Global models of planetary system formation in radiatively-inefficient protoplanetary discs

We present the results of N-body simulations of planetary system formation in radiatively-inefficient disc models, where positive corotation torques may counter the rapid inward migration of low-mass planets driven by Lindblad torques. The aim of this work is to examine the nature of planetary systems that arise from oligarchic growth in such discs. We adapt the commonly used Mercury-6 symplectic integrator by including simple prescriptions for planetary migration (types I and II), planetary atmospheres that enhance the probability of planetesimal accretion by protoplanets, gas accretion on to forming planetary cores, and gas disc dispersal. We perform a suite of simulations for a variety of disc models with power-law surface density and temperature profiles, with a focus on models in which unsaturated corotation torques can drive outward migration of protoplanets. In some models, we account for the quenching of corotation torques which arises when planetary orbits become eccentric. Approximately half of our simulations lead to the successful formation of gas giant planets with a broad range of masses and semimajor-axes. Giant planetary masses range from being approximately equal to that of Saturn up to approximately twice that of Jupiter. The semimajor-axes of these range from being ∼0.2 au up to ∼75 au, with disc models that drive stronger outward migration favouring the formation of longer period giant planets. Out of a total of 20 giant planets being formed in our simulation suite, we obtain three systems that contain two giants. No super-Earth or Neptune-mass planets were present in the final stages of our simulations, in contrast to the large abundance of such objects being discovered in observation surveys. This result arises because of rapid inward migration suffered by massive planetary cores that form early in the disc lifetime (for which the corotation torques saturate), combined with gas accretion on to massive cores which leads them to become gas giants. Numerous low-mass planets are formed and survive in the simulations, with masses ranging from a few tenths of an Earth mass up to ∼3 Earth masses. Simulations in which the quenching of corotation torques for planets on modestly eccentric orbits was included failed to produce any giant planets, apparently because Lindblad torques induce rapid inward migration of planetary cores in these systems. We conclude that convergent migration induced by corotation torques operating during planetary formation can enhance the growth rate of planetary cores, but these often migrate into the central star because corotation torques saturate. Outward migration of planetary cores of modest mass can lead to the formation of gas giant planets at large distances from the central star, similar to those observed recently through direct imaging surveys. The excitation of planetary eccentricities through planet–planet scattering during oligarchic growth may quench the effects of corotation torques, however, such that inward migration is driven by Lindblad torques.