Top panels: evolution of the normalised torque, along with the smoothing function, over the integration (left) for a planet with q = 0.003 in a low-viscosity disc (α = 10⁻⁴) with Σ₀ = 10⁻⁴, and h = 0.05. Distribution of the azimuthally averaged gas-disc density around the planet’s initial location at three different integration times (right). Bottom panels: evolution of the semi-major axis (left) and eccentricity (right) of the planet during the integration. The vertical lines mark the times when the torque changes sign, indicating a reversal in the direction of the planet’s migration. Time is expressed in units of t₀, the orbital period of the planet at r = r₀.