Axions and SN 1987A: Axion trapping

If an axion of mass between about ${10}^{-3\mathrm{}}$ and 10 eV exists, axion emission would have significantly affected the cooling of the nascent neutron star associated with SN 1987A. For an axion of mass less than about ${10}^{-2\mathrm{}}$ eV axions produced deep inside the neutron star simply stream out; in a previous paper we have addressed this case. Remarkably, for an axion of mass greater than about ${10}^{-2\mathrm{}}$ eV axions would, like neutrinos, have a mean free path that is smaller than the size of a neutron star, and thus would become "trapped" and radiated from an "axion sphere." In this paper we treat the "trapping regime" by using numerical models of the initial cooling of a hot neutron star that incorporate a diffusion approximation for axion-energy transport. We compute the axion opacity due to inverse nucleon-nucleon, axion bremsstrahlung, and then use our numerical models to calculate the integrated axion luminosity, the temperature of the axion sphere, and the effect of axion emission on the neutrino bursts detected by the Kamiokande II (KII) and Irvine-Michigan-Brookhaven (IMB) water-Cherenkov detectors. The larger the axion mass, the stronger the trapping and the smaller the axion luminosity. We confirm and refine the earlier estimate of the axion mass above which trapping is so strong that axion emission does not significantly affect the neutrino burst: Based upon the neutrino-burst duration—the most sensitive "barometer" of axion cooling—we conclude that for an axion mass of greater than about 3 eV axion emission would not have had a significant effect on the neutrino bursts detected by KII and IMB. The present work, together with our previous work, strongly suggests that an axion with mass in the interval ${10}^{-3\mathrm{}}$ to 3 eV is excluded by the observation of neutrinos from SN 1987A.