  Debris disks or exo-Kuiper belts, detected through their thermal or scattered
emission from their dusty components, are ubiquitous around main-sequence
stars. Since dust grains are short-lived, their sustained presence is thought
to require dynamical excitation, i.e., "stirring", of a massive reservoir of
large planetesimals, such that mutual collisions are violent enough to
continually supply fresh dust. Several mechanisms have been proposed to explain
debris disk stirring, with the commonly accepted being long-term, secular
planet-debris disk interactions. However, while effective, existing
planet-stirring models are rudimentary; namely, they ignore the (self-)gravity
of the disk, treating it as a massless reservoir of planetesimals. Here, using
a simple analytical model, we investigate the secular interactions between
eccentric planets and massive, external debris disks. We demonstrate that the
disk gravity drives fast apsidal precession of both planetesimal and planetary
orbits, which, depending on the system parameters, may well exceed the
planet-induced precession rate of planetesimals. This results in strong
suppression of planetesimal eccentricities and thus relative collisional
velocities throughout the disk, often by more than an order of magnitude when
compared to massless disk models. We thus show that massive debris disks may
hinder secular stirring by eccentric planets orbiting near, e.g., the disk's
inner edge, provided the disk is more massive than the planet. We provide
simple analytic formulae to describe these effects. Finally, we show that these
findings have important implications for planet inferences in debris-bearing
systems, as well as for constraining the total masses of debris disks (as done
for $\beta$ Pic).
