Projected mass surface density for particles selected as kpc km s⁻¹ at t = 3 Gyr (left panel) inside ±50 kpc. Their distribution at t = 10.54 Gyr (right panel). The log colourscale is common to both figures (in M_⊙ pc⁻²). Black isodensities are spaced by 0.2 dex. Circles show the position for the ILR (dot-dashed line), the UHR and outer m​ = ​ + 4 resonance (short-dashed), the CR (full line), and the OLR (long-dashed). In red, the following resonances for the stellar bar are shown: UHR_B, CR_B, and OLR_B, as defined in Sect. 6. Using the same linestyle, the white circles represent the intermediate spiral: ILR_iS (close to UHR_B), CR_iS (close to OLR_B), outer m = +4 resonance, and OLR_iS. The black circles represent the outer wave ILR_oW (close to intermediate spiral outer m = +4 resonance), UHR_oW, and CR_oW.