2025MNRAS.538.2149L

The High-Altitude Water Cherenkov Telescope (HAWC) has detected TeV haloes associated with two nearby pulsars/pulsar wind nebulae - Geminga and B0656+14. These TeV haloes extend up to tens of pc from the central accelerators, indicating that the diffusion of ultrarelativistic electrons and positrons in the interstellar medium has been suppressed by two orders of magnitude. Although Geminga and B0656+14 are at similar distances and in the same field of view, they have distinct histories. Notably, B0656+14 probably still resides within its parent supernova remnant, the Monogem Ring, which can be observed in X-rays. In this work, we perform high-resolution simulations of the propagation and emission of relativistic lepton pairs around B0656+14 using a two-zone diffusion model using the GALPROP numerical code. We compared the predicted inverse-Compton spectrum to the observations made by HAWC and Fermi-LAT and found physically plausible model parameters that resulted in a good fit to the data. Additionally, we estimated the contribution of this TeV-halo to the positron flux observed on Earth and found it to be smaller than 10 per cent of the measured flux. We conclude that future observations of the TeV halo and its synchrotron emission counterpart in radio and X-ray frequencies will be crucial to distinguish between various possible models.