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Results of calculations

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..