Final period ratio of GJ 163’s inner planets as a function of the dissipation balance between both planets (Δt₂/κΔt₁). We fix M₁ = 100° (left), 140° (right), and compare the results obtained with Δt₁ = 10⁷, 10⁶, 10⁵, and 10⁴ s (top) with an integration time of respectively 0.1, 1, 10, and 100 Myr, which roughly corresponds to 10 Gyr for a realistic value of Δt₁ (100 s). We also compare these results with integrations taking into account the third planet that has been detected in the system (bottom; see Bonfils et al. 2013). For this last comparison we use Δt₁ = 10⁷ s. We observe only small variations when changing the timescale of the dissipation (Δt₁) and no systematic trend. The third planet also does not seem to have a strong effect. The vertical black lines mark the range of Δt₂/κΔt₁ that may conduct to internal circulation according to our analytical model. The green lines highlight the same range obtained with the simulations. The lower bound (solid green line) is at Δt₂/κΔt₁ = 260 in the case M₁ = 100° (left) and 240 for M₁ = 140° (right). It does not vary much between the experiments and it is close to the analytical value (300). The upper bound (dashed green line) is at 750 (left) and 900 (right) while the analytical value is 1450. The difference between the numerical results, and between the numerical and analytical values can easily be explained (see Sect. 4.1.3).