Density of the change in $\widehat{[\mathrm{Fe}/\mathrm{H}]}(R_{\mathrm{birth}}$ = 0 kpc, τ) as a function of time after a (left) massive or (right) minor merger for all galaxies after all massive/minor mergers, until either another massive/minor merger occurs or no more stars form in the central 1 kpc. A positive change in [Fe/H] indicates that the projected metallicity in the central 1 kpc increased, while a negative value indicates that the projected [Fe/H] in the central kpc decreased. The projected metallicity at the galactic center does not necessarily decrease immediately after a merger, and a dilution in $\widehat{[\mathrm{Fe}/\mathrm{H}]}(R_{\mathrm{birth}}$ = 0 kpc, τ) can take up to a few Gyr before diluting the projected galactic center in [Fe/H]. Even if $\widehat{[\mathrm{Fe}/\mathrm{H}]}(R_{\mathrm{birth}}$ = 0 kpc, τ) does not dilute, there is a general trend that [Fe/H] enrichment slows down.