Pulsar Wind Nebula Magnetization

What you are seeing: a pulsar wind nebula. The pulsar's spin-down luminosity drives a relativistic wind that terminates at a shock $R_{TS} = \sqrt{L_{sd} / (4\pi c P_{ext})}$ . The magnetization $\sigma = U_B / U_{\rm particle}$ controls the post-shock dynamics.

Figure 1. Schematic PWN with termination shock and magnetization.

log10(L_sd erg/s)38.7

log10(P_ext dyn)-9.0

σ0.003

WHAT TO TRY

Raise the spin-down luminosity L_sd: the termination shock R_TS = sqrt(L_sd/(4 pi c P_ext)) pushes outward. A more powerful pulsar inflates a bigger bubble against the same pressure.
Raise the external pressure P_ext: the shock is squeezed inward. R_TS balances the wind ram pressure against confinement by the surrounding medium.
Tune sigma (magnetization): it sets how much wind energy is in fields versus particles. The sigma problem is that real nebulae need surprisingly low values.