The traveling-PWN modeling attempt on the enigmatic LHAASO dumbbell-like structure

The first LHAASO catalog presents six enigmatic ultra-high-energy (UHE) gamma-ray sources with lonely > 25 TeV emission being detected, which are indicated as 1LHAASO: J0007+5659u, J0206+4302u, J0212+4254u, J0216+4237u, J1740+0948u, and J1959+1129u. No counterparts of the six sources have been observed, except two energetic pulsars, PSR J0218+4232 and PSR J1740+1000. Among them, 1LHAASO: J0206+4302u, J0212+4254u, and J0216+4237u are connected on the significance map and constituted a dumbbell-like structure. They are close in position and show a similar spectral shape, suggesting a physical association among them. To explain the origin of the six LHAASO sources, especially the intriguing dumbbell-like structure, we conducted the leptonic and hadronic modeling research according to our multiwavelength and multimessenger study. For the dumbbell-like structure, models with traveling-PWNe were considered. The multiwavelength and multimessenger study was based on the Fermi-LAT, Swift-XRT, Planck, CfA 12CO survey, and IceCube neutrino datasets. In the traveling-PWN modeling research, we assumed an isotropic and homogeneous diffusion condition and discussed the influence of diffusion coefficient, distance, and proper motion velocity. No counterparts are discovered in our multiwavelength and multimessenger study, except the two known pulsars. The traveling-PWN modeling attempt with a single PWN appears implausible to explain the dumbbell-like structure, as the diffusion coefficient needs to be much lower than the Bohm limit. A double traveling-PWNe model is also explored and can account for the results of LHAASO-KM2A observation. However, the probability of occurrence of this explanation is significantly lower than that of a conventional triple PWNe explanation.