  In order to address the question of whether spiral disturbances in galaxy
discs are gravitationally coupled to the halo, we conduct simulations of
idealized models of disc galaxies. We compare growth rates of spiral
instabilities in identical mass models in which the halo is held rigid or is
represented by particles drawn from an equilibrium distribution function. We
examine cases of radial and azimuthal bias in the halo velocity ellipsoid in
one of our models, and an isotropic velocity distribution in both. We find at
most marginal evidence for an enhanced growth rate of spiral modes caused by a
halo supporting response. We also find evidence for very mild dynamical
friction between the spiral disturbance and the halo. We offer an explanation
to account for the different behaviour between spiral modes and bar modes,
since earlier work had found that bar instabilities became significantly more
vigorous when a responsive halo was substituted for an equivalent rigid mass
distribution. The barely significant differences found here justify the usual
simplifying approximation of a rigid halo made in studies of spiral
instabilities in galaxies.
