Emission and detectability of hadronic axions from SN 1987A

We show that axions emitted by SN 1987A, with coupling strengths to nucleons in the range 9×${10}^{\mathrm{-}7}$≲${\mathit{g}}_{\mathit{a}\mathit{N}}$≲1×${10}^{\mathrm{-}3}$, would have produced an unacceptably large signal at the Kamiokande proton-decay experiment. Axions with ${10}^{\mathrm{-}10}$≲${\mathit{g}}_{\mathit{a}\mathit{N}}$≲1.4×${10}^{\mathrm{-}6}$ would have altered the neutrino flux from that observed, so using results from SN 1987A alone, one may nominally rule out the entire range ${10}^{\mathrm{-}10}$≲${\mathit{g}}_{\mathit{a}\mathit{N}}$≲${10}^{\mathrm{-}3}$. Uncertainties in our estimates prevent us from categorically excluding a small window around ${\mathit{g}}_{\mathit{a}\mathit{n}}$≃${10}^{\mathrm{-}6}$, which could have interesting consequences for supernova theory and cosmology.