High Velocity Pulsar Kicks via Anisotropic Neutrino Emission*

Many neutron stars (NS) have been observed with unusually high velocities—exceeding 1000 km/s in some instances. This phenomenon, known as a pulsar kick, is yet to be fully understood. Among proposed mechanisms, anisotropic neutrino emission remains a compelling candidate and is the focus of this work. Unlike previous models that invoke parity violation to bias emission direction, our research explores the consequences of spatial asymmetry in neutrino formation, which is possible within the chaotic conditions of NS birth.

 

Neutrino transport is analyzed in two regimes. In the optically thick phase, stochastic absorption and reemission yield a macroscopic diffusion process. An analytic solution to the diffusion equation for a spherical Gaussian source offset from the stellar center produces a net momentum flux consistent with typical observed pulsar velocities, given a compact source displaced 10-25% from the stellar radius. In the optically thin regime—relevant for muon and tau neutrinos, and for  electron neutrinos post NS cooling—ballistic trajectories dominate.

 

General-relativistic effects are incorporated via the interior Schwarzschild metric for a uniform-density sphere. We found an exact solution for null geodesics in this spacetime, enabling efficient Monte Carlo simulations of GR-modified diffusion treated as random walks to compare with numerical solutions of GR diffusion models. Results indicate that spacetime curvature biases neutrino paths in the opposing direction of the source, but significant offsets remain necessary to reproduce observed velocities.

 

While spatially asymmetric neutrino sources can account for substantial velocities, the relatively large source offsets required deems this unlikely to explain pulsar kicks in isolation.  Nonetheless, it seems a comprehensive theory of pulsar kicks should include anisotropic neutrino emission and relativistic biases in its considerations.