Density and velocity-divergence at t = 140 t₀ for an isothermal and a non-isothermal disc (with and without SG). Left column: relative density (σ/σ₀). The main vortex is masked to distinguish the annular over-density and the spiral waves. Right column: normalised relative velocity field divergence (∇ · v′/(2Ω_k)). From top to bottom: self-gravitating vortex in an isothermal disc, self-gravitating vortex in a non-isothermal disc, and the reference vortex (without SG and in a non-isothermal disc), respectively.