Acceleration of particles at the termination shock of a relativistic striped wind

Abstract

The relativistic wind of obliquely rotating pulsars consists of toroidal stripes of opposite magnetic field polarity, separated by current sheets of hot plasma. By means of two- and three-dimensional particle-in-cell simulations, we investigate particle acceleration and magnetic field dissipation at the termination shock of a relativistic striped wind. At the shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Irrespective of the stripe wavelength λ or the wind magnetization σ (in the regime σ ≫ 1 of magnetically dominated flows), shock-driven reconnection transfers all the magnetic energy of alternating fields to the particles, whose average Lorentz factor increases by a factor of σ with respect to the pre-shock value. The shape of the post-shock spectrum depends primarily on the ratio λ/(rL σ), where rL is the relativistic Larmor radius in the wind. The spectrum becomes broader as the value of λ/(rL σ) increases, passing from a relativistic Maxwellian to a flat power-law tail with slope around -1.5, populated by particles accelerated by the reconnection electric field. Close to the equatorial plane of the wind, where the stripes are symmetric, the highest energy particles resulting from magnetic reconnection can escape ahead of the shock, and be injected into a Fermi-like acceleration process. In the post-shock spectrum, they populate a power-law tail with slope around -2.5, which extends beyond the flat component produced by reconnection. Our study suggests that the spectral break between the radio and the optical band in Pulsar Wind Nebulae can be a natural consequence of particle acceleration at the termination shock of striped pulsar winds.