Observational constraint on axion dark matter in a realistic halo profile with gravitational waves

Axions are considered as a candidate of dark matter. The axions form coherent clouds which delay and amplify gravitational waves (GWs) at a resonant frequency. That is, the coherent axion clouds produce secondary GWs following a primary wave. All GWs from compact binary mergers detected so far propagate in the Milky Way halo composed of dark matter so that such GWs are followed by the secondary GWs. Since the properties of the secondary GWs depend on the axion mass and coupling with the parity violating sector of gravity, we can search for a characteristic signal produced by axions. In our previous study, we have developed a search method optimized for the axion signals, and obtained about ten times stronger constraint on the coupling than the previous best one for the axion mass range, $[1.7 \times 10^{-13},\,8.5 \times 10^{-12}]\,\mathrm{eV}$. However, in our previous search, we assume that dark matter is homogeneously distributed in the Milky Way halo, which is unrealistic. In this paper, we extend the dark matter profile to a more realistic one called the core NFW profile, and find that the constraint in our previous study is robust to the dark matter profile.