Prospect of detecting X-ray haloes around middle-aged pulsars with eROSITA

The detection of extended TeV gamma-ray emission (dubbed 'TeV haloes') around Geminga and Monogem pulsars by High Altitude Water Cherenkov collaboration implies that the halo-like morphologies around middle-aged pulsars may be common. The gamma-ray emission above 10 TeV is thought to arise from inverse Compton scattering of relativistic electrons/positrons in the pulsar haloes off cosmic microwave background photons. In the meanwhile, these electrons and positrons can produce X-ray synchrotron emission in the interstellar magnetic field, resulting in a diffuse emission in the X-ray band (namely X-ray haloes). Here, we study the prospect of detecting X-ray haloes with extended Roentgen Survey with an Imaging Telescope Array (eROSITA) from 10 middle-aged pulsars with characteristic age tau(c) larger than tens of thousands of years in the Australia Telescope National Facility pulsar catalogue. Assuming a benchmark value (i.e. B = 3 mu G) for the magnetic field, most of the X-ray haloes are found to be bright enough to be detected by eROSITA in the energy range of 0.5-2 keV with a 20 ks targeted survey. Among these pulsar haloes, four are detectable in the ongoing 4-yr eROSITA all-sky survey. Thanks to the large grasp in the soft X-ray band, eROSITA is expected to be able to measure the surface brightness profiles of the X-ray haloes from sub-pc up to tens of pc scales, which can be used to constrain the magnetic field and the diffusion coefficient in the pulsar haloes.