SAXO+ upgrade: system choices and numerical simulations

SPHERE+ is a proposed upgrade of the SPHERE instrument on the ESO's Very Large Telescope which aims at improving detection and characterization capabilities of young giant planets by means of a second-stage AO system, including dedicated wavefront sensor and deformable mirror to remove the residual wavefront errors left by the primary AO loop. This paper is focused on the numerical simulations of the second stage (SAXO+) and conclude on the impact of the main AO parameters used to build the design strategy.