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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>ω</a:mi><a:mi>pl</a:mi></a:msub><a:mo>≈</a:mo><a:msub><a:mi>m</a:mi><a:mi>a</a:mi></a:msub></a:math>. The Euler-Heisenberg assisted resonance occurs where the axion energy satisfies <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ω</c:mi><c:mo>≈</c:mo><c:mo stretchy="false">(</c:mo><c:mn>2</c:mn><c:msubsup><c:mi>ω</c:mi><c:mi>pl</c:mi><c:mn>2</c:mn></c:msubsup><c:mo>/</c:mo><c:mn>7</c:mn><c:msub><c:mi>g</c:mi><c:mrow><c:mi>γ</c:mi><c:mi>γ</c:mi><c:mi>γ</c:mi><c:mi>γ</c:mi></c:mrow></c:msub><c:msup><c:mover accent="true"><c:mi>B</c:mi><c:mo stretchy="false">¯</c:mo></c:mover><c:mn>2</c:mn></c:msup><c:msup><c:mo stretchy="false">)</c:mo><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:msup></c:math>. This second resonance is made possible though the strong background magnetic field <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mover accent="true"><i:mi>B</i:mi><i:mo stretchy="false">¯</i:mo></i:mover></i:math>, as well as the nonzero Euler-Heisenberg four-photon self-interaction, which has the coupling <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>g</m:mi><m:mrow><m:mi>γ</m:mi><m:mi>γ</m:mi><m:mi>γ</m:mi><m:mi>γ</m:mi></m:mrow></m:msub><m:mo>=</m:mo><m:mn>8</m:mn><m:msup><m:mi>α</m:mi><m:mn>2</m:mn></m:msup><m:mo>/</m:mo><m:mn>45</m:mn><m:msubsup><m:mi>m</m:mi><m:mi>e</m:mi><m:mn>4</m:mn></m:msubsup></m:math>. 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 <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>g</o:mi><o:mrow><o:mi>a</o:mi><o:mi>γ</o:mi><o:mi>γ</o:mi></o:mrow></o:msub></o:math> and different amplitudes for the axion flux onto the neutron star <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi mathvariant="normal">Φ</q:mi><q:mi>a</q:mi></q:msub></q:math>. We briefly discuss several possible sources of axion dark radiation. Achieving a sufficiently strong axion flux to induce a detectable electromagnetic signal seems unlikely. Published by the American Physical Society 2024