It proves to be teachful to have a look at the calculated distribution
(Fig.
). It is seen that a sharp boundary exists (minimal
E at a given 
)
corresponding to circular orbits at the galactic plane. If all
stars were moving strictly along circular orbits, only positive part
of the curve would be seen and all particles would be set in this boundary.
The galactic z-distribution of stars and peculiar velocities slightly
smear out this narrow boundary. It is clear that the present shape of
the isodenses in this plot are made by peculiar velocities of the neutron
stars aquired during supernova explosions. However, the majority of stars
lies close to the positive boundary, as in case of unperturbed motion.
This is connected with the typical velocity of 100 km/s which is
less than the orbital velocity. The part of -plane
with high energies and negative angular momenta corresponding
to the retrograde motion are
due to high-velocity tail of the velocity distribution.
Second picture of importance is that of equipotential surfaces (Fig.).
If a test particle were moving with given 
, the ergodic hypothesis
states that ultimately it will be found at any
point inside the equipotential surface
(with equal probability density in the
phase space). It is convenient to
mark the equipotential surfaces with the value of energy difference between
E and the energy the star would have at the circular orbit at a certain
r and, hence, with a certain (recall that this corresponds to the
minimum of the effective potential defined
by 
),
expressed in units of the velocity component of the star
in the direction which does not contribute to the .
The final picture (Fig.) of the old neutron star density distribution is
obviously the sum of filled equipotential lobes with different
weighted with the probability
shown in the Fig..