Left: Ratio of the interaction rate between IDM and IDR (Γ_{idm − dr}) and comoving Hubble rate (ℋ) as a function of the dark-radiation-to-photon temperature ratio ξ_idr and interaction strength a_dark, computed at the redshift z_ini = 49 at which the N-body simulations used to construct the ETHOS emulator are initialised. We display the contours of equal ratio as solid white lines and highlight the threshold value of 0.1 in black. We further depict the region with a_dark = 10 Mpc⁻¹ (dashed grey) and ξ_idr = 0.25 (dash-dotted grey). Right: Power spectrum suppression 𝒮_ETHOS(k, z) predicted by the emulator for parameters chosen along each of the two grey lines of the left panel.