Adapting a gas accretion scenario for migrating planets in fargo3d

FARGO3D has been proposed to investigate numerically the gravitational interaction of a planet with the gas disc, providing original outcomes. However, FARGO3D does not consider the gas accretion of the planet which may affect the planetary migration process. Thus, the aim of this paper is to include a model for the gas accretion in the FARGO3D code. For this task, we choose Russell's scheme, which is an adaptation of Kley's model for the gas accretion on to migrating planets. Initially, we study the influence of the gas accretion on to the planet on type II migration of giant planets. For this purpose, we follow the evolution of planets in a 2D locally isothermal disc with a specific accretion rate and different values of viscosity and planetary mass considering two scenarios. In the first, the gas mass is withdrawn from the disc and is not added to the planet. In the second, the planets migrate, while their masses grow due to the gas accretion. Then, we extend our study to estimate the time needed for a low-mass planet to open a gap in the gas disc and compare its value with the characteristic time of type I migration.