Prospects for the detection of synchrotron halos around middle-age
  pulsars
  The origin of cosmic-ray positrons detected with an energy above 10 GeV is
one of the most intriguing mysteries in Astroparticle Physics. Different
interpretations have been invoked to solve this puzzle such as pulsar wind
nebulae (PWNe), supernovae remnants or interactions of dark matter particles.
The HAWC and Milagro experiments have measured an extended emission of photons
above 10 TeV in the direction of Geminga and Monogem PWNe which can be
interpreted by photons emitted through inverse Compton scattering by positrons
and electrons accelerated by these sources. These HAWC and Milagro detections
are extremely important to estimate the PWN contribution to the positron
excess. Positrons and electrons emitted by PWNe and injected in the
interstellar medium can produce photons with an energy between radio and X-ray
through synchrotron radiation with the Galactic magnetic field. In this white
paper we show that Astrophysics Probe mission concepts, such as AMEGO (the
All-sky Medium Energy Gamma-ray Observatory) and AdEPT (The Advanced Energetic
Pair Telescope), are suitable to detect the synchrotron halos from Monogem and
Geminga PWNe and we will report the list of the most promising PWNe that AMEGO
could be able to detect.
