Ratio of the linear (solid lines) and non-linear (dashed lines) power spectra of several free-streaming ETHOS n = 0 models to that of a pure ΛCDM model with the same cosmological parameters, parameterised by the dark-radiation-to-photon temperature ratio ξ_idr and interaction strength a_dark. The effects are displayed in the basis (ξ_idr, a_dark ξ_idr⁴) to show that the combination a_dark ξ_idr⁴, which gives the scattering rate of IDR off IDM, controls the amplitude of the small-scale suppression of the linear matter power spectrum. The other parameters (${\mathrm{\Omega }}_{\mathrm{dm}}^{\mathrm{ini}}$, Ω_b, h, A_s, n_s) are kept fixed, and the spectra are computed today (z = 0). The non-linear spectra are predicted by the emulator introduced in Sect. 3.4 and plotted up to the maximum wavenumber at which this emulator is trusted.