Attempt to use traveling pulsar wind nebula modeling on the enigmatic LHAASO dumbbell-like structure

Context. The first Large High Altitude Air Shower Observatory (LHAASO) catalog presents six enigmatic ultra-high-energy (UHE) γ -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 constitute a dumbbell-like structure. They are close in position and show a similar spectral shape, suggesting a physical association among them. Aims. To explain the origin of the six LHAASO sources, especially the intriguing dumbbell-like structure, we conducted leptonic and hadronic modeling research according to our multiwavelength and multimessenger study. For the dumbbell-like structure, models with traveling pulsar wind nebulae (PWNe) were considered. Methods. The multiwavelength and multimessenger study was based on the Fermi -LAT, Swift -XRT, Planck , CfA 12 CO survey, and IceCube neutrino datasets. In the traveling PWN modeling research, we assumed an isotropic and homogeneous diffusion condition and discussed the influence of the diffusion coefficient, distance, and proper motion velocity. Results. We do not discover any counterparts in the multiwavelength and multimessenger study except the two known pulsars. The traveling PWN modeling attempt with a single PWN appears to be implausible for explaining the dumbbell-like structure, as the diffusion coefficient needs to be much lower than the Bohm limit. We also explored a double traveling PWNe model, and it could account for the results of the LHAASO observations. However, the probability of the occurrence of this explanation is significantly lower than that of a conventional triple PWNe explanation. Furthermore, according to our model, the only known pulsar, PSR J0218+4232, is unlikely to be associated with the dumbbell-like structure in an isotropic and homogeneous diffusion environment. The expected teraelectronvolt emission of this pulsar is far from explaining even the eastern part of the structure.