Pulsar kicks by anisotropic neutrino emission from quark matter in strong magnetic fields

Aims. We critically discuss a pulsar acceleration mechanism based on asymmetric neutrino emission from the direct quark Urca process in the interior of proto neutron stars. Methods. The neutrinos are emitted by the cooling strange quark matter core with an anisotropy caused by a strong magnetic field. We calculate the kick velocity of the proto neutron star in dependence of the temperature and radius of the quark phase. The results are compared with the necessary magnetic field strength, as well as the neutrino mean free path. Results. We find that within a quark phase radius of 10 km and temperatures higher than 5 MeV kick velocities of 1000 km s-1 can be reached only when neutrino quark scattering is ignored. When taking the neutrino mean free paths in quark matter into account kick velocities higher than 100 km s-1 cannot be reached. The same holds even when effects from colour superconductivity are included. For pulsar kicks powered by quark phase transitions from an ungapped quark phase to the CFL phase the final velocity depends crucially on the pairing gap and the quark chemical potential and reaches 1000 km s-1 only in marginal cases. Conclusions. We find that the phenomenon of pulsar kick velocities higher than 100 km s-1 cannot be explained by asymmetric neutrino emission from either cooling normal strange quark or colour superconducting quark matter due to the small neutrino mean free paths. If neutrinos are produced by a phase transition to colour-superconducting quark matter, high kick velocities can only be reached for temperatures below 1 MeV