Axions constituting dark matter (DM) are often considered to form a non-relativistic oscillating field. We explore bursts of relativistic axions from transient astrophysical sources, such as axion star explosions, where the sources are initially non-relativistic. For the QCD axion, bursts from collapsing axion stars lead to potentially detectable signals over a wide range of axion masses $10^{-15} , textrm{eV} lesssim m lesssim 10^{-7} , textrm{eV}$ in future experiments, such as ABRACADABRA, DMRadio and SHAFT. Unlike conventional cold axion DM searches, the sensitivity to axion bursts is not necessarily suppressed as $1/f$ for large decay constants $f$. The detection of axion bursts could provide new insights into the fundamental axion potential, which is challenging to probe otherwise. An ensemble of bursts in the distant past, in direct analogy with neutrinos, would give rise to a diffuse axion background distinct from the usual cold axion DM. Coincidence with other signatures, such as electromagnetic and gravitational-wave emission, would provide a new beyond-the-standard-model window into multi-messenger astronomy.
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