We determine an expression for the Type I planet migration torque involving a locally isothermal disk , with moderate turbulent viscosity ( 5 \times 10 ^ { -4 } \lesssim \alpha \lesssim 0.05 ) , based on three-dimensional nonlinear hydrodynamical simulations .
The radial gradients ( in a dimensionless logarithmic form ) of density and temperature are assumed to be constant near the planet .
We find that the torque is roughly equally sensitive to the surface density and temperature radial gradients .
Both gradients contribute to inward migration when they are negative .
Our results indicate that two-dimensional calculations with a smoothed planet potential , used to account for the effects of the third dimension , do not accurately determine the effects of density and temperature gradients on the three-dimensional torque .
The results suggest that substantially slowing or stopping planet migration by means of changes in disk opacity or shadowing is difficult and appears unlikely for a disk that is locally isothermal .
The scalings of the torque and torque density with planet mass and gas sound speed follow the expectations of linear theory .
We also determine an improved formula for the torque density distribution that can be used in one-dimensional long-term evolution studies of planets embedded in locally isothermal disks .
This formula can be also applied in the presence of mildly varying radial gradients and of planets that open gaps .
We illustrate its use in the case of migrating super-Earths and determine some conditions sufficient for survival .