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We study the tidal interaction between a low-mass companion (e.g., aprotoplanet or a black hole) in orbit about a central mass, and the accretiondisk within which it is submerged. We present results for a companion on acoplanar orbit with eccentricity e between 0.1 and 0.6. For theseeccentricities, dynamical friction arguments in its local approximation, thatis, ignoring differential rotation and the curvature of the orbit, providesimple analytical expressions for the rates of energy and angular momentumexchange between the disk and the companion. We examine the range of validityof the dynamical friction approach by conducting a series of hydrodynamicalsimulations of a perturber with softening radius R_soft embedded in atwo-dimensional disk. We find close agreement between predictions and thevalues in simulations provided that R_soft is chosen sufficiently small, belowa threshold value Rtilde_soft, which depends on the disk parameters and oneccentricity. We give Rtilde_soft for both razor-thin disks and disks with afinite scaleheight. For point-like perturbers, the local approximation is validif the accretion radius is smaller than Rtilde_soft. This condition imposes anupper value on the mass of the perturber.

Orbital evolution of eccentric low-mass companions embedded in gaseous disks: testing the local approximation