Dissecting the emission from LHAASO J0341+5258: implications for future multi-wavelength observations

The Large High Altitude Air Shower Observatory (LHAASO) has detected multiple ultra-high energy (UHE; E$_\gamma \ge$ 100 TeV) gamma-ray sources in the Milky Way Galaxy, which are associated with Galactic ``PeVatrons'' that accelerate particles up to PeV (= 10$^{15}$ eV) energies. Although supernova remnants (SNRs) and pulsar wind nebulae (PWNe), as source classes, are considered the leading candidates, further theoretical and observational efforts are needed to find conclusive proof to confirm the nature of these PeVatrons. This work aims to provide a phenomenological model to account for the emission observed from the direction of LHAASO J0341+5258, an unidentified UHE gamma-ray source observed by LHAASO. 15 years of Fermi-LAT data was analyzed to find the high energy (HE; 100 MeV $\le$ E$_\gamma$ $\le$ 100 GeV) GeV gamma-ray counterpart of LHAASO J0341+5258, in the 4FGL-DR3 catalog. We have explained the spectrum of the closest 4FGL source, 4FGL J0340.4+5302, by a synchro-curvature emission formalism typically used in the case of GeV pulsars. Escape-limited hadronic interaction between protons accelerated in an old, now invisible SNR and cold protons inside associated molecular clouds (MCs) and leptonic emission from a putative TeV halo was explored to explain the multi-wavelength (MWL) spectral energy distribution (SED) observed from the LHAASO source region. We have further discussed possible observational avenues that can be explored in the near future and predicted the outcome of those observational efforts from the model explored in this paper.