet migration timescales under different disc kinematic conditions using SPH simulations, highlighting the impact of turbulence and boundary effects.

Findings

Earth-like planets migrate in a few orbital periods in sub-Keplerian discs.

Jupiter-like planets require about 10,000 orbital periods to halve their orbit.

Migration timescales depend strongly on the planet's position relative to the disc's shock region.

Abstract

Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, inviscid 2D simulations are performed, using the SPH method, to study the migration of one protoplanet, to evaluate the effectiveness of the accretion disc in the protoplanet dragging towards the central star, as a function of the mass of the planet itself, of disc tangential kinematics. To this purpose, the SPH scheme is considered suitable to study the roles of turbulence, kinematic and boundary conditions, due to its intrinsic advective turbulence, especially in 2D and in 3D codes. Simulations are performed both in disc sub-Keplerian and in Keplerian kinematic conditions as a parameter study of protoplanetary migration if moderate and consistent deviations from Keplerian Kinematics occur. Our results show migration times of a few orbital periods for Earth-like planets in sub-Keplerian conditions, while for Jupiter-like planets estimates give that about $10^4$ orbital periods are needed to half the orbital size. Timescales of planet migration are strongly dependent on the relative position of the planet with respect to the shock region near the centrifugal barrier of the disc flow.