Abstract
Axions provide a natural and well-motivated dark matter candidate, with the capability to convert directly to photons in the presence of an electromagnetic field. A particularly compelling observational target is the conversion of dark matter axions into photons in the magnetospheres of highly magnetised neutron stars, which is expected to produce a narrow spectral peak centred at the frequency of the axion mass. We point the MeerKAT radio telescope towards the isolated neutron star J0806.4$-$4123 for $10$-hours of observation and obtain the radio spectra in the frequency range $769$-$1051$ MHz. By modelling the conversion process of infalling axion dark matter (DM) we then compare these spectra to theoretical expectations for a given choice of axion parameters. Whilst finding no signal above $5\sigma$ in the data, we provide a unique constraint on the Primakoff coupling of axion DM, $g_{{\rm a}\gamma\gamma}\lesssim 9.3 \times 10^{-12}\,{\rm GeV}^{-1}$ at the $95\%$ confidence level, in the mass range $3.18$-$4.35\,\mu$eV. This result serves the strongest constraint in the axion mass range $4.20$-$4.35\,\mu$eV.
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