Effects of Rotation on the Gravitational Momentum Transfer in Neutron-Star Kicks and Implications for Spin-Kick Alignment

Abstract

Neutron stars are often born with large recoil velocities, or natal kicks, whose physical origin remains an open question in core-collapse supernova theory. Observations suggest that the spin-kick angle distribution is not isotropic but skewed toward a spin-kick vector alignment. One possible kick mechanism is the gravitational tug-boat effect, in which anisotropic ejecta gravitationally accelerate the proto-neutron star over a timescale of seconds after shock revival, although the long-term importance of this effect relative to other hydrodynamic forces remains debated. Previous derivations of the tug-boat mechanism do not include the effect of initial stellar rotation. Here we derive a minimalist extension to assess how rotation of the expanding asymmetric mass distribution influences spin-kick alignment of gravitational momentum transfer. We show that the spin-kick angle is determined by the product of two factors, one that depends on the ratio of shock expansion time to the rotation period and the other which depends on the orientation of the asymmetric mass distribution with respect to the spin-axis. For fast enough rotation, the first factor amounts to axially averaging out non-axisymmetry thereby suppressing the perpendicular tug and leaving only a spin-aligned force. However, the rotation speed required for this effect would be unrealistically large unless magnetic fields could transport angular momentum from the core to the outflow efficiently. Spin-kick alignment by the tug-boat mechanism would otherwise require the second factor, namely a preferentially spin-aligned mass flux asymmetry. The rotational-averaging framework developed here suggests that, in general, for any kick mechanism that is not sourced by rotation, including rotation will have some tendency to spin-align the kick, but reduce the kick magnitude.