Scattering of Giant Planets Around M-dwarf: The Implication for the Origin of the Hierarchical and Eccentric Two-planet System like GJ 1148

GJ 1148 is an M-dwarf star, which has two well-separated Saturn mass planets with an orbital period ratio of around 13 and eccentricities of around 0.375 at the current epoch. A plausible scenario for producing the orbital architecture of the GJ 1148 system is planet-planet scattering. To test this scenario, we perform scattering experiments, assuming the third planet of 0.1 M_J (Jupiter’s mass) in the initial GJ 1148 system with initial orbital separations set to 3.5, 4, and 4.5 mutual Hill radii R_m,H respectively and initial semi-major axis of the innermost planet a_i,1 in the range of 0.10-0.50 AU. The majority of scattering results in planet-planet collisions, followed by planet ejections, and planet removals as its distance to the star are smaller than a critical value of 0.02 AU. Among them, only the post-ejection two-planet systems have similar properties to the GJ 1148 system, and when a_i,1 is around 0.21 AU, the semi-major axis of the inner planet GJ 1148 b can be reproduced. We further perform simulations with a_i,1 in a narrower range between 0.16 and 0.30 AU, and found one system with similar orbital properties to the GJ 1148 system. Therefore, the simulation results suggest that the GJ 1148 system may have lost a giant planet. The two-sample Kolmogorov–Smirnov (KS) test on simulations with and without GR apsidal precession shows that it does not affect the ejection outcomes. When setting the mass of the third planet to 0.227 MJ of GJ1148 c, the optimal a_i,1 move to about 0.29 AU.