A number of 3-D N-body simulations of barred disc galaxies have been reported in recent years (Combes & Sanders 1981, Combes et al. 1990 and Raha et al. 1991) in which the bar always acquired a box-peanut shape when viewed from the side. Here, I compare a model which exhibits this behaviour with the COBE surface photometry and recent kinematic data from the Milky Way bulge.
The initial bar unstable model contains 50K particles chosen so as to create
a disc with a Kuz'min-Toomre density profile in the plane and to have a small
but finite thickness. This component contains 70% of the total mass, the
remaining 30% is in a rigid Plummer sphere which has half the scale length
of that of the disc. (Raha et al. showed that the behaviour studied here is
not greatly affected by this rigid bulge/halo approximation.) The disc
particles were given initial velocities to create an equilibrium 
disc. The model was evolved using a 3-D Cartesian particle-mesh code having
cubic grid cells (double the resolution in each dimension
of that used by Raha et al.).
Figure 1: Three orthogonal projections of the particle distribution at
equal time intervals throughout the simulation. The boundaries
represent the grid edges and the length units are those of the KT disc.
Notice the formation of the peanut shape sometime after the bar has
formed.
Figure 1 shows that the model undergoes a normal bar instability, as
expected, which saturates before time 80, though the disc continues to
display weak spiral activity and the bar to intensify further up to time 120.
The initial bar rotation period is 20 time units, but slows to about 26
units by the end. The bar gradually bends out of the plane, reaching a
maximum around time 140. After this time, the bar abruptly regains symmetry
about the disc plane, but is significantly fatter normal to the plane and
noticeably shorter. The z-thickness of the bar is greatest at its ends,
giving it a pronounced peanut shape when viewed from the side. The thickness
of the disc at larger radii is not much affected by the bending of the bar,
however. This new model confirms much of the behaviour seen previously using
codes of lower spatial resolution. The peanut shape of the object is visible
from viewing angles in the plane which are greater than about 30
to
the bar major axis, but at even smaller angles, the object still appears boxy
(e.g. time 160).
Figure 2: The projected surface brightness as ``observed'' towards the
inner galaxy from the position marked in the last frame of Figure 1.
The contours levels are spaced by factors of 3.