  Stimulated decays of axion dark matter, triggered by a source in the sky,
could produce a photon flux along the continuation of the line of sight,
pointing backward to the source. The strength of this so-called axion "echo"
signal depends on the entire history of the source and could still be strong
from sources that are dim today but had a large flux density in the past, such
as supernova remnants (SNRs). This echo signal turns out to be most observable
in the radio band. We study the sensitivity of radio telescopes such as the
Square Kilometer Array (SKA) to echo signals generated by SNRs that have
already been observed, and show that SKA could reach axion-photon couplings of
order $g_{a\gamma\gamma} \sim \mathcal{O}(10^{-11}) \,\mathrm{GeV}^{-1}$ for
axion masses $m_a \lesssim 10^{-5}\;\mathrm{eV}$. In addition, we show
projections of the detection reach for signals coming from old SNRs and from
newly born supernovae that could be detected in the future. Intriguingly, an
observable echo signal could come from old "ghost" SNRs which were very bright
in the past but are now so dim that they haven't been observed.
