Spin-kick correlation in neutron stars: Alignment conditions and implications

Recent observations of pulsar wind nebulae and radio polarization profiles revealed a tendency for alignment between the spin and velocity directions in neutron stars. We study the condition for spin-kick alignment using a toy model, in which the kick consists of many off-centered, randomly oriented thrusts. Both analytical considerations and numerical simulations indicate that spin-kick alignment cannot be easily achieved if the proto-neutron star does not possess some initial angular momentum, contrary to some previous claims. To obtain the observed spin-kick misalignment angle distribution, the initial spin period of the neutron star must be smaller than the kick timescale. Typically, an initial period of 100 ms or less is required.