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}$$\mathrm{.}Thesecondensateconstraintson$g_{a\gamma}$probedowntotheQCDaxionbandfor$m_a \gtrsim$10$\mu$eV.