Axion Condensate Dark Matter Constraints from Resonant Enhancement of Background Radiation

We investigate the possible parametric growth of photon amplitudes in a background of axion-like particle (ALP) dark matter. The observed extragalactic background radiation limits the allowed enhancement effect. We derive the resulting constraints on the axion-photon coupling constant $g_{a\gamma}$ from Galactic ALP condensates as well as over-densities. If ALP condensates of size $R$ exist in our Galaxy, a scan for extremely narrow unresolved spectral lines with frequency $\nu$ can constrain the axion-photon coupling at ALP mass $m_a=4\pi\nu$ to $g_{a\gamma}\lesssim2\times10^{-14}(10\,{\rm kpc}/R)\,{\rm GeV}^{-1}$. Radio to optical background data yield constraints at this level within observed wavebands or ALP mass windows over a broad range $0.08\, \mu \text{eV} \lesssim m_a \lesssim 8 \text{ eV}$. These condensate constraints on $g_{a\gamma}$ probe down to the QCD axion band for $m_a \gtrsim$ 10 $\mu$eV.