Exploring the non-thermal physics behind the pulsar wind nebula PSR,J2030$+$4415 through radio observations

PSR,J2030$+$4415 is a gamma-ray pulsar with an X-ray pulsar wind nebula elongated along the north--south direction. The system shows a prominent X-ray filament oriented at an angle of 130° to the nebula axis. To improve our understanding of the non-thermal processes occurring in the pulsar wind nebula, we attempted to determine the possible existence of a radio counterpart, study its morphology, and obtain restrictive upper limits of the pulsar and filament emission at radio wavelengths. We performed observations of the pulsar PSR,J2030$+$4415 and its surroundings with the upgraded Giant Metrewave Radio Telescope (uGMRT) at two frequency bands, and put the results in context with findings at other wavelengths. We obtained radio images at 736 and 1274 MHz that reveal a structure trailing the pulsar, with a morphology overlapping the X-ray nebula. This radio structure is the radio counterpart of the X-ray pulsar wind nebula. The derived spectral index along this structure shows spatial variation. There are no hints of the pulsar and the filament at any of the explored radio frequencies, but we obtained restrictive upper limits. A physical scenario that combines the radio and the X-ray observations, and consistent with IR data, of the nebula and the filament is presented. We propose that particle acceleration occurs in the nebula tail due to the presence of a re-collimation shock, and the highest energy particles gradually escape from it through energy-dependent diffusion. We also find a lower limit in the energy of the particles escaping along the X-ray filament of ∼ GeV.