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Figure 1: The velocity profile inside a PWN. Three lines are different magneization just before the termination shock. Dissipation length-scales are also diffrent for three lines. posed of relativistic magnetized plasma wind supplied from their central pulsars. The basis of the pulsar wind is a magnetosphere of the pulsar, where the magnetization σ (the ratio of the magnetic to particle energy) is much larger than unity (e.g., [1]). On the other hand, the magnetization of the PWN plasma is considered much smaller than unity from both the observed non-relativistic expansion velocity of PWN and the observed broadband spectrum of PWNe (e.g., [2]). This is the σ-problem of the pulsar wind [3, 4]. It is known that reducing from σ ≫ 1 to σ ≪ 1 is difficult for ideal magnetohydrodynamics outflows. We study a steady and spherically symmetric model of PWNe. Although the dissipation of the magnetic energy in the pre-shock pulsar wind region have been discussed [5], here, we discuss the magnetic energy dissipation at the post shock PWN region. We adopt the phenomenological expression of the magnetic dissipation from [6], where they applied the magnetic dissipation to accelerate the supersonic outflow. We find that the significant dissipation of the magnetic field allows to decelerate the post shock flow to non-relativistic velocity (Figure 1). Recently, the similar results for the deceleration of outflow was also obtained by [7]. We also discuss the broadband spectrum of PWNe.

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