Proc. Neutrino Astrophysics - MPP Theory Group

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becomes neutron-rich. On the one hand, the unequal concentrations of neutrons and protons
cause different opacities for νe and ¯νe, on the other hand the growing abundance of neutrons
implies an increase of the total polarization of the nucleonic medium because the contributions
from neutrons and protons have opposite signs and partly cancel. For a typical post-collapse
composition, Yp ≈ 0.35 and Yn ≈ 0.65, this cancellation is severe and reduces the polarization
to roughly 1/8 of the value for a neutronized medium with Yp ≈ 0.1 and Yn ≈ 0.9. The latter
composition is representative of the late Kelvin-Helmholtz cooling phase after the deleptonization
of the proto-neutron star. Most (60–90%) of the neutrino energy is radiated during this
phase which is therefore decisive for a “rocket engine” effect by asymmetric neutrino emission.
Of course, the estimated velocity in Eq. (2) is an upper limit which could be realized only
if the interior magnetic field were uniform in the z-direction throughout the neutron star.
Convective processes that reach deep into the star will certainly destroy the ordered structure
of the field. In case of rapid rotation of the newly formed neutron star (rotation periods of
a few milliseconds), however, convection can develop only near the equatorial plane but is
suppressed near the rotation axis where an ordered field structure could persist in a large
fraction of the neutron star volume.
Conclusions
If parity violation of weak interactions plays the crucial role to kick pulsars and if convection
is important during the early phases of a neutron star’s life, one would therefore conclude
that the observed velocities of fast pulsars between several 100km/s and more than 1000km/s
require interior magnetic fields from a few 10 13 G to ∼ 10 14 G, and that the largest velocities
might indicate rapid rotation of the newly formed neutron star.
Acknowledgements
This work was supported by the “Sonderforschungsbereich 375-95 für Astro-Teilchenphysik”
der Deutschen Forschungsgemeinschaft. Stimulating discussions with S. Hardy, G. Raffelt,
and S. Yamada are acknowledged.
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