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The formation of multiple close-in low-mass exoplanets is still a mystery.The challenge is to build a system wherein the outermost planet is beyond 0.2AU from the star. Here we investigate how the prescription for type I planetmigration affects the ability to trap multiple planets in a resonant chain nearthe inner edge of the protostellar disc. A sharp edge modelled as a hyperbolictangent function coupled with supersonic corrections to the classical type Imigration torques results in the innermost planets being pushed inside thecavity through resonant interaction with farther planets because migration isstarward at slightly supersonic eccentricities. Planets below a few Earthmasses are generally trapped in a resonant chain with the outermost planet nearthe disc edge, but long-term stability is not guaranteed. For more massiveplanets the migration is so fast that the eccentricity of the innermostresonant pair is excited to highly supersonic levels due to decreased dampingon the innermost planet as it is pushed inside the cavity; collisionsfrequently occur and the system consists one or two intermediate-mass planetsresiding closer to the star than the disc's inner edge. We found a neat pileupof resonant planets outside the disc edge only if the corotation torque doesnot rapidly diminish at high eccentricity. We call for detailed studies onplanet migration near the disc's inner edge, which is still uncertain, and foran improved understanding of eccentricity damping and disc torques in thesupersonic regime.

Trapping low-mass planets at the inner edge of the protostellar disc