Confinement of pulsar wind nebulae by their supernova remnants and magnetic dissipation

The standard model of the pulsar wind nebula states that the pulsar wind should be low-magnetization just upstream the termination shock, called the 'sigma-problem'. Low-magnetization is required in order to confine the pulsar wind nebula inside the slowly expanding supernova remnant whose expansion velocity is much smaller than the speed of light. Although the standard model is based on the ideal magnetohydrodynamic approximation, the recent studies indicate that the non-ideal magnetohydrodynamic effects would be important to resolve the sigma-problem. In this study, we extend the standard model including the turbulent magnetic field and the magnetic dissipation. The conversion of the toroidal magnetic field to the turbulent magnetic field and the magnetic dissipation terms are treated phenomenologically. We find that the conversion of the toroidal magnetic field to the turbulent magnetic field decelerates the nebular flow to fit the observed value of the expansion velocity. On the other hand, the magnetic dissipation hardly contributes the flow deceleration, although the magnetic dissipation is important to reproduce the observed emission properties of the PWNe.