Magnetohydrodynamic model of the Crab Nebula and its radiation
The interaction of the Crab pulsar with its surrounding nebula is modeled as a steady state, spherically symmetric relativistic wind which is confined by the outer layers of the supernova remnant. The pulsar wind is assumed to contain only positrons and electrons, and is terminated by a strong shock at a distance of 10 arcseconds from the pulsar, at the outer edge of the underluminous region. Down-stream of the shock, the flow decelerates and increases its pressure in order to match the boundary conditions imposed by outer nebula. Consistent flow solutions can be found if the magnetic luminosity of the pulsar wind is about 0.3 percent of its particle luminosity. The immediate postshock plasma is modeled as a power law distribution whose density and pressure moments satisfy the strong shock Rankine-Hugoniot relations. Using the downstream flow solution, the synchrotron continuum is calculated. The parameters of the pulsar wind and assumed power law spectral index are adjusted until the calculated total synchrotron power and the spectral distribution of the nebular continuum from optical to gamma-rays, are in reasonable accord with observations.