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Results of calculations next up previous
Next: Discussion Up: Old neutron star distribution Previous: Galactic potential

Results of calculations

It proves to be teachful to have a look at the calculated distribution tex2html_wrap_inline199 (Fig.gif). It is seen that a sharp boundary exists (minimal E at a given tex2html_wrap_inline191 ) 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 tex2html_wrap_inline199 -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.gif). If a test particle were moving with given tex2html_wrap_inline251 , 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 tex2html_wrap_inline191 (recall that this corresponds to the minimum of the effective potential defined by tex2html_wrap_inline355 ), expressed in units of the velocity component of the star in the direction which does not contribute to the tex2html_wrap_inline191 .

The final picture (Fig.gif) of the old neutron star density distribution is obviously the sum of filled equipotential lobes with different tex2html_wrap_inline191 weighted with the probability tex2html_wrap_inline199 shown in the Fig.gif.


next up previous
Next: Discussion Up: Old neutron star distribution Previous: Galactic potential

Mike E. Prokhorov
Fri Jul 19 19:16:07 MSD 1996