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Binary Pulsar Diversity and High Neutron Star Birth Velocity

We assumed that in the artificial galaxy we modeled the number of single stars is equal to the number of stars entering binaries. The calculations were done for the initial mass ratio power tex2html_wrap_inline8881 ranging from 0 to 2.


Figure 23: Binary pulsar fractions among the total number of pulsars  as a function of the mean kick velocity for a maxwellian distribution  (left-hand panel) and that fitting Lyne and Lorimer's data (right-hand panel). The width of each curve reflects the dispersion of power index tex2html_wrap_inline8885 in the initial mass ratio spectrum. The number for pulsars+planets  is reduced 10 times for clarity. 

Figure 23 (left-hand panel) shows the dependence of the fraction of different types of binary pulsars among the total number of radiopulsars (including those produced by single massive stars) on the mean maxwellian  kick velocity tex2html_wrap_inline10668 (three-dimensional). For completeness, we added the computed number of PSR+BH binaries (assuming a critical mass of the pre-collapsing star of tex2html_wrap_inline10276 and the mass fraction forming the BH of 0.3; see Lipunov et al., (1994b)[124]).

The upper axis shows the mean transverse recoil velocity of pulsars corresponding to the assumed tex2html_wrap_inline10668 . The right-hand panel shows the same curves obtained for the kick velocity distribution [equation (7.4.2)] fitting the pulsars' transverse velocity distribution given by Lyne and Lorimer (1994)[132]. As expected, increasing the mean kick velocity decreases all binary pulsar fractions. In this figure, the fraction of pulsars with planets (PSR+PL) is reduced by a factor of 10 for clarity.

The non-monotonic character of the PSR+PL curve is explained by the fact that in the general case a small kick velocity reduces the new periastron of the binary system making dissipative processes more efficient, which leads to WD Roche lobe overflow  with subsequent planet formation. A more rapid decline for the PSR+NS and PSR+BH systems is caused by the system's undergoing two collapses  (and hence, two kicks), and thus these binaries are subjected to the danger of disruption twice as much.

Obviously, the ``maxwellian'' curves decreases faster (left-hand panel of Figure 23) than the ``Land L'' ones. This is due to the flat power-law asymptotics of Lyne and Lorimer's two-dimensional distribution at low velocities. Indeed,  for large mean kick velocities the maxwellian distribution  has an asymptotic behavior like tex2html_wrap_inline10723 in the crucial region of slow velocities ( tex2html_wrap_inline10725 300 km stex2html_wrap_inline8853 ) which are less or comparable with a characteristic binary orbital velocity, whereas tex2html_wrap_inline10729 is much flatter. We also note that analogous calculations for the delta-function-like kick velocity distribution (not shown in these figures) naturally lead to an even faster decrease of the binary radiopulsar fractions.


Figure: The COOC criterion for binary radiopulsar species from Table 4 as a function of the mean kick velocity. 

Figure 24 shows the COOC criterion (equation 7.2.1) taken over PSR+
[2]OB, PSR+NS and PSR+WD systems (PSR+PL were excluded because there could be other ways such systems formed that are not accounted for by our code as yet) as a function of mean kick velocity. It is clearly seen from this figure that the combined calculated and observed numbers differ by less than three times for the mean kick velocities tex2html_wrap_inline10731  km stex2html_wrap_inline8853 , with the minimum (COOC tex2html_wrap_inline9044 2.3) at tex2html_wrap_inline9044 75-100 km stex2html_wrap_inline8853 .

Let us turn now to a two-dimensional distribution of the pulsars' transverse velocities which are really observed (Lyne and Lorimer, 1994[132]; Frail et al., 1994[53]). As mentioned above, it is well reproduced by the distribution given by equation (7.4.2) with tex2html_wrap_inline8895 km stex2html_wrap_inline8853, which corresponds to the mean velocity tex2html_wrap_inline10745 tex2html_wrap_inline10747 km stex2html_wrap_inline8853 (we note that the mean recoil space velocity of pulsars subjected to such kick distribution is tex2html_wrap_inline9044 370 km stex2html_wrap_inline8853 ; obviously, for high velocities kick and recoil should be the same). This mean kick velocity corresponds to COOC tex2html_wrap_inline8919 5 (Figure 24), that is to a fivefold disagreement with the observed situation. The higher mean recoil transverse velocities reported by Frail et al., (1994)[53], 500-1000 km stex2html_wrap_inline8853 , would give a more dramatic inconsistency. Figure 23 clearly demonstrates that for high mean space velocities >300 km stex2html_wrap_inline8853 the observed binary pulsars  ``Zoo'' would rapidly vanish.

Figure 25: The simulated pulsar transverse velocity distribution (bottom panel) and cumulative distribution (upper panel) for different kicks. The dots are the observed distribution from Lyne and Lorimer (1994).[132] 

In Figure 25 we present the calculated pulsars' transverse recoil velocity distribution for three specific cases: with zero kick (curve (1)), the maxwellian kick with tex2html_wrap_inline10763 km stex2html_wrap_inline8853 (curve (2)) and the distribution (3) giving the best fit to Lyne and Lorimer's data (shown by filled circles). The cumulative distribution is shown for comparison (upper panel).

The calculations presented above clearly demonstrate a strong decrease in number of binary pulsars with diverse secondary components on the assumed kick velocity the NS acquires at birth. On the other hand, high birth velocities for pulsars seem to be really observed (Lyne and Lorimer, 1994[132];  Frail et al, 1994[53]). Thus, a paradoxical situation emerges: we have to make a choice between the high birth space velocities for the pulsars and the observed reach ``Zoo'' of binary pulsars in the galactic disk! Putting aside a thorough analysis of the observational data (which could well be influenced by a number of selection effects leading to an underestimation of low-velocity pulsars; e.g. Tutukov et al., 1984[198]), a possible cause could be the slow steady acceleration of NS which would not disrupt the binary system, but would impart a high space velocity for single pulsars (for example, the rocket mechanism  suggested by Tademary and Harrison (1975)[185] caused by an asymmetric pulsar's emission). The recently reported one-sided X-ray jet from the Vela pulsar (Markwardt and Ögelman, 1995)[136] may provide fresh support for this idea.

What to do with the fast pulsars moving with velocities >1000 km stex2html_wrap_inline8853 ? The highest pulsar velocities resulting from the disruption of a NS - massive helium star   binary during a spherically-symmetric collapse of the helium star cannot be greater than tex2html_wrap_inline8945 700-800 km stex2html_wrap_inline8853 . The mechanism recently suggested by Bisnovatyi-Kogan (1993)[14] allows one to obtain pulsar birth velocities as high as 3000 km stex2html_wrap_inline8853 , but still requires a very strong magnetic field ( tex2html_wrap_inline10777 tex2html_wrap_inline8845 tex2html_wrap_inline10781  G) at birth. Imshennik's (1992)[77] mechanism of double NS formation during the collapse with subsequent Roche lobe overflow of the less massive NS and its explosion after a minimum mass of about tex2html_wrap_inline10783 has been reached, although not requiring such a high magnetic field,  could lead to very high individual space velocities, but hardly to the high mean kicks required to fit the observations.

Therefore, the observed diversity and number of binary pulsars, while requiring a small kick velocity ( tex2html_wrap_inline8945100-150 km stex2html_wrap_inline8853) to be present, are, at the same time, in strong contradiction with the presently derived high mean transverse velocities of pulsars.

next up previous contents index
Next: X-ray Galactic Sources and Up: Restrictions on the Scenario Previous: The Effect of Kick

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