Constraining the properties of the magnetic turbulence in the Geminga region using HAWC $\gamma$-ray data

Observations of extended gamma-ray emission around Galactic cosmic-ray (CR) sources can be used as novel probes of interstellar magnetic fields. Using very-high-energy gamma-ray data from the HAWC Observatory, we place constraints on the properties of the magnetic turbulence within $\approx 25$ pc from Geminga. We inject and propagate individual CR electrons in 3D realizations of turbulent magnetic fields, calculate the resulting gamma-ray emission, and compare with HAWC measurements of this region. We find that HAWC data is compatible with expectations for Kolmogorov or Kraichnan turbulence, and can be well fitted for reasonable coherence lengths and strengths of the turbulence, despite implying a CR diffusion coefficient significantly smaller than those suggested by Galactic CR propagation codes. The best fit is found for a coherence length $L_{\rm c} \approx 1$ pc and a magnetic field strength $B_{\rm rms} \approx 3 \mu$G, and the preferred value for $L_{\rm c}$ increases with $B_{\rm rms}$. Moreover, the apparent lack of strong asymmetries in the observed emission allows us to constrain the coherence length to $L_{\rm c} \lesssim 5$ pc in this region.
Comment: submitted to MNRAS