  We determine an expression for the Type I planet migration torque involving a
locally isothermal disk, with moderate turbulent viscosity (~0.0005 < alpha <
~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.
