On the X-ray Image of The Crab Nebula: Comparison with Chandra Observations

An axisymmetric model for the Crab Nebula is constructed to examine the flow dynamics in the nebula. The model is based on that of Kennel and Coroniti (1984), although we assume that the kinetic-energy-dominant wind is confined in an equatorial region. The evolution of the distribution function of the electron-positron plasma flowing out in the nebula is calculated. Given viewing angles, we reproduce an image of the nebula and compare it with Chandra observation. The reproduced image is not a ring-like but rather 'lip-shaped'. It is found that the assumption of toroidal field does not reproduce the Chandra image. We must assume that there is disordered magnetic field with an amplitude as large as the mean toroidal field. In addition, the brightness contrast between the front and back sides of the ring cannot be reproduced if we assume that the magnetization parameter $\sigma$ is as small as $\sim 10^{-3}$. The brightness profile along the semi-major axis of the torus is also examined. The non-dissipative, ideal-MHD approximation in the nebula appears to break down. We speculate that if the magnetic energy is released by some process that produce turbulent field in the nebula flow and causes heating and acceleration, e.g. by magnetic reconnection, then the present difficulties may be resolved (i.e. we can reproduce a ring image, and a higher brightness contrast). Thus, the magnetization parameter $\sigma$ can be larger than previously expected.
Comment: 8 pages, 4 figures. accepted for publication in MNRAS