Evaluation of hadronic emission in starburst galaxies and star-forming galaxies

In this work, we reanalyzed 11 years of spectral data from the \textit{Fermi} Large Area Telescope (\textit{Fermi}-LAT) of currently observed starburst galaxies (SBGs) and star-forming galaxies (SFGs). We used a one-zone model provided by \textbf{NAIMA} and the hadronic origin to explain the GeV observation data of the SBGs and SFGs. We found that a protonic distribution of a power-law form with an exponential cutoff can explain the spectra of most SBGs and SFGs. However, it cannot explain the spectral hardening components of NGC 1068 and NGC 4945 in the GeV energy band. Therefore, we considered the two-zone model to well explain these phenomena. We summarized the features of various model parameters, including the spectral index, cutoff energy, and protonic total energy. Similar to the evolution of supernova remnants (SNRs) in the Milky Way, we estimated the protonic acceleration limitation inside the SBGs to be likely in the order of 10$^{2}$ TeV using the one-zone model; this is close to those of SNRs in the Milky Way.