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Initial velocity next up previous
Next: Galactic potential Up: Space and velocity distributions Previous: Space position

Initial velocity

The initial velocity of young neutron stars can be taken either from the observed pulsar velocity distribution (which is still not firmly established), or from some model-dependendent assumptions based on current ideas about neutron star formation. Both ways are not seemed to be problem free. Here we will use the second way, that is we will calculate initial velocity of a new-born pulsar as the sum of its regular velocity in the Galaxy and a velocity which the pulsar acquires at the moment of the burth. The former is defined by the assumed galactic potential and is typically of order of 200 km/s, and the latter is caused by a chaotic motion of the progenitor star and a regular motion of the pulsar progenitor in a binary system and usually tex2html_wrap_inline285  km/s. We also take into account possible assymetry in the supernova explosion mechanism (for example, neutrino anisotropy in a strong magnetic field (Chugaj 1984), breaking of magnetic field symmetry during magneto-rotational collapse (Bisnovatyj-Kogan & Moiseenko 1992) or splitting of fast rotating newborn neutron star into two neutron stars with subsequent explosion of the easier component (Imshennik and Nadyozhin 1992)) by introducing a ``kick'' velocity for the pulsar. This ``kick'' velocity is supposed to be as high as tex2html_wrap_inline287  km/s and randomly oriented. (Note that if Imshennik and Nadyozhin mechanism is actually under work, which is supposed to occur in a few percent of supernovae, one should expect a subclass of very fast moving pulsars ( tex2html_wrap_inline289  km/s) to exist which ultimately will populate a very extended halo around the Galaxy).

We have performed a Monte-Carlo calculation of evolution of 50,000 massive binaries with an initial mass of primary star tex2html_wrap_inline291 to obtain initial velocity distribution of young pulsars. Description of the method of statistical simulation we use can be found elsewhere (Kornilov and Lipunov (1983) and Lipunov and Postnov (1987)). The results are presenred in Fig.gif. One can see that the velocity distribution tex2html_wrap_inline271 have a maximum centered on the value of the assumed ``kick'' velocity and high-velocity tail of the distribution is obeyed a power law with a slope of tex2html_wrap_inline295 . This probably reflects a power-law shape of the assumed (Salpeter) distribution for the initial stellar masses, and power-law parametrization of binary system evolutionary tracks we used for statistical calculations of a large number of systems. We assume the distribution tex2html_wrap_inline265 to be isotropical. At the same time we need know the distribution of projected velocities on the direction of the systematic motion in the Galaxy (i.e. on the direction of tex2html_wrap_inline227 ) tex2html_wrap_inline273 . This is required because we need calculate distribution on energy E (which depends on tex2html_wrap_inline271 ) and on angular momentum tex2html_wrap_inline191 (which is determined by tex2html_wrap_inline273 ). These two distribution are connected through the well known relation

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next up previous
Next: Galactic potential Up: Space and velocity distributions Previous: Space position

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