Variation in θ = δΣ/Σ, the ratio of the perturbation surface density to the unperturbed surface density, with τ, dimensionless time in the sheared frame, plotted for gravitationally-coupled two-fluid (stars and gas) system. In the top panel, both fluids are modelled as infinitesimally-thin whereas in the bottom panel, both fluid disks have finite thickness. In both cases, Qs = 1.8, Qg = 1.2, ϵ = 0.15, η = 1, and X = 1. For the infinitesimally-thin case (top panel), a high gas-fraction induces finite swing amplification in the stellar disk, but the introduction of finite thickness prevents the growth of swing-amplified modes almost completely (bottom panel). The net amplitude αθ ≪1 at all τ, where α is a scale factor.
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