Resonant conversion of axion dark radiation into terahertz electromagnetic radiation in a neutron star magnetosphere

In the strong magnetic field of a neutron star's magnetosphere, axions coupled to electromagnetism develop a nonzero probability to convert into photons. Past studies have revealed that the axion-photon conversion can be resonantly enhanced. We recognize that the axion-photon resonance admits two parametrically distinct resonant solutions, which we call the mass-matched resonance and the Euler-Heisenberg assisted resonance. The mass-matched resonance occurs at a point in the magnetosphere where the radially-varying plasma frequency crosses the axion mass $\omega_\mathrm{pl} \approx m_a$. The Euler-Heisenberg assisted resonance occurs where the axion energy satisfies $\omega \approx (2 \omega_\mathrm{pl}^2 / 7 g_{\gamma\gamma\gamma\gamma} \bar{B}^2 )^{1/2}$. This second resonance is made possible though the strong background magnetic field $\bar{B}$ as well as the nonzero Euler-Heisenberg four-photon self interaction, which has the coupling $g_{\gamma\gamma\gamma\gamma} = 8 \alpha^2 / 45 m_e^4$. We study the resonant conversion of relativistic axion dark radiation into photons via the Euler-Heisenberg assisted resonance, and we calculate the expected electromagnetic radiation assuming different values for the axion-photon coupling $g_{a\gamma\gamma}$ and different amplitudes for the axion flux onto the neutron star $\Phi_a$. We briefly discuss several possible sources of axion dark radiation. Achieving a sufficiently strong axion flux to induce a detectable electromagnetic signal seems unlikely.