On the Validity of Bounds on Light Axions for $f\lesssim {10}^{13}$ GeV

Light bosonic dark matter fields that can be treated like a classical wave have non-linear field values close to massive bodies. Here we make the important observation that the quadratic interactions of axion dark matter lead to non-perturbative axion field values for values of the decay constant of $f\lesssim {10}^{13}$ GeV and masses $m_a\lesssim 7\times {10}^8\mathrm{/}f\mathrm{e}{\mathrm{V}}^2$ and generalise this result for axion-like particles. We identify experimental observables impacted by this effect.