Synchrotron nebulae created by anisotropic magnetized pulsar winds

In this paper, we give a detailed description of the first attempt to study the properties of the flow produced by a magnetized pulsar wind within a pier-ionic nebula via fully relativistic magnetohydrodynamic (MHD) simulations. Following the current theoretical models of pulsar winds, we assume that in the equatorial direction the magnetization of the wind drops to zero but its energy flux reaches a maximum. The results of our 2D axisymmetric simulations reveal complex dynamics of the post-shock flow, very different from the steady quasi-radial outflow assumed in earlier analytical models for plerions. The termination shock has the shape of a distorted torus and most of the downstream flow is initially confined to the equatorial plane. Provided the wind magnetization is higher than a certain value, the magnetic hoop stress stops the outflow in the surface layers of the equatorial disc and redirects it into magnetically confined polar jets. The outflow in the inner layers of the equatorial disc continues until it reaches the slowly expanding outer shell and then turns back and forms the vortex flow filling the nebular volume at intermediate latitudes. We simulated the synchrotron images of the nebula taking into account the relativistic beaming effect and the particle energy losses. These images are strikingly similar to the well-known images of the Crab and other pulsar wind nebulae obtained by Chandra and the Hubble Space Telescope. They exhibit both a system of rings, which makes an impression of an equatorial disc-like or even a toroidal structure, and well-collimated polar jets, which appear to originate from the pulsar. A number of fine details of the inner Crab nebula find natural explanation including the bright knot discovered by Hester et al. in 1995 very close to the Crab pulsar.