Constraining the hadronic properties of star-forming galaxies above $1\, GeV$ with 15-years Fermi-LAT data

Star-forming and starburst galaxies (SFGs and SBGs) are powerful emitters of non-thermal γ-rays and neutrinos, due to their intense phases of star-formation activity, which should confine high-energy Cosmic-Rays (CRs) inside their environments. In this paper, using the publicly-available fermitools, we analyse 15.3 years of γ-ray between 1-1000\, GeV data for 70 sources, 56 of which were not previously detected. We find at~4σ level an indication of γ-ray emission for other two SBGs, namely M 83 and NGC 1365. By contrast, we find that, even with the new description of background, the significance for the γ-ray emission of M 33~(initially reported as discovered) still stands at ~ \, 4σ (as already reported by previous works). Along with previous findings, the flux of each detected source is consistent with a ~ E-2.3/2.4 spectrum, compatible with the injected CR flux inferred for CRs in the Milky-Way. We notice that the correlation between the calorimetric fraction~Fcal of high-energy protons in SFGs and SBGs (the fraction of high-energy protons actually producing high-energy γ-rays and neutrinos) and the SFR is in accordance with the expected scaling relation for CR escape dominated by advection. We remark that undiscovered sources strongly constrain Fcal at 95% CL, providing fundamental information when we interpret the results as common properties of SFGs and SBGs. Finally, we find that these sources might contribute (12± 3)% to the EGB, while the corresponding diffuse neutrino flux strongly depends on the spectral index distribution along the source class.