Geminga's pulsar halo: a multiwavelength view

Geminga is the first pulsar around which a remarkable TeV gamma-ray halo extending over a few degrees was discovered by MILAGRO, HAWC and later by H.E.S.S., and by Fermi-LAT in the GeV band. Similar emission has been detected for other middle-aged pulsars in their late evolution stages, and is most plausibly explained by inverse Compton scattering of CMB and interstellar photons by relativistic electrons and positrons. These observations pose a number of theoretical challenges. Tackling these questions requires constraining the ambient magnetic field properties, which can be achieved through X-ray observations. If gamma-ray halos originate from a distribution of highly energetic electrons, synchrotron losses in the ambient magnetic fields of the same particles are expected to produce a diffuse X-ray emission with a similar spatial extension. In this contribution I will present the most comprehensive multi-wavelength study of the Geminga pulsar halo to date. In addition to gamma rays, we use archival X-ray data from XMM-Newton and NuSTAR, covering a broad bandwidth (0.5-79 keV) and large field of view (~4 degrees) for the first time. We find no significant emission and set robust constraints on the X-ray halo flux. These are translated to stringent constraints on the ambient magnetic field strength and the diffusion coefficient by using a physical model considering particle injection, diffusion and cooling over the pulsar's lifetime, which is tuned by fitting multi-wavelength data. Finally, I will discuss the application of our novel methodology to the modelling and searching for synchrotron X-ray counterparts of other pulsar halo candidates.