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.
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