Constraining the Magnetic Field in the TeV Halo of Geminga with X-Ray Observations

Recently, the High Altitude Water Cherenkov (HAWC) collaboration reported the discovery of a TeV halo around the Geminga pulsar. The TeV emission is believed to originate from the inverse Compton scattering of pulsar-injected electrons/positrons off cosmic microwave background photons. During this time, these electrons should inevitably radiate X-ray photons via synchrotron radiation, providing a useful constraint on the magnetic field in the TeV halo. In this work, we analyze the data of XMM-Newton and Chandra, and obtain an upper limit for the diffuse X-ray flux in a 600 '' region around the Geminga pulsar, which is at a level of less than or similar to 10(-14) erg cm(-2)s(-1). By numerically modeling both the X-ray and TeV observations assuming the isotropic diffusion of injected electrons/ positrons, we find that the magnetic field inside the TeV halo is required to be <1 mu G, which is significantly weaker than the typical magnetic field in the interstellar medium. The weak magnetic field together with the small diffusion coefficient inferred from the HAWC observation implies that the Bohm limit of particle diffusion may probably have been achieved in the TeV halo. We also discuss alternative possibilities for the weak X-ray emission, such as the hadronic origin of the TeV emission or a specific magnetic field topology, in which a weak magnetic field and a very small diffusion coefficient might be avoided.