Within the equilibrium-diffusion approximation for radiation, we perform a linear stability analysis of the compressible Rayleigh-Taylor instability in a stratified, isothermal background. Radiation alters the growth rate by modulating the fluid's effective compressibility. Radiative diffusion enhances compressibility, driving the growth rate from the adiabatic toward the isothermal limit as the Péclet number $\mathrm{Pe}$ decreases. In contrast, radiation pressure reduces compressibility, steering the growth rate toward the incompressible limit as the Mihalas number $R$ decreases. These competing effects are governed by the key dimensionless groups $\mathrm{Pe}$ (convective versus diffusive transport) and $R$ (material versus radiation pressure). The impact of radiation is most pronounced at low Atwood numbers ($\mathrm{At}$), high stratification parameters ($\mathrm{Sr}$), or large interface thicknesses ($\delta$).

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• Compressible flows
• High-energy-density plasmas
• Rayleigh-Taylor instability