Type I migration in radiatively efficient discs

We study Type I migration of a planet in a radiatively efficient disc using global two-dimensional hydrodynamic simulations. The large positive corotation torque is exerted on a planet by an adiabatic disc at early times when the disc has the steep negative entropy gradient. The gas on the horseshoe orbit of the planet is compressed adiabatically during the change of the orbit from the slow orbit to the fast orbit, increasing its density and exerting the positive torque on the planet. The planet would migrate outward in the adiabatic disc before saturation sets in. We further study the effect of energy dissipation by radiation on Type I migration of the planet. The corotation torque decreases when the energy dissipates effectively because the density of the gas on the horseshoe orbit does not increase by the compression compared with the gas of the adiabatic disc. The total torque is mainly determined by the negative Lindblad torque and becomes negative. The planet migrates inwards towards the central star in the radiatively efficient disc. The migration velocity is dependent on the radiative efficiency and is greatly reduced if the radiative cooling works inefficiently.