  In order to reproduce the statistical properties of the observed exoplanets,
population synthesis models have shown that the migration of protoplanets
should be significantly slowed down, and that processes stalling migration
should be at work. Much current theoretical efforts have thus been dedicated to
find physical effects that slow down, halt or even reverse migration. Many of
these studies rely on the horseshoe drag, whose long term-evolution (saturated
or not) is intimately related to the disk viscosity in laminar disk models. We
investigate how the horseshoe drag exerted on a low-mass planet is altered by a
more realistic treatment of the turbulence in protoplanetary disks.
Two-dimensional hydrodynamic simulations are performed with a turbulence model
that reproduces the main turbulence properties of three-dimensional
magnetohydrodynamic calculations. We find that the horseshoe drag can remain
unsaturated on the long term, depending on the turbulence strength. We show
that the desaturation of the horseshoe drag by turbulence can be modeled by
vortensity diffusion across the time-averaged planet's horseshoe region. At
low-turbulence, the running-time averaged torque is in good agreement with the
total torque obtained for an equivalent laminar model, with a similar
vortensity's diffusion coefficient. At high-turbulence, differences arise due
to the time-evolution of the averaged density profile with turbulence.
