  We determine the response of a self-similar isothermal stellar system to
small adiabatic gravitational perturbations. For odd spherical harmonics, the
response is identical to the response of the analogous isothermal fluid system.
For even spherical harmonics, the response can be regarded as an infinite
series of wavetrains in $\log r$, implying alternating compression and
rarefaction in equal logarithmic radius intervals. Partly because of the
oscillatory nature of the solutions, tidal fields from external sources are not
strongly amplified by an intervening isothermal stellar system, except at radii
$\lta 10^{-3.5}$ times the satellite radius; at some radii the stellar system
can even screen the external tidal field in a manner analogous to Debye
screening. As Weinberg has pointed out, individual resonances in a stellar
system can strongly amplify external tidal fields over a limited radial range,
but we cannot address this possibility because we examine only adiabatic
perturbations. We also discuss the application of our method to the halo
response caused by the slow growth of an embedded thin disk.
