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 Fcal 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 Fcal for each source and then study its correlation with the star formation rate of the sources. Firstly, 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 in the Milky-Way. We also notice that the correlation between Fcal 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.