After the pulsar stage of evolution, evolved (radio quiet) pulsars and magnetars are still strongly magnetized and rotating objects. They continue to generate a magnetically dominated (Poynting flux) wind from the region of the light cylinder. Part of the magnetic energy converts to energy of relativistic particles (pulsar wind). Expansion of the magnetic field and relativistic particles outward significantly increases the effective size of the magnetosphere of these objects and thus the cross-section for their interaction with the interstellar medium (ISM). The interaction leads to the formation of a bow shock wave and a highly elongated magnetotail. The standoff distance of the bow shock is determined by the Poynting power outflow from the light cylinder of the pulsar. We performed axisymmetric MHD simulations of propagation of rotating magnetized stars through the ISM, and observed that a prominent bow shock stands in front of magnetosphere. The magnetosphere is stretched by the ISM forming elongated magnetotail. We observed that a rotating star has an expanded cross-section compared to a non-rotating one. In the case of a non-moving star, a disk-like equatorial MHD wind is observed. We conclude that the closest evolved pulsars and magnetars may be observable owing to interaction with the ISM. The origin of the shock wave near the object RX J1856.5-3754 is discussed.

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