Explanations of pulsar velocities

The proper motions of pulsars [1] present an intriguing astrophysical puzzle. The measured velocities of pulsars exceed those of the ordinary stars in the galaxy by at least an order of magnitude. The data suggest that neutron stars receive a powerful \kick" at birth. Whatever the cause of the kick, the same mechanism may also explain the rotations of pulsars under some conditions [2]. The origin of the birth velocities is unclear. Born in a supernova explosion, a pulsar may receive a substantial kick due to the asymmetries in the collapse, explosion, and the neutrino emission a ected by convection [3]. Evolution of close binary systems may also produce rapidly moving pulsars [4]. It was also suggested [5] that the pulsar may be accelerated during the rst few months after the supernova explosion by its electromagnetic radiation, the asymmetry resulting from the magnetic dipole moment being inclined to the rotation axis and o set from the center of the star. Most of these mechanisms, however, have di culties explaining the magnitudes of pulsar spatial velocities in excess of 100 km/s. Although the average pulsar velocity is only a factor of a few higher, there is a substantial population of pulsars which move faster than 700 km/s, some as fast as 1000 km/s [1]. Neutrinos carry awaymost of the energy, 10 erg, of the supernova explosion. A 1% asymmetry in the distribution of the neutrino momenta is su cient to explain the pulsar \kicks". A strong magnetic eld inside the neutron star could set the preferred direction. However, the neutrino interactions with the magnetic eld are hopelessly weak. Ordinary electroweak processes [6] cannot account for the necessary anisotropy of the neutrino emission [7]. The possibility of a cumulative build-up of the asymmetry due to some parity-violating scattering e ects has also been considered [8]. However, in statistical equilibrium, the asymmetry does not build up even if the scattering amplitudes are asymmetric [7,9]. Although some net asymmetry develops because of the departure from equilibrium, it is too small to explain the pulsar velocities for realistic values of the magnetic eld inside the neutron star [7,10]. There is a class of mechanisms, however, that can explain the birth velocities of pulsars as long as the magnetic eld inside a neutron star is 10 10 G. These mechanisms [11{14] have some common features. First, the conversions of some neutrino into a di erent type of neutrino, , occurs when one of these neutrinos is free-streaming while the other one is not. The free-streaming component is out of equilibrium with the rest of the star, which prevents the wash-out of the asymmetry. Second, the position of the transition point it a ected by the magnetic eld. I will review two possible explanations, which do not require any exotic neutrino interactions and rely only on the established neutrino properties, namely matter-enhanced neutrino oscillations. The additional assumptions about the existence of sterile neutrinos [15] and the neutrino masses appear plausible from the point of view of particle physics.