Fresh look at the diffuse ALP background from supernovae

Protoneutron stars, highly compact objects formed in the core of exploding supernovae (SNe), are powerful sources of axion-like particles (ALPs). In the SN core, ALPs are dominantly produced via nucleon-nucleon bremsstrahlung and pion conversion, resulting in an energetic ALP spectrum peaked at energies $\mathcal{O}(100)\,\rm MeV$. In this work, we revisit the diffuse ALP background, produced from all past core-collapse supernovae, and update the constraints derived from Fermi-LAT observations. Assuming the maximum ALP-nucleon coupling allowed by the SN 1987A cooling, we set the upper limit $g_{a \gamma \gamma} \lesssim 2 \times 10^{-13}\,\rm GeV^{-1}$ for ALP mass $m_a\lesssim 10^{-10}\,\rm eV$, which is approximately a factor of two improvement with respect to the existing bounds. On the other hand, for $m_a \gtrsim 10^{-10}\,\rm eV$, we find that including pion conversion strengthens the bound on $g_{a\gamma \gamma}$, approximately by a factor of two compared to the constraint obtained from bremsstrahlung alone. Additionally, we present a sensitivity study for future experiments such as AMEGO-X, e-ASTROGAM, GRAMS-balloon, GRAMS-satellite, and MAST. We find that the expected constraint from MAST would be comparable to Fermi-LAT bound. However, SN 1987A constraint remains one order of magnitude stronger as compared to the bound derived from the current and future gamma-ray telescopes.