State evolution approach for the axion conversion probability in magnetosphere of a neutron star

Neutron stars (NS), with their extreme gravitational and magnetic fields, provide an exceptional astrophysical laboratory for studying axion dark matter (DM). Through the Primakoff effect, axions can convert into photons within the magnetospheres of NS, a process that may produce observable radio and X-ray signals. In this work, we investigate axion-photon conversion using a novel, time-dependent state evolution formalism, moving beyond the commonly used stationary-path approximations. We derive a generic analytical expression for the conversion probability and calculate the associated radiated power. Our analysis demonstrates that this approach allows NS to strongly constrain the axion-photon coupling constant, reaching sensitivities of gaγγ ≃ 10−14 −10−15 GeV−1 for axion masses of ma ≃ 10−3 −10−10 eV. These results establish a new pathway to constrain gaγ via NS observations. Future campaigns using powerful observatories like the James Webb Space Telescope (JWST), Green Bank Telescope (GBT), and More Karoo Array Telescope (MeerKAT) array will be ideally suited to probe the distinct spectral signatures predicted by our model across multiple frequency domains.