Self-confinement of relativistic pair beams in magnetized interstellar plasmas: the case of pulsar X-ray filaments

Abstract

The observation of filamentary X-ray structures near bow-shock pulsar wind nebulae (PWNe) -- such as the Guitar, Lighthouse, and PSR J2030$+$4415 nebulae -- and of slow-diffusion regions around pulsars like Geminga, Monogem, and PSR J0622$+$3749, challenges the standard picture of cosmic-ray transport in the interstellar medium, implying a diffusion coefficient two orders of magnitude smaller than the Galactic average. The suppressed diffusion can be attributed to self-generated magnetic turbulence, driven -- via the non-resonant streaming instability -- by electron--positron pairs escaping the PWNe. This instability requires a net current, yet the beam of escaping pairs is expected to be charge-neutral. We show that a charge-neutral pair beam propagating through an electron--proton plasma can spontaneously generate a net current. Using fully kinetic two- and three-dimensional particle-in-cell simulations with realistic mass ratio, we find that beam electrons get focused into self-generated magnetic filaments produced by the nonlinear evolution of the Weibel instability, while beam positrons remain unconfined. The resulting net (positron) current drives the non-resonant streaming instability, further amplifying the magnetic field. This mechanism provides a pathway for the onset of charge asymmetries in initially charge-neutral pair beams and for the growth of magnetic fluctuations that efficiently scatter the beam particles, with implications for the formation of X-ray filaments and, more broadly, for particle self-confinement in TeV halos around PWNe.

Figures (6)

• Figure 1: Evolution of $(B_\perp/B_0)^2$ (first column) and of the spatial distribution of beam positrons and electrons (second and third columns, respectively), for the reference case with $\gamma_b \alpha = 10^{-1}$, $\sigma = 2 \times 10^{-2}$, and $\Delta{\gamma_b}=10^{-4}$.
• Figure 2: Fraction of beam energy converted into magnetic energy (a) and charge separation between beam electrons and positrons (b) for various $\sigma$ and $\gamma_b\alpha$, at fixed $\Delta\gamma_b = 10^{-4}$. The horizontal purple line is the theoretical prediction in Eq. \ref{['eq:saturation']}.
• Figure 3: (a) $(B_\perp/B_0)^2$ during the growth of the cavitation instability; (b) $(B_\perp/B_0)^2$ showing the development of the NRI (in red, driven by beam $e^+$) at later times, together with the cavities generated by beam $e^-$ (in green, as in (a)). Magnetic-field streamlines within the $e^+$-driven NRI regions are also shown. We adopt $\sigma=10^{-1}$ and $\gamma_b \alpha= 5 \times 10^{-1}$.
• Figure 4: Same as Figure \ref{['Fig:no_refresh']} but for the case in which we "refresh" the beam particles. We use $\Delta \gamma_b=10^{-4}$.
• Figure 5: Same as Figure \ref{['Fig:no_refresh']} of our reference case, with $\gamma_b \alpha = 10^{-1}$, $\sigma = 2\times 10^{-2}$, and $\Delta \gamma_b=10^{-4}$. The three curves correspond to different box sizes, $48 \times 48 \, d_e^2$ and $200 \times 200 \, d_e^2$, and to different ppc.