Stars as Laboratories for Fundamental Physics - MPP Theory Group

444 Chapter 11
Another possibility is that the SN explosion itself is not spherically
symmetric and thus imparts a kick velocity on the neutron star
(Shklovskiĭ 1970). Indeed, as discussed in Sect. 11.1.3 SN explosions
likely involve large-scale convective overturns below and above the neutrino
sphere which could lead to an explosion asymmetry of a few
percent, enough to accelerate the compact core to a speed of order
100 km s −1 , but not enough to account for the typically observed pulsar
velocities (Janka and Müller 1994).
An interesting acceleration mechanism was proposed by Harrison
and Tademaru (1975) who considered the rotation of an oblique magnetic
dipole which is off-center with regard to the rotating neutron star.
The radiation of electromagnetic power is then asymmetric relative to
the rotation axis and so a substantial accelerating force obtains, enough
to cause velocities of several 100 km s −1 . The velocity reached should
not depend on the magnitude of the magnetic dipole moment while its
direction should correlate with the pulsar rotation axis. These predictions
do not seem to be borne out by the data sample of Anderson
and Lyne (1983) although the more recent observations may be less
disfavorable to the “electromagnetic rocket engine.” The correlation
between peculiar velocity and pulsar magnetic moment may now be less
convincing (Harrison, Lyne, and Anderson 1993; Itoh and Hiraki 1994).
Another intriguing mechanism first proposed by Chugaĭ (1984) relies
on the asymmetric emission of neutrinos (“neutrino rocket engine”).
Recall that the total amount of binding energy released in neutrinos is
about 3×10 53 erg; because neutrinos are relativistic they carry the same
amount of momentum. If the neutron-star mass is taken to be 1 M ⊙ ,
and if all neutrinos were emitted in one direction, a recoil velocity of
0.17 c = 5×10 4 km s −1 would obtain. Thus an asymmetric emission of
1.5% would be enough to impart a kick velocity of 800 km s −1 .
Neutrino emission deviates naturally from spherical symmetry if
large-scale convection obtains in the region of the neutrino sphere.
Janka and Müller (1994) believe that 500 km s −1 is a generous upper
limit on the kick velocity that can be achieved by this method. For a
reliable estimate one needs to know the typical size of the convective
cells as well the duration of the convective phase in the protoneutron
star. To this end one needs to perform a fully 3-dimensional calculation.
No such results are available at the present time.
An asymmetric neutrino emission would also obtain in strong magnetic
fields because the opacity is directional for processes involving
initial- or final-state charged leptons, i.e. URCA processes of the type
e − + p → n + ν e or e + + n → p + ν e . The rates for such processes in the