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 considered to be 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. On this regard, the Fermi-LAT collaboration has found a correlation between the γ -ray and infrared luminosities for a sample of local sources. Yet, the physics behind these non-thermal emission is still under debate. We provide novel constraints on the tight relation between γ -rays and star formation rate (SFR) exploiting 15 years of public Fermi-LAT data. Thus, we probe the calorimetric fraction F cal of high-energy protons in SFGs and SBGs, namely, the fraction of high-energy protons actually producing high-energy γ -rays and neutrinos. Further, we extrapolate this information to their diffuse γ -ray and neutrino emissions constraining their contribution to the extra-galactic gamma-ray background (EGB) and the diffuse neutrino flux. 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 relate this emission to a theoretical model for SBGs in order to constrain F cal for each source and then study its correlation with the star formation rate of the sources. Firstly, we find at 4 σ 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 ~ 4 σ (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 in the Milky-Way. We also notice that the correlation between F cal and the SFR is in accordance with the expected scaling relation for CR escape dominated by advection. We remark that undiscovered sources strongly constrain F cal 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.