Capture and migration of Jupiter and Saturn in mean motion resonance in a gaseous protoplanetary disc

We study the dynamical evolution of Jupiter and Saturn embedded in a gaseous, solar nebula-type disc by means of hydrodynamics simulations with the FARGO2D1D code. We study the evolution for different initial separations of the planets' orbits, Δa_SJ, to investigate whether they become captured in mean motion resonance (MMR) and the direction of the subsequent migration of the planet (inwards or outwards). We also provide an assessment of the planet's orbital dynamics at different epochs of Saturn's growth. We find that the evolution of initially compact orbital configurations is dependent on the value of Δa_SJ. This implies that an evolution as that proposed in the Grand Tack model depends on the precise initial orbits of Jupiter and Saturn and on the time-scales for their formation. Capture in the 1:2 MMR and inward or (nearly) stalled migration are highly favoured. Within its limits, our work suggests that the reversed migration, associated with the resonance capture of Jupiter and Saturn, may be a low-probability evolutionary scenario, so that other planetary systems with giant planets are not expected to have experienced a Grand Tack-like evolutionary path.