Long term planet migration simulations demonstrate an attractor for gas giant planets in 1-10 AU range

Long term planet migration simulations demonstrate an attractor for gas giant planets in 1-10 AU range

The conventional picture of giant planet migration in protoplanetary discs involves an inexorable inspiral towards the star through the process of Type II migration, thus providing a popular scenario for the creation of hot Jupiters. In Scardoni et al 2022[1] we explored very long term (0.6M planetary orbits)[2] simulations of Type II migration in the limit that the planet is relatively massive compared with the local disc and uncovered the fact that there are situations where planets migrate outwards or else stall. The reason is that in this (`light disc’) limit, the planet migration time is relatively long compared with the viscous flow time in the disc and there is therefore time for the disc to achieve a condition close to a steady state interior to the planet. In this steady state the disc edge interior to the planet self-adjusts to deliver a (positive) torque on the planet which depends only on the accretion rate through the disc, irrespective of the thermal properties of the disc. On the other hand, the disc exterior to the planet is not in a steady state and therefore the (negative) torque that it imposes on the planet depends on the structure of the inner edge of the exterior disc, being smaller in the case of the wide and deep gaps associated with colder (geometrically thinner) discs.

In practice this means that when planets enter the inner disc (which is geometrically thinner) the balance of torques shifts towards there being a net positive torque on the planet and, in consequence, outward migration. The change in sign of planet migration as a function of the gap width parameter, K (itself a function of the geometric aspect ratio) is shown in the left hand panel below, while the right hand panel depicts how this sign change would affect planet migration over timescales of Myr.  It is notable that this effect is expected to drive planetary migration towards the location in the disc where the torques from the inner and outer disc are in balance. The location of this attractor is expected to be at a few A.U. from the star, depending on the disc temperature.

While future calculations will be required to discover whether this effect persists in 3D simulations, these results have profound consequences for the orbital architecture of exoplanetary systems, explaining the prevalence of gas giants at a few A.U. from their host stars. A corollary of this result is that hot Jupiters would not be expected to form via disc mediated migration but would instead likely result from planet scattering at a later evolutionary stage.

[1] MNRAS 514,5478

[2] These calculations made use of the CSD3 and DIaL services