Forecast constraints on the axion-photon coupling from interstellar medium heating

In interstellar media characterized by a nonrelativistic plasma of electrons and heavy ions, we study the effect of axion dark matter coupled to photons on the dynamics of an electric field. In particular, we assume the presence of a background magnetic field aligned in a specific direction. We show that there is an energy transfer from the oscillating axion field to photons and then to the plasma induced by forced resonance. This resonance is most prominent for the axion mass $m_{\phi}$ equivalent to the plasma frequency $\omega_p$. Requiring that the heating rate of the interstellar medium caused by the energy transfer does not exceed the observed astrophysical cooling rate, we place forecast constraints on the axion-photon coupling $g$ for several different amplitudes of the background magnetic field $B_0$. By choosing a typical value $B_0=10^{-6}$ G, we find that, for the resonance mass $m_{\phi}=\omega_p$, the upper limit of $g$ can be stronger than those derived from other measurements in the literature. With increased values of $B_0$, it is possible to put more stringent constraints on $g$ for a wider range of the axion mass away from the resonance point.