Origin and evolution of the orbits and spins of the giant planets in the GJ 1148 system

Abstract

GJ 1148 is an M-dwarf star with two Saturn mass giant planets orbiting around it. Dynamical analysis shows that the two planets are well separated with an orbital period ratio of around 13, and both planets have eccentricities of around 0.375 at the current epoch. A likely scenario for producing the architecture of the GJ 1148 system is planet-planet scattering. We firstly perform scattering experiments with a hypothetical third planet of 0.1 MJ (Jupiter’s mass) in the original GJ 1148 system, and with initial orbital separations of 3.5, 4, and 4.5 mutual Hill radii Rm,H. The majority of scattering outcomes are planet-planet collisions, followed by planet ejections, and the removal of the planet due to its distance to the star smaller than a critical value of 0.02 AU. We find that only the post-ejection two-planet systems have similar properties to GJ 1148 system. In addition, initial three-planet systems, in which the innermost planet has a semi-major axis around 0.21 AU, can reproduce the semi-major axis of the inner planet GJ 1148 b. To reproduce the semi-major axis of GJ 1148 c, a wider initial orbital separation of 4.5 Rm,H is preferred. When we assume the third planet has a mass same as GJ 1148 c of 0.227 MJ, the optimal initial semi-major axis for the initial innermost planet move to around 0.29 AU. We study the spin evolution of GJ 1148 b with and without including the GJ 1148 c, using the constant Q and constant ∆t tidal model. We find that the spin rate of GJ 1148 is not significantly altered due to the secular variation of eccentricity because the secular timescale is much smaller than the spin-down timescale. To explore the influence of the ratio between the secular timescale and the spin-down timescale, we systematically move both planets closer to the star by multiplying the semi-major axes by a factor β. We find that as β decreases, the spin evolution is more affected by the eccentricity variation. The planet can reach the synchronous state for a short time at β around 0.12 in the constant Q tidal model and β around 0.15 in the constant ∆t model. When β becomes even smaller, we observe significant tidal decay of eccentricity and semimajor axis. Anderson et al. (2020) studied the evolution of warm Jupiters under the scenario of in situ scattering with the N-body code REBOUND. We try to reproduce their results for the initially three-planet systems with the SyMBA-GR and REBOUND. We find that our simulations with two different integrators give very similar results statistically. Surprisingly, the two-planet systems in our simulations arise from planet-planet collisions or planet ejections, while the two-planet systems arise exclusively from planet-planet collisions in Anderson et al. (2020). Stability test shows that more than half of our two-planet systems resulting from ejection are stable. Thus, our simulations suggest that the outcomes shown in Anderson et al. (2020) may not be correct.