Anisotropic Diffusion in Pulsar Halos: Interpreting the asymmetric morphology of Geminga and Monogem halos measured by HAWC

Abstract

Pulsar halos are produced by electrons and positrons diffusing in the interstellar medium around their parent pulsar wind nebulae. Recent observations by HAWC and LHAASO have revealed asymmetric morphologies in the halos surrounding Geminga and Monogem. The anisotropic diffusion model provides a natural explanation for such asymmetries, where the morphology is determined by the viewing angle of the mean magnetic field, the Alfvénic Mach number ($M_{\rm A}$), and the pulsar distance. In this work, we model the measured morphologies based on this framework and constrain the properties of interstellar magnetic turbulence. We find that the mean magnetic field orientations within the two halos are different, implying that they reside in different magnetic coherence regions, whereas the Alfvénic Mach numbers are relatively close ($M_{\rm A}\sim 0.2$). The results suggest a local magnetic field coherence length of approximately 100pc. Our study demonstrates that the morphology of pulsar halos serves as a powerful diagnostic tool for the properties of interstellar magnetic fields, highlighting the need for more accurate morphological measurements and sophisticated diffusion modeling in future studies.

Figures (6)

• Figure 1: Sketch figure for the definition of $\phi$ and $\chi$. The location of $B$-field represents the projection of the mean magnetic field direction on the celestial sphere. Please refer to the appendix for the formula used to calculate the equatorial coordinates of the magnetic field direction.
• Figure 2: Variation of the characteristic diffusion angle $\theta_d$ with azimuth $\zeta$ for Geminga and Monogem with different integration radius. The colored dashed line represents the characteristic diffusion angle at each azimuth, calculated from the median of the posterior distribution of the anisotropic model parameters. The solid colored line and the shaded region indicate the median and the 68% error range fitted for each quadrant, respectively.
• Figure 3: Spectra fitting to the spectra of Geminga (left panel) and Monogem (right panel), with blue and orange bands being uncertainty bands of 68% confidence intervals for the cases of $r_{\rm max}=100\,$pc and 200 pc respectively. Gray bands show for comparison the results obtained by HAWC with the diffusion template 2024HAWC_Observation. The black data points indicate the data used in the $\eta_e$ fit, while the gray data points are shown for reference only and not included in the fitting.
• Figure 4: The 90% confidence interval contour of the magnetic field direction distribution in the celestial sphere for Geminga and Monogem. The solid and dashed lines represent the results obtained with integration radii $r_{\rm max}$ of 100 pc and 200 pc, respectively.
• Figure 5: The corner plots for Geminga (left) and Monogem (right) with integration radius $r_{\rm max}=100$ pc obtained using the MCMC method.