The vertical gradients of disk stars in the simulations. The top panel shows the [Z] vertical gradient of Apollo (purple, grad =  −0.08) with the [O/H] gradient of g15784 (orange, grad =  − 0.06) and observational data from Marsakov & Borkova (2005, 2006) of [Mg/H] gradients in the thin (blue, grad =  − 0.16) and thick (green, grad =  −0.07) disk of the Milky Way. The lower panel shows the [Fe/H] gradients of the Marsakov & Borkova (2005, 2006) thin (grad =  −0.29) and thick (grad =  −0.13) disk data along with the g15784 (grad =  −0.07) [Fe/H] gradient. Overplotted vertically are the softening length of the MUGS (orange) and the minimum grid size of the RaDES (purple) simulations. The bold red lines show the region used to calculate the gradient.