Getting the most on supernova axions

Axion-like particles (ALPs) coupled to nucleons might be copiously emitted from a supernova (SN) core. We extend existing bounds on free-streaming ALPs to the case in which these are so strongly-interacting with the nuclear matter to be trapped in the SN core. For strongly-interacting ALPs, we also extend the bound from the absence of an ALP-induced signal in Kamiokande-II neutrino detector at the time of SN 1987A. We find that combining the different arguments, SNe exclude values of ALP-nucleon coupling $g_{aN}\gtrsim {10}^{-9}$ for ALP masses $m_a\lesssim 1\mathrm{M}\mathrm{e}\mathrm{V}$. Remarkably, in the case of canonical QCD axion models, the SN bounds exclude all values of $m_a\gtrsim {10}^{-2}\mathrm{e}\mathrm{V}$. This result prevents the possibility for current and future cosmological surveys to detect any signatures due to hot dark matter QCD axion mass.