The observed spatial distribution of $\gamma$-ray bursts indicates that they probably originate at cosmological distances. At this distance scale their variability time scale and flux above MeV imply an initial optical depth to pair production ≳${10}^{10}$. This appears to be in conflict with their highly nonthermal spectra. We show that this difficulty can be removed if axion bursts from supernovae are converted to $\gamma$ rays over cosmological distances. Nonthermal bursts with the relevant flux, duration, variability, and spectra are obtained just for the range of axion masses of ${10}^{-5\mathrm{}}$-${10}^{-4\mathrm{}}$ eV that accounts for the cold dark matter in the Universe. The observed rate of $\gamma$-ray bursts implies that axions should be converted efficiently to photons in only one out of ∼${10}^4$ supernovae.

• Received 23 July 1993

DOI:https://doi.org/10.1103/PhysRevD.48.R3419