Three-dimensional hydrodynamic simulations of asymmetric pulsar wind bow shocks

We present three-dimensional, non-relativistic, hydrodynamic simulations of bow shocks in pulsar wind nebulae. The simulations are performed for a range of initial and boundary conditions to quantify the degree of asymmetry produced by latitudinal variations in the momentum flux of the pulsar wind, radiative cooling in the post-shock flow and density gradients in the interstellar medium (ISM). We find that the bow shock is stable even when travelling through a strong ISM gradient. We demonstrate how the shape of the bow shock changes when the pulsar encounters density variations in the ISM. We show that a density wall can account for the peculiar bow shock shapes of the nebulae around PSR J2124-3358 and PSR B0740-28. A wall produces kinks in the shock, whereas a smooth ISM density gradient tilts the shock. We conclude that the anisotropy of the wind momentum flux alone cannot explain the observed bow shock morphologies but it is instead necessary to take into account external effects. We show that the analytic (single layer, thin shell) solution is a good approximation when the momentum flux is anisotropic, fails for a steep ISM density gradient and approaches the numerical solution for efficient cooling. We provide analytic expressions for the latitudinal dependence of a vacuum-dipole wind and the associated shock shape, and compare the results to a split-monopole wind. We find that we are unable to distinguish between these two wind models purely from the bow shock morphology.