Magnetic Flux Tubes Illuminated by Pulsar Winds

Abstract

Observations of linear structure connecting pulsars to gamma-ray halos reveal injection of TeV electrons into the interstellar medium (ISM). In some cases, this could be attributed to nearly scattering-free electron transport along large-scale magnetic fields connected to pulsar winds with very slow diffusion across the field lines. In this work we model this process with a magnetic flux tube emerging from the pulsar and attached to the ISM magnetic field. We show that particles in this case have an anisotropic distribution of magnetic pitch angle, such that the overall emission is highly beamed. We apply this model to pulsar tails and filaments, including the extended X-ray and TeV emission associated with PSR J1740+1000 and the misaligned X-ray jet in the Guitar Nebula, to constrain their particle population and magnetic fields.

Figures (7)

• Figure 1: Illustration of magnetic flux tube model. High-energy electrons accelerated in the PWN are injected into the magnetic flux tube and transport to the right. The magnetic field is assumed to be pointing to $+z$-direction and $B\propto z^{-2}$ for this figure. The flux tube has length $L$ and radius $R_L$ at the exit end. $\phi$ is the global viewing angle defined using the axis.
• Figure 2: Synchrotron spectral intensity, i.e., energy per unit time per steradian per frequency, for a group of particles evolving along the magnetic flux tube at different photon energies. This assumes a view angle of $\phi=0.1$ and the magnetic field strength of $B_0=100\,{\rm\mu G}$ at the injection end. The electron distribution is taken as an exponential cutoff power law $dN/dE\propto E^{-1}\exp(-E/110\,{\rm TeV})$. The solid lines show the emission from the predicted evolution of an isotropic electron population injection. The dashed line shows the emission from the same population of electrons but without pitch angle evolution, consistent with standard semianalytical formula. They agree until some cutoff point, where the pitch angle of all particles becomes smaller than the view angle $\phi$, indicating a finite viewable length of the magnetic flux tube.
• Figure 3: Simulated synchrotron X-ray images at 1 keV (left column) and IC gamma-ray images (right column) for the magnetic flux tube viewed at different $\phi$. The red dots indicate the center of the injection end. We assume $R_L=2'$, $B_L=3\,{\rm \mu G}$, and an electron distribution of $dN/dE\propto E^{-1}\exp(-E/110\,{\rm TeV})$. The projected length is fixed at $12'$ by changing the physical length of the flux tube with $L=12'/\sin{\phi}$. The magnetic field at the injection end is set by $B_0=B_L/\sin^2{\phi}$.
• Figure 4: Left: merged and exposure-corrected XMM-Newton image of J1740 tail from MOS 1 and MOS 2 in 0.4--7.2 keV range (ObsIDs: 0803080201, 0803080301, 0803080401, and 0803080501). The white cross marks the position of J1740 and the red cross indicates the center of the TeV source 1LHAASO J1740+0948u. The green region shows the tail as detected by XMM and the full extension assumed in our modeling. Right: VLA total intensity radio map of J1740 at 10 cm. The beam size is shown in lower left. The tail is not detected in the data.
• Figure 5: Synchrotron X-ray image at 1 keV (left) and IC gamma-ray image 10 TeV (right), generated using the best-fit parameters described in Section \ref{['sec:j1740']}.