Constraints on the properties of the turbulent magnetic field around Geminga using HAWC measurements

Abstract

We place constraints on the properties of the interstellar turbulence that surrounds Geminga pulsar, using the recent measurements from the HAWC Observatory in this region. We propagate very-high-energy electrons in realizations of 3D isotropic Kolmogorov or Kraichnan turbulence, calculate their gamma-ray emission, and compare with HAWC measurements. We show that the measurements can be well fitted for both models of the turbulence and for reasonable values of its strength, $B_{\rm rms}$, and coherence length, $L_{\rm c}$. Our best fits are obtained for $B_{\rm rms} \simeq 3 \mu$G and $L_{\rm c} \simeq 1$ pc. Furthermore, the absence of strong asymmetries in the observed emission favours $L_{\rm c} \leq 5$ pc.