Rotating neutron stars, or pulsars, are plausibly the source of power behind many astrophysical systems, such as gamma-ray bursts, supernovae, pulsar wind nebulae and supernova remnants. In the past several years, 3D numerical simulations made it possible to compute pulsar spindown luminosity from first principles and revealed that oblique pulsar winds are more powerful than aligned ones. However, what causes this enhanced power output of oblique pulsars is not understood. In this work, using time-dependent 3D magnetohydrodynamic (MHD) and force-free simulations, we show that, contrary to the standard paradigm, the open magnetic flux, which carries the energy away from the pulsar, is laterally non-uniform. We argue that this non-uniformity is the primary reason for the increased luminosity of oblique pulsars. To demonstrate this, we construct simple analytic descriptions of aligned and orthogonal pulsar winds and combine them to obtain an accurate 3D description of the pulsar wind for any obliquity. Our approach describes both the warped magnetospheric current sheet and the smooth variation of pulsar wind properties outside of it. We find that generically the magnetospheric current sheet separates plasmas that move at mildly relativistic velocities relative to each other. This suggests that the magnetospheric reconnection is a type of driven, rather than free, reconnection. The jump in magnetic field components across the current sheet decreases with increasing obliquity, which could be a mechanism that reduces dissipation in near-orthogonal pulsars. Our analytical description of the pulsar wind can be used for constructing models of pulsar gamma-ray emission, pulsar wind nebulae, and magnetar-powered core-collapse gamma-ray bursts and supernovae.
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