Mapping the Three-Dimensional "X-Shaped Structure" in Models of the
  Galactic Bulge
  Numerical simulations have shown that the X-shaped structure in the Milky Way
bulge can naturally arise from the bar instability and buckling instability. To
understand the influence of the buckling amplitude on the morphology of the
X-shape, we analyze three self-consistent numerical simulations of barred
galaxies with different buckling amplitudes (strong, intermediate and weak). We
derive the three-dimensional density with an adaptive kernel smoothing
technique. The face-on iso-density surfaces are all elliptical, while in the
edge-on view, the morphology of buckled bars transitions with increasing
radius, from a central boxy core to a peanut bulge and then to an extended thin
bar. Based on these iso-density surfaces at different density levels, we find
no clear evidence for a well-defined structure shaped like a letter X. The
X-shaped structure is more peanut-like, whose visual perception is probably
enhanced by the pinched inner concave iso-density contours. The peanut bulge
can reproduce qualitatively the observed bimodal distributions which were used
as evidence for the discovery of the X-shape. The central boxy core is shaped
like an oblong tablet, extending to $\sim$ 500 pc above and below the Galactic
plane ($|b| \sim 4^\circ$). From the solar perspective, lines of sight passing
through the central boxy core do not show bimodal distributions. This generally
agrees with the observations that the double peaks merge at $|b| \sim 4^\circ -
5^\circ$ from the Galactic plane, indicating the presence of a possibly similar
structure in the Galactic bulge.
