  Recent observational studies have revealed that the Galactic bulge has
cylindrical rotation and a steeper vertical metallicity gradient. We adopt two
representative models for the bulge formation and thereby investigate whether
the two models can explain both the observed cylindrical rotation and vertical
metallicity gradient in a self-consistent manner. One is the "pure disk
scenario" (PDS) in which the bulge is formed from a pure thin stellar disk
through spontaneous bar instability. The other is the "two-component disk
scenario" (TCDS) in which the bulge is formed from a disk composed of thin and
thick disks through bar instability. Our numerical simulations show that
although PDS can reproduce the cylindrical rotation, it shows a rather flatter
vertical metallicity gradient that is inconsistent with observations. The
derived flatter metallicity gradient is due to the vertical mixing of stars
with different initial metallicities by the stellar bar. This result implies
that the bulge can not be simply formed from a pure thin stellar disk. On the
other hand, the bulge formed from the two-component disk in TCDS can explain
both the observed cylindrical rotation and vertical metallicity gradient of the
Galactic bulge reasonably well. In TCDS, more metal-poor stars at higher |z|
(vertical distance) which originate from the already dynamically hotter thick
disk can not be strongly influenced by vertical mixing of the bar so that they
can stay in situ for longer timescales and thus keep the lower metallicity at
higher |z|. Consequently, the vertical metallicity gradient of the bulge
composed of initially thin and thick disk stars can not be so flattened, even
if the gradient of the thin disk can be flattened significantly by the bar in
TCDS.
