  We systematically study late-time tails of scalar waves propagating in
neutron star spacetimes. We consider uniform density neutron stars, for which
the background spacetime is analytic and the compaction of the star can be
varied continously between the Newtonian limit 2M/R << 1 and the relativistic
Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off
neutron stars of different compactions 2M/R and find that a Newtonian, an
intermediate, and a highly relativistic regime can be clearly distinguished. In
the highly relativistic regime, the reflected signal is dominated by
quasi-periodic peaks, which originate from the wave packet bouncing back and
forth between the center of the star and the maximum of the background
curvature potential at R ~ 3 M. Between these peaks, the field decays according
to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between
the center and the maximum or the curvature potential grows without bound, so
that the first peak arrives only at infinitely late time. The modes of neutron
stars can therefore no longer be excited in the ultra-relativistic limit, and
it is in this sense that the late-time radiative decay from neutron stars
looses all its features and gives rise to power-law tails reminiscent of
Schwarzschild black holes.
