Multi-wavelength spectral modelling of the candidate neutrino blazar PKS 0735+178

The BL Lac object PKS 0735+178 was in its historic $\gamma$-ray brightness state during December 2021. This period also coincides with the detection of a neutrino event IC211208A, which was localized close to the vicinity of PKS 0735+178. We carried out detailed $\gamma$-ray timing and spectral analysis of the source in three epochs (a) quiescent state ($E_{1}$), (b) moderate activity state ($E_{2}$) and (c) high activity state ($E_{3}$) coincident with the epoch of neutrino detection. During the epoch of neutrino detection ($E_{3}$), we found the largest variability amplitude of 95%. The $\gamma$-ray spectra corresponding to these three epochs are well fit by the power law model and the source is found to show spectral variations with a softer when brighter trend. In the epoch $E_{3}$, we found the shortest flux doubling/halving time of 5.75 hrs. Even though the spectral energy distribution in the moderate activity state and in the high activity state could be modeled by the one-zone leptonic emission model, the spectral energy distribution in the quiescent state required an additional component of radiation over and above the leptonic component. Here we show that a photo-meson process was needed to explain the excess $\gamma$-ray emission in the hundreds of GeV which could not be accounted for by the synchrotron self-Compton process.