  We investigate the unsaturated horseshoe drag exerted on a low-mass planet by
an isothermal gaseous disk. In the globally isothermal case, we use a formal-
ism, based on the use of a Bernoulli invariant, that takes into account
pressure effects, and that extends the torque estimate to a region wider than
the horse- shoe region. We find a result that is strictly identical to the
standard horseshoe drag. This shows that the horseshoe drag accounts for the
torque of the whole corotation region, and not only of the horseshoe region,
thereby deserving to be called corotation torque. We find that evanescent waves
launched downstream of the horseshoe U-turns by the perturbations of vortensity
exert a feed-back on the upstream region, that render the horseshoe region
asymmetric. This asymmetry scales with the vortensity gradient and with the
disk's aspect ratio. It does not depend on the planetary mass, and it does not
have any impact on the horseshoe drag. Since the horseshoe drag has a steep
dependence on the width of the horseshoe region, we provide an adequate
definition of the width that needs to be used in horseshoe drag estimates. We
then consider the case of locally isothermal disks, in which the tempera- ture
is constant in time but depends on the distance to the star. The horseshoe drag
appears to be different from the case of a globally isothermal disk. The
difference, which is due to the driving of vortensity in the vicinity of the
planet, is intimately linked to the topology of the flow. We provide a
descriptive inter- pretation of these effects, as well as a crude estimate of
the dependency of the excess on the temperature gradient.
