Dynamical Origin of the Vertical Metallicity Gradient of the Milky Way Bulge

A vertical metallicity gradient in the Milky Way bulge is well-established. Yet, its origin has not been fully understood under the Galactic secular evolution scenario. We construct single-disk and triple-disk $N$-body models with an initial radial metallicity gradient for each disk. These models generate a vertical metallicity gradient through a ``two-step heating" mechanism: first the outer, metal-poor particles move inward via the bar instability and subsequently undergo more significant vertical heating during the buckling instability, so they end up at greater vertical height. The ``two-step heating" mechanism nearly linearly transforms the radial metallicity gradients in precursor disks into vertical metallicity gradients. Comparing the models with a triple-disk model tagged with radially independent Gaussian metallicity, we find that, despite certain limitations, the ``two-step heating" mechanism is still important in shaping the Galactic vertical metallicity gradient. If the bar and buckling instabilities contributed to the formation of boxy/peanut-shaped bulges, then the ``two-step heating" mechanism is inevitable in the secular evolution of a boxy/peanut-shaped bulge.