Distribution of the orbital eccentricities as a function of [M/H] for the thin disc metal-rich sample. The solid (dashed) lines indicate the required eccentricity to reach R = 8 kpc (±300 pc) without the need for churning (see Eq. (2)). For a fixed zero point, ISM_[M/H](R_⊙) = 0.0, we studied three different ISM metallicity gradients (black, red, and orange). The green curve corresponds to the gradient from Genovali et al. (2014). The stars to the right require churning to reach the solar neighbourhood.