Shining ALP Dark Radiation

String scenarios typically not only predict axion-like particles (ALPs) but also significant amounts of ALP dark radiation originating from the decay of the inflaton or a more general modulus. In this paper, we study the decay of such non-thermally produced relativistic (but massive) ALPs to photons. If the ALPs are sufficiently highly energetic, contribute to $\Delta N_{\rm eff} \gtrsim {\cal O}(0.001)$ and have a mass $m_a\gtrsim$ MeV we find that, using observations of X-, and $\gamma$-rays, the CMB and BBN, very small values of the ALP-photon coupling can be probed, corresponding to an origin of this coupling at the string (or even Planck) scale.Comment: 12 pages, 10 figure