Prospects for combined analyses of hadronic emission from $γ$-ray sources in the Milky Way with CTA and KM3NeT

The Cherenkov Telescope Array and the KM3NeT neutrino telescopes are major upcoming facilities in the fields of $γ$-ray and neutrino astronomy, respectively. Possible simultaneous production of $γ$ rays and neutrinos in astrophysical accelerators of cosmic-ray nuclei motivates a combination of their data. We assess the potential of a combined analysis of CTA and KM3NeT data to determine the contribution of hadronic emission processes in known Galactic $γ$-ray emitters, comparing this result to the cases of two separate analyses. In doing so, we demonstrate the capability of Gammapy, an open-source software package for the analysis of $γ$-ray data, to also process data from neutrino telescopes. For a selection of prototypical $γ$-ray sources within our Galaxy, we obtain models for primary proton and electron spectra in the hadronic and leptonic emission scenario, respectively, by fitting published $γ$-ray spectra. Using these models and instrument response functions for both detectors, we employ the Gammapy package to generate pseudo data sets, where we assume 200 hours of CTA observations and 10 years of KM3NeT detector operation. We then apply a three-dimensional binned likelihood analysis to these data sets, separately for each instrument and jointly for both. We find that the largest benefit of the combined analysis lies in the possibility of a consistent modelling of the $γ$-ray and neutrino emission. Assuming a purely leptonic scenario as input, we obtain, for the most favourable source, an average expected 68% credible interval that constrains the contribution of hadronic processes to the observed $γ$-ray emission to below 15%.