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Phenomenological Kick Velocity


Now we turn to the discussion of the influence of the kick velocity  imparted to NS at birth. The formation of a NS during a supernova explosion  is usually accompanied by a catastrophic mass loss,  which in the majority of cases leads to disruption of the binary system; a young NS can thus "remember" the orbital velocity of the progenitor star of the order of a few 100 km stex2html_wrap_inline8853 before the collapse (``Blaauw mechanism'',  Blaauw, 1955[17]; Gott et al., 1970[57]). However, the range of stellar parameters (masses, radii, orbital separations, etc.) is so wide that some of the systems must survive as binaries during the cataclysmic processes of stellar collapse (see Bhattacharia and van den Heuvel, 1991[12]). Thus, the standard scenario of binary system evolution naturally produces diverse species of pulsars, on the one hand, and explains the velocities of radiopulsars  of about 100-200 km stex2html_wrap_inline8853 measured shortly after their discovery (Manchester and Taylor, 1977[133]), on the other hand.

Recently reported new measurements of the radiopulsars' proper motion (Lyne and Lorrimer, 1994[132]) and of young pulsar positions inside the associated supernova remnants (Frail et al., 1994[53]) imply much higher birth velocities of tex2html_wrap_inline8945 500-900 km stex2html_wrap_inline8853 for pulsars than follows from the standard scenario. This revives the idea of an asymmetrical supernova  collapse which was put forward for the first time by I.S. Shklovskii (1970)[179]. Owing to an enormous energy liberated during the collapse, which is comparable to the rest-mass energy of the whole star, tex2html_wrap_inline10654 , a small anisotropy tex2html_wrap_inline10656 would be sufficient for the remnant to leave the Galaxy, tex2html_wrap_inline10658 , where c is the speed of light. A number of anisotropy mechanisms have been proposed: asymmetric neutrino emission  in a strong magnetic field during collapse (Chugai, 1984[32], Bisnovatyi-Kogan, 1993[14]); double NS formation during core collapse (Imshennik, 1992[77]); tidally induced asymmetric ignition of the WD during the AIC (Lipunov, 1983[103], Lipunov et al., 1987b[121]) etc. However, a reliable reason for such anisotropy still remains unclear. Thus, as for the cosmological constant term, the anisotropy was released away (like a jinnee from the bottle) as a possible but not necessary thing.

It seems natural to assume that the kick velocity is arbitrarily directed in space. The value of the kick velocity w can be quite different and may well depend on a number of parameters, such as magnetic field strength, angular velocity and so on; we consider two extreme assumptions of a strongly determined distribution, tex2html_wrap_inline10664 and of a maxwellian-like one,


which is natural to expect if several independent approximately equally powerful anisotropy mechanisms operates randomly. Here tex2html_wrap_inline10666 is a parameter which is connected with the mean kick velocity tex2html_wrap_inline10668 by the relation tex2html_wrap_inline10670 .

In addition, we performed calculations for the kick velocity distribution taken so as to fit the observed transverse pulsars' velocity obtained by Lyne and Lorimer (1994)[132]:  


where tex2html_wrap_inline10672 , tex2html_wrap_inline10666 is a parameter. The best-fit to Lyne and Lorimer's two-dimensional distribution is reached at tex2html_wrap_inline8895   km stex2html_wrap_inline8853 .

next up previous contents index
Next: The Effect of Kick Up: Restrictions on the Scenario Previous: Test of the Initial

Mike E. Prokhorov
Sat Feb 22 18:38:13 MSK 1997